Product-Form Queueing Networks Bibliography

Disclaimer: This bibliography is maintained using Claude Opus 4.8 based on my personal collection of PDF files, accumulated over more than 20 years. The entries, one-line summaries, and publisher links are generated automatically and may contain errors or omissions.

Normalizing-Constant / Convolution Algorithms (44)top

M. Reiser, H. Kobayashi. (1975). Horner's rule for the evaluation of general closed queueing networks. Communications of the ACM 18, 592-593.
Applies a Horner-rule polynomial-evaluation scheme to compute normalizing constants of general closed networks efficiently.
M. Reiser, H. Kobayashi. (1976). On the convolution algorithm for separable queuing networks. Proceedings of the 1976 ACM SIGMETRICS conference on Computer performance modeling measurement and evaluation - SIGMETRICS '76, 109-117.
Formalizes and analyzes the convolution algorithm for separable (product-form) networks, establishing its recursion and numerical properties.
A. C. Williams, R. A. Bhandiwad. (1976). A generating function approach to queueing network analysis of multiprogrammed computers. Networks 6, 1-22.
Uses a generating-function formulation to analyze multiprogrammed computer systems modeled as closed queueing networks.
Simon S. Lam, Y. Luke Lien. (1981). An Analysis of the Tree Convolution Algorithm for Queueing Networks.
Analyzes the computational complexity and ordering strategies of the tree convolution algorithm for sparsely routed multichain networks.
Martin Reiser. (1981). Mean-value analysis and convolution method for queue-dependent servers in closed queueing networks. Performance Evaluation 1, 7-18.
Extends MVA and the convolution method to networks with queue-dependent (load-dependent) service rates.
Simon S. Lam. (1982). Dynamic Scaling and Growth Behavior of Queuing Network Normalization Constants. Journal of the ACM 29, 492-513.
Studies dynamic scaling to prevent floating-point overflow and characterizes the growth behavior of normalization constants with population.
K. G. Ramakrishnan, D. Mitra. (1982). An Overview of PANACEA, a Software Package for Analyzing Markovian Queueing Networks.
Overviews PANACEA, an integral-representation and asymptotic-expansion package for analyzing large closed and mixed product-form networks.
Lam. (1983). A Simple Derivation of the MVA and LBANC Algorithms from the Convolution Algorithm. IEEE Transactions on Computers C-32, 1062-1064.
Shows that both MVA and LBANC (Buzen's convolution) follow as simple algebraic consequences of the convolution recursion.
Simon S. Lam, Y. Luke Lien. (1983). A tree convolution algorithm for the solution of queueing networks. Communications of the ACM 26, 203-215.
Introduces tree convolution, exploiting the routing chains' sparsity by convolving stations along a tree to cut cost for networks with many chains.
Hisao Kameda. (1984). A Property of Normalization Constants for Closed Queueing Networks. IEEE Transactions on Software Engineering SE-10, 856-857.
Proves a monotonicity/structural property of normalizing constants and uses it to derive performance relations for closed networks.
Lindsey E. Stephens, Lawrence W. Dowdy. (1984). Convolutional bound hierarchies. ACM SIGMETRICS Performance Evaluation Review 12, 120-133.
Derives hierarchies of throughput and response-time bounds directly from partial convolution of the normalizing constant, trading computation for tightness.
G. L. Choudhury, K. K. Leung, W. Whitt. (1985). Calculating Normalization Constants of Closed Queueing Networks by Numerically Inverting Their Generating Functions.
Computes normalizing constants of closed networks by numerically inverting their generating function, avoiding the numerical-range problems of the convolution algorithm.
A. E. Conway, N. D. Georganas. (1985). RECAL-a new efficient algorithm for the exact analysis of multiple-chain closed queueing networks (abstract). ACM SIGMETRICS Performance Evaluation Review 13, 14.
Extended abstract introducing RECAL, a recursion by chain whose cost grows polynomially with the number of chains, enabling exact analysis of many-chain closed networks.
A. E. Conway, N. D. Georganas. (1985). RECAL-a new efficient algorithm for the exact analysis of multiple-chain closed queueing networks (abstract). ACM SIGMETRICS Performance Evaluation Review 13, 14.
Technical-report version of RECAL, the recursion-by-chain algorithm for exact multichain closed-network analysis.
P. G. Harrison. (1985). On Normalizing Constants in Queueing Networks.
Obtains closed-form and asymptotic expressions for normalizing constants in a class of closed networks using generating-function analysis.
A. E. Conway, N. D. Georganas. (1986). RECAL-a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks. Journal of the ACM 33, 768-791.
Journal presentation of RECAL, deriving the recursion on normalizing constants by successively adding chains for efficient exact multichain analysis.
J. van Doremalen. (1986). A Note on RECAL.
Short note offering a simplified derivation and interpretation of the RECAL recursion.
Ernest Koenigsberg. (1986). Comments on "On Normalizing Constants in Queueing Networks" by P. G. Harrison. Operations Research 34, 330-330.
Short commentary clarifying and correcting results on normalizing constants in closed queueing networks.
J.George Shanthikumar, David D. Yao. (1986). The preservation of likelihood ratio ordering under convolution. Stochastic Processes and their Applications 23, 259-267.
Proves that likelihood-ratio ordering is preserved under convolution, a stochastic-ordering result underpinning monotonicity of network measures.
James McKenna. (1988). Extensions and applications of recal in the solution of closed product-form queueing networks. Communications in Statistics. Stochastic Models 4, 235-276.
Extends RECAL to compute additional measures (moments, marginal distributions) and applies it to load-dependent and mixed networks.
A.E. Conway, E. de Souza e Silva, S.S. Lavenberg. (1989). Mean value analysis by chain of product form queueing networks. IEEE Transactions on Computers 38, 432-442.
Develops MVA-by-chain, a mean-value recursion over chains dual to RECAL that computes exact mean measures with cost polynomial in the number of chains.
A. G. Greenberg, J. McKenna. (1989). Solution of closed, product form, queueing networks via the RECAL and tree-RECAL methods on a shared memory multiprocessor. ACM SIGMETRICS Performance Evaluation Review 17, 127-135.
Presents parallel RECAL and tree-RECAL implementations on shared-memory multiprocessors for solving large closed product-form networks.
J. J. Gordon. (1990). The Evaluation of Normalizing Constants in Closed Queueing Networks. Operations Research 38, 863-869.
Analyzes and compares algorithms for evaluating closed-network normalizing constants, addressing overflow and scaling in the convolution recursion.
James McKenna. (1991). Calculating joint queue length moments with recal. Communications in Statistics. Stochastic Models 7, 47-66.
Extends the RECAL recursion to compute joint queue-length moments across stations in closed product-form networks.
Andrea Bertozzi, James Mckenna. (1993). Multidimensional Residues, Generating Functions, and Their Application to Queueing Networks. SIAM Review 35, 239-268.
Uses multidimensional complex-residue and generating-function techniques to represent and compute normalizing constants of multichain closed networks.
G. L. Choudhury, K. K. Leung, W. Whitt. (1993). An Algorithm for Closed Queueing Networks Based on Numerical Transform Inversion.
Applies numerical inversion of the multidimensional generating function to obtain normalizing constants and performance measures of closed multichain networks.
Man Li, Nicolas D. Georganas. (1993). ACAL-An efficient adaptive chain oriented algorithm for the analysis of multiple chain closed queueing networks. Performance Evaluation 18, 225-235.
Presents ACAL, an adaptive chain-oriented recursion that reduces RECAL's cost by adapting the chain-addition order to the network structure.
A. I. Gerasimov. (1994). Evaluation of normalizing constants in closed queueing networks with several types of messages. Cybernetics and Systems Analysis 29, 889-896.
Provides methods to evaluate normalizing constants of multiclass (multiple message type) closed networks, addressing numerical scaling issues.
Keith W. Ross, Danny H. K. Tsang, Jie Wang. (1994). Monte Carlo summation and integration applied to multiclass queuing networks. Journal of the ACM 41, 1110-1135.
Applies Monte Carlo summation and integration to estimate normalizing constants of large multiclass closed networks with controlled variance.
Gagan L. Choudhury, Kin K. Leung, Ward Whitt. (1995). Calculating normalization constants of closed queueing networks by numerically inverting their generating functions. Journal of the ACM 42, 935-970.
Journal version of the numerical-transform-inversion method for computing closed-network normalizing constants robustly across large populations.
Alexander I. Gerasimov. (1995). On Normalizing Constants in Multiclass Queueing Networks. Operations Research 43, 704-711.
Studies structural properties and recursive computation of normalizing constants in multiclass closed networks.
Keith W. Ross, Jie Wang. (1997). Implementation of Monte Carlo integration for the analysis of product-form queueing networks. Performance Evaluation 29, 273-292.
Details efficient implementation and variance-reduction of Monte Carlo integration for evaluating product-form network normalizing constants.
K. Sakurai. (2003). Laplace Transform Inversion (PhD Thesis).
PhD thesis developing Laplace-transform inversion methods for computing performance distributions and normalizing constants of queueing models.
Giuliano Casale. (2006). On Single-Class Load-Dependent Normalizing Constant Equations. Third International Conference on the Quantitative Evaluation of Systems - (QEST'06), 333-342.
Establishes recursive equations for the normalizing constant of single-class closed networks with load-dependent stations, improving numerical stability of convolution.
J. Anselmi, P. Cremonesi. (2009). Bounding the Partition Function of BCMP Multiclass Queueing Networks.
Derives computable upper and lower bounds on the normalizing constant (partition function) of multiclass BCMP networks, yielding bounds on throughput and queue lengths without full evaluation.
G. Casale. (2009). CoMoM: Efficient Class-Oriented Evaluation of Multiclass Performance Models. IEEE Transactions on Software Engineering 35, 162-177.
Introduces CoMoM, a class-oriented recursion over moments of the normalizing constant that evaluates multiclass closed networks in polynomial space in the number of classes.
Giuliano Casale. (2011). A generalized method of moments for closed queueing networks. Performance Evaluation 68, 180-200.
Generalizes the Method of Moments to compute exact mean performance measures of multiclass closed networks via a linear system over normalizing-constant moments.
Giuliano Casale. (2011). Exact analysis of performance models by the Method of Moments. Performance Evaluation 68, 487-506.
Presents the Method of Moments (MoM), an exact algorithm whose cost is polynomial in populations, solving multiclass closed networks previously intractable by convolution or RECAL.
A. E. Conway. (n.d.). An Efficient Algorithm for Semi-Homogeneous Queueing Network Models.
Gives an efficient exact algorithm exploiting semi-homogeneity (identical service demands across subsets of classes) to reduce the state space of closed networks.
P.G. Harrison, Ting Ting Lee. (n.d.). A new recursive algorithm for computing generating functions in closed multi-class queueing networks. The IEEE Computer Society's 12th Annual International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems, 2004. (MASCOTS 2004). Proceedings., 231-238.
Introduces a recursive algorithm for the generating function of closed networks, yielding normalizing constants and moments more efficiently.
H. Kobayashi. (n.d.). A Computational Algorithm for Queue Distribution via the Polya Theory of Enumeration.
Uses Polya enumeration (cycle-index) theory to derive a computational algorithm for queue-length distributions in closed networks.
Y. Kogan, A. Yakovlev. (n.d.). Asymptotics of the partition function in large closed BCMP networks with bottlenecks. MASCOTS '95. Proceedings of the Third International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, 89-93.
Derives asymptotic expansions of the partition function of large closed BCMP networks in the presence of bottleneck stations.
M. Reiser, H. Kobayashi. (n.d.). On the Convolution Algorithm for Separable Queuing Networks.
Discusses the computational aspects of the convolution algorithm for separable queueing networks, including a scaling rule to control numerical range.
K.W. Ross, J. Wang. (n.d.). Solving product form stochastic networks with Monte Carlo summation. 1990 Winter Simulation Conference Proceedings, 270-275.
Proposes Monte Carlo summation as a randomized estimator of the partition function of product-form networks intractable by exact recursion.

Mean Value Analysis (Exact) (31)top

M. Reiser, S. S. Lavenberg. (1980). Mean-Value Analysis of Closed Multichain Queuing Networks. Journal of the ACM 27, 313-322.
Seminal paper introducing exact MVA, computing mean queue lengths and response times recursively via the arrival theorem without normalizing constants.
G. Balbo. (1981). Mean Value Analysis of Closed Load-Dependent Queueing Networks.
Extends exact MVA to closed networks with load-dependent service rates.
M. Reiser, S. S. Lavenberg. (1981). Corrigendum: Mean-Value Analysis of Closed Multichain Queuing Networks. Journal of the ACM 28, 629.
Corrigendum correcting details of the Reiser-Lavenberg exact MVA algorithm for closed multichain networks.
John Zahorjan, Eugene Wong. (1981). The solution of separable queueing network models using mean value analysis. ACM SIGMETRICS Performance Evaluation Review 10, 80-85.
Describes practical solution of separable network models via MVA, including implementation considerations.
Raymond M. Bryant, Anthony E. Krzesinski, Peter Teunissen. (1983). The MVA Pre-empt resume priority approximation. Proceedings of the 1983 ACM SIGMETRICS conference on Measurement and modeling of computer systems - SIGMETRICS '83, 12-27.
Proposes an MVA-based approximation for closed networks with preemptive-resume priority scheduling, outside product form.
S.C Bruell, G Balbo, P.V Afshari. (1984). Mean value analysis of mixed, multiple class BCMP networks with load dependent service stations. Performance Evaluation 4, 241-260.
Develops exact MVA for mixed (open and closed) multiclass BCMP networks that include load-dependent stations.
John Zahorjan, Edward D. Lazowska. (1984). Incorporating load dependent servers in approximate mean value analysis. Performance Evaluation 4, 219.
Shows how to incorporate load-dependent servers within Schweitzer/Bard approximate MVA fixed-point iteration.
John Zahorjan, Edward D. Lazowska. (1984). Incorporating load dependent servers in approximate mean value analysis. Performance Evaluation 4, 219.
Shows how load-dependent servers are incorporated into approximate MVA fixed-point iteration for closed networks.
Salvatore Tucci, Charles H. Sauer. (1985). The tree MVA algorithm. Performance Evaluation 5, 187-196.
Presents tree MVA, exploiting routing-tree sparsity to reduce the cost of exact MVA for networks with many chains.
K. P. Hoyme, S. C. Bruell, P. V. Afshari, R. Y. Kain. (1986). A tree-structured mean value analysis algorithm. ACM Transactions on Computer Systems 4, 178-185.
Introduces a tree-structured MVA that exploits routing sparsity, analogous to tree convolution, to reduce cost for many-chain networks.
Johann Strelen. (1986). A generalization of mean value analysis to higher moments. ACM SIGMETRICS Performance Evaluation Review 14, 129-140.
Generalizes the MVA recursion to compute higher-order moments of queue lengths, not only their means.
R. J. Wijbrands. (1987). A Note on Enumeration Methods for the Mean Value Analysis Algorithm.
Note comparing population-enumeration strategies used within the exact MVA recursion.
Ian F Akyildiz, Gunter Bolch. (1988). Mean Value Analysis Approximation for multiple server queueing networks. Performance Evaluation 8, 77-91.
Gives an MVA-based approximation for closed networks containing multiple-server (queue-dependent) stations.
John Zahorjan, Derek L Eager, Hisham M Sweillam. (1988). Accuracy, speed, and convergence of approximate mean value analysis. Performance Evaluation 8, 255-270.
Empirically characterizes the accuracy, computational cost, and convergence of approximate MVA methods.
Arnold O. Allen, Gary Hynes. (1990). Approximate MVA solutions with fixed throughput classes. ACM SIGMETRICS Performance Evaluation Review 18, 31-40.
Extends approximate MVA to handle classes constrained to fixed (prescribed) throughput, as arising in transaction workloads.
K. R. Pattipati, M. M. Kostreva, J. L. Teele. (1990). Approximate mean value analysis algorithms for queuing networks. Journal of the ACM 37, 643-673.
Provides a rigorous analysis of existence, uniqueness, and convergence of the fixed points of approximate MVA schemes.
P. J. Schweitzer. (1990). A Survey of Mean Value Analysis, Its Generalizations, and Applications in Networks of Queues.
Comprehensive survey of MVA, its exact and approximate generalizations, and its applications.
P. J. Schweitzer. (1991). A Fixed-Point Methodology for Exact Mean Value Analysis with Large Populations.
Presents a fixed-point methodology that makes exact MVA tractable at large populations by reformulating the recursion.
J. Luthi. (1997). MVA for Queueing Networks with Intervals as Input Parameters.
Extends MVA to interval-valued input parameters, propagating parameter uncertainty to interval bounds on performance measures.
S. Wang. (1997). Approximate MVA Algorithms for Solving Queueing Network Models (PhD Thesis).
PhD thesis developing and evaluating improved approximate MVA algorithms for separable queueing network models.
Claudio Gennaro, Peter J.B. King. (1999). Parallelising the Mean Value Analysis Algorithm. SIMULATION 72, 148-148.
Presents a parallelization of the MVA recursion to accelerate solution of large multichain closed networks.
M. Reiser. (2000). Mean Value Analysis: A Personal Account. Lecture Notes in Computer Science, 491-504.
Encyclopedic/tutorial entry summarizing the mean value analysis method and its arrival-theorem foundation.
Hai Wang, Kenneth C. Sevcik. (2000). Experiments with improved approximate mean value analysis algorithms. Performance Evaluation 39, 189-206.
Reports experiments comparing improved approximate MVA algorithms against Schweitzer-Bard on accuracy and cost.
Hai Wang, Kenneth C. Sevcik. (2000). Experiments with improved approximate mean value analysis algorithms. Performance Evaluation 39, 189-206.
Journal version reporting experimental evaluation of improved approximate MVA algorithms.
Kenneth C. Sevcik, Hai Wang. (2002). Solution properties and convergence of an approximate mean value analysis algorithm. ACM SIGMETRICS Performance Evaluation Review 29, 3-10.
Studies solution existence and convergence properties of an improved approximate MVA algorithm for separable networks.
Lei Zhang, Douglas Down. (2017). A Stable Mean Value Analysis Algorithm for Closed Systems with Load-dependent Queues. Proceedings of the 10th EAI International Conference on Performance Evaluation Methodologies and Tools.
Proposes a numerically stable MVA variant for closed systems with load-dependent queues (conference version).
Lei Zhang, Douglas Down. (2017). A Stable Mean Value Analysis Algorithm for Closed Systems with Load-dependent Queues. Proceedings of the 10th EAI International Conference on Performance Evaluation Methodologies and Tools.
Presents a stable MVA algorithm avoiding the numerical instabilities of load-dependent MVA at large populations.
J. van Doremalen. (n.d.). Mean Value Analysis in Multichain Queueing Networks.
Discusses mean value analysis techniques and implementation for multichain closed queueing networks.
P. J. Schweitzer. (n.d.). The Correction Terms in Approximate Mean Value Analysis.
Analyzes the correction (error) terms neglected by Schweitzer approximate MVA and quantifies their impact on accuracy.
S. Wang, K. C. Sevcik. (n.d.). An Improved Approximate Mean Value Analysis Algorithm for Solving Separable Queueing Network Models.
Proposes an improved approximate MVA with better accuracy than Schweitzer-Bard for separable closed networks.
S. Wang, K. C. Sevcik. (n.d.). An Improved Approximate Mean Value Analysis for Solving Separable Queueing Network Models.
Introduces an improved approximate MVA that increases accuracy for separable closed networks.

Approximate MVA (17)top

G. S. Graham. (1978). Queueing Network Models of Computer System Performance: Guest Editor's Overview.
Guest editor's overview introducing a special issue on queueing network models of computer system performance.
P. J. Schweitzer. (1979). Approximate Analysis of Multiclass Closed Networks of Queues.
Seminal paper proposing Schweitzer's approximate MVA, assuming a customer sees the mean population unchanged upon arrival.
P. J. Schweitzer. (1980). A Nonlinear Vector Finite Difference Scheme. SIAM Review 22, 503-503.
Formulates approximate network analysis as a nonlinear vector finite-difference scheme and studies its solution.
K. Mani Chandy, Doug Neuse. (1982). Linearizer. Communications of the ACM 25, 126-134.
Introduces Linearizer, a widely used approximate MVA that corrects Schweitzer's estimate using population-shift derivatives, greatly improving accuracy.
D. Neuse, K. M. Chandy. (1982). HAM: The Heuristic Aggregation Method for Solving General Closed Queueing Network Models of Computer Systems.
Introduces HAM, a heuristic aggregation method for approximate solution of large closed queueing networks.
Paul J. Schweitzer. (1982). Bottleneck Determination in Networks of Queues. Applied Probability-Computer Science: The Interface Volume 1, 471-485.
Presents methods to determine bottleneck stations in closed queueing networks.
A. Krzesinski, J. Greyling. (1984). Improved lineariser methods for queueing networks with queue dependent centres. ACM SIGMETRICS Performance Evaluation Review 12, 41-51.
Improves Linearizer-type approximations to handle queue-dependent (load-dependent) service centres.
De Souza E Silva, Lavenberg, Muntz. (1986). A Clustering Approximation Technique for Queueing Network Models with a Large Number of Chains. IEEE Transactions on Computers C-35, 419-430.
Presents a clustering approximation that groups populations to analyze closed networks with very large customer populations.
Dinkar Sitaram. (1987). The inconsistency index method for estimating the accuracy of Schweitzer's approximation. IBM Journal of Research and Development 31, 475-483.
Introduces an inconsistency-index heuristic to estimate the error of Schweitzer's approximate MVA a posteriori.
Ching-Tarng Hsieh, Simon S Lam. (1989). PAM-A noniterative approximate solution method for closed multichain queueing networks. Performance Evaluation 9, 119-133.
Introduces PAM, a non-iterative approximate solution method for closed multichain networks avoiding fixed-point iteration.
E. de Souza e Silva, R.R. Muntz. (1990). A note on the computational cost of the Linearizer algorithm for queueing networks. IEEE Transactions on Computers 39, 840-842.
Analyzes and reduces the computational cost of the Linearizer family of approximate MVA algorithms.
Johann Christoph Strelen. (1990). Moment analysis for closed queuing networks and its linearizer. Performance Evaluation 11, 127-142.
Extends Linearizer-style approximation to compute higher moments of queue lengths in closed networks.
William C. Cheng, Richard R. Muntz. (1996). Bounding errors introduced by clustering of customers in closed product-form queuing networks. Journal of the ACM 43, 641-669.
Bounds the error incurred when customers are clustered (aggregated) to reduce state space in closed product-form networks.
Paul J. Schweitzer, Giuseppe Serazzi, Marco Broglia. (1998). A Queue-Shift Approximation Technique for Product-Form Queueing Networks. Lecture Notes in Computer Science, 267-279.
Proposes a queue-shift approximation refining Schweitzer's assumption to improve accuracy of approximate MVA.
Hai Wang, Kenneth C. Sevcik, Giuseppe Serazzi, Shouhong Wang. (2008). The general form linearizer algorithms: A new family of approximate mean value analysis algorithms. Performance Evaluation 65, 129-151.
Unifies and generalizes the Linearizer family into a common parametric form clarifying their accuracy-cost trade-offs.
Y. Dallery, R. Suri. (n.d.). Approximate Disaggregation and Performance Bounds for Queueing Networks with Multiple-Server Stations.
Uses approximate disaggregation to derive performance bounds for networks containing multiple-server stations.
P. J. Schweitzer. (n.d.). Bottleneck Analysis in a Network of Queues.
Analyzes bottleneck behavior and asymptotic saturation in closed networks of queues.

Performance Bounds (23)top

J. Zahorjan, K. C. Sevcik, D. L. Eager, B. I. Galler. (1981). Balanced job bound analysis of queueing networks. ACM SIGMETRICS Performance Evaluation Review 10, 58.
Introduces balanced job bounds, simple asymptotic throughput/response-time bounds based on a balanced-demand reference network.
D. L. Eager, K. C. Sevcik. (1982). Performance bound hierarchies for queueing networks. ACM SIGMETRICS Performance Evaluation Review 11, 213-214.
Introduces performance bound hierarchies giving progressively tighter throughput/response-time bounds at increasing cost.
D. L. Eager, K. C. Sevcik. (1982). Performance bound hierarchies for queueing networks. ACM SIGMETRICS Performance Evaluation Review 11, 213-214.
Journal presentation of performance bound hierarchies for single-class closed networks.
Jiri Kriz. (1984). Throughput bounds for closed queueing networks. Performance Evaluation 4, 1-10.
Derives throughput bounds for closed queueing networks from balanced and asymptotic arguments.
Y. C. Tay, Rajan Suri. (1985). Error bounds for performance prediction in queuing networks. ACM Transactions on Computer Systems 3, 227-254.
Derives rigorous error bounds quantifying the accuracy of approximate performance predictions in queueing networks.
Derek L. Eager, Kenneth C. Sevcik. (1986). Bound hierarchies for multiple-class queuing networks. Journal of the ACM 33, 179-206.
Extends performance bound hierarchies to multiple-class closed queueing networks.
Teemu Kerola. (1986). The composite bound method for computing throughput bounds in multiple class environments. Performance Evaluation 6, 1-9.
Introduces the composite bound method combining several bounding techniques for multiclass throughput bounds.
Ching-Tarng Hsieh, Simon S Lam. (1987). Two classes of performance bounds for closed queueing networks. Performance Evaluation 7, 3-30.
Presents two complementary classes of performance bounds for closed networks and compares their tightness.
M. M. Srinivasan. (1987). Successively Improving Bounds on Performance Measures for Single Class Product Form Queueing Networks. IEEE Transactions on Computers C-36, 1107-1112.
Provides a scheme yielding successively tighter bounds on performance measures of product-form networks.
J.George Shanthikumar, David D. Yao. (1988). Throughput bounds for closed queueing networks with queue-dependent service rates. Performance Evaluation 9, 69-78.
Establishes throughput bounds for closed networks with queue-dependent (load-dependent) service using stochastic ordering.
Yves Dallery. (1989). An improved balanced job bound analysis of closed queueing networks. Operations Research Letters 8, 59.
Improves the balanced-job-bounds technique to obtain tighter throughput bounds for closed networks.
Lawrence W. Dowdy, Brian M. Carlson, Alan T. Krantz, Satish K. Tripathi. (1992). Single-class bounds of multi-class queuing networks. Journal of the ACM 39, 188-213.
Derives single-class bounds that bracket the performance of multiclass closed networks.
S. Majumdar. (1992). Robust Box Bounds for Queueing Networks.
Introduces robust box bounds that bracket performance when service demands lie within specified intervals.
R. R. Muntz. (1993). Optimization, Error Bounds, and Workload Characterization in Closed Product-Form Queueing Networks.
Combines optimization, error bounds, and workload characterization to bound performance of closed product-form networks.
J. Lüthi, S. Majumdar, G. Kotsis, G. Haring. (1997). Performance bounds for distributed systems with workload variabilities and uncertainties. Parallel Computing 22, 1789-1806.
Uses bounding techniques to analyze distributed-system performance under workload variabilities and parameter uncertainty.
Shikharesh Majumdar, C.Murray Woodside. (1998). Robust bounds and throughput guarantees for closed multiclass queueing networks. Performance Evaluation 32, 101-136.
Derives robust throughput guarantees for closed multiclass networks under uncertain workload parameters.
Arie Harel, Su Namn, Jacob Sturm. (1999). Simple bounds for closed queueing networks. Queueing Systems 31, 125-135.
Derives simple closed-form bounds on throughput and mean queue length for closed networks.
Jonatha Anselmi, Paolo Cremonesi. (2008). Bounding the Performance of BCMP Networks with Load-Dependent Stations. 2008 IEEE International Symposium on Modeling, Analysis and Simulation of Computers and Telecommunication Systems, 1-8.
Derives performance bounds for BCMP networks with load-dependent stations from partial evaluation of the partition function.
Giuliano Casale, Richard Muntz, Giuseppe Serazzi. (2008). Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks. IEEE Transactions on Computers 57, 780-794.
Presents Geometric Bounds, tight and cheap balanced-population bounds on throughput and response time for multiclass closed networks.
G. Casale, R.R. Muntz, G. Serazzi. (n.d.). A New Class of Non-Iterative Bounds for Closed Queueing Networks. 14th IEEE International Symposium on Modeling, Analysis, and Simulation, 69-76.
Introduces non-iterative bounds on throughput and response time for closed multiclass networks, computable in closed form.
N. M. van Dijk. (n.d.). Error Bounds for Comparing Open and Closed Queueing Networks with an Application to Performability Analysis.
Provides error bounds for approximating closed networks by open ones, applied to performability analysis.
S. H. Namn. (n.d.). Bounds and Some Properties of Performance Measures in Closed Queueing Models of Telecommunication Networks (PhD Dissertation).
Extends the dual property of queueing systems to closed product-form networks and derives closed-form upper and lower bounds on network throughput.
L. E. Stephens, L. W. Dowdy. (n.d.). Convolutional Bound Hierarchies.
Derives hierarchies of throughput and response-time bounds from partial convolution of the normalizing constant, trading computation for tightness.

Asymptotic and Scaling Analysis (42)top

R. R. Muntz, J. W. Wong. (1972). Asymptotic Properties of Closed Queueing Network Models.
Early study of the asymptotic (saturation) properties of closed queueing network models.
B. Pittel. (1979). Closed Exponential Networks of Queues with Saturation: The Jackson-Type Stationary Distribution and Its Asymptotic Analysis. Mathematics of Operations Research 4, 357-378.
Rigorously analyzes saturation and limiting behaviour of large closed exponential networks.
Lester Lipsky, Chee-Min Henry Lieu, Abolfazl Tehranipour, Appie van de Liefvoort. (1982). On the asymptotic behavior of time-sharing systems. Communications of the ACM 25, 707-714.
Studies the asymptotic (saturation) behaviour of time-sharing systems modeled as closed networks.
J. McKenna, D. Mitra. (1982). Integral Representations and Asymptotic Expansions for Closed Markovian Queueing Networks: Normal Usage.
Develops integral representations and asymptotic expansions for performance measures of large closed networks (the PANACEA approach).
Debasis Mitra, J. A. Morrison. (1983). Asymptotic expansions of moments of the waiting time in closed and open processor-sharing systems with multiple job classes. Advances in Applied Probability 15, 813-839.
Derives asymptotic expansions of the moments of waiting time in closed and open networks.
Debasis Mitra, J. A. Morrison. (1983). Asymptotic expansions of moments of the waiting time in closed and open processor-sharing systems with multiple job classes. Advances in Applied Probability 15, 813-839.
Derives asymptotic expansions of waiting-time moments in closed and open networks using integral methods.
J. McKenna, Debasis Mitra. (1984). Asymptotic Expansions and Integral Representations of Moments of Queue Lengths in Closed Markovian Networks. Journal of the ACM 31, 346-360.
Provides integral representations and asymptotic expansions for moments of queue lengths in closed networks.
J. A. Morrison, D. Mitra. (1985). Heavy-usage asymptotic expansions for the waiting time in closed processor-sharing systems with multiple classes. Advances in Applied Probability 17, 163-185.
Derives heavy-usage asymptotic expansions for the waiting time in closed networks.
Debasis Mitra, J. McKenna. (1986). Asymptotic expansions for closed Markovian networks with state-dependent service rates. Journal of the ACM 33, 568-592.
Part I deriving asymptotic expansions for closed Markovian networks with state-dependent service rates.
Debasis Mitra, J. McKenna. (1986). Asymptotic expansions for closed Markovian networks with state-dependent service rates. Journal of the ACM 33, 568-592.
Part II continuing the asymptotic expansions for state-dependent closed Markovian networks.
Debasis Mitra, J. McKenna. (1986). Asymptotic expansions for closed Markovian networks with state-dependent service rates. Journal of the ACM 33, 568-592.
Provides asymptotic expansions for closed Markovian networks with state-dependent service rates.
J.A. Morrison. (1986). Moments of the conditioned waiting time in a large closed processor-sharing system. Communications in Statistics. Stochastic Models 2, 293-321.
Computes asymptotic moments of the conditioned waiting time in a large closed processor-sharing system.
James McKenna. (1987). Asymptotic expansions of the sojourn time distribution functions of jobs in closed, product-form queuing networks. Journal of the ACM 34, 985-1003.
Derives asymptotic expansions of sojourn-time distribution functions for jobs in closed networks.
Jing Dong Mei, Charles Tier. (1991). Asymptotic analysis of multiple class queueing networks. Applied Mathematics Letters 4, 35-38.
Presents an asymptotic analysis of multiclass closed queueing networks.
Alexander Birman, YAAKOV KOGAN. (1992). Asymptotic evaluation of closed queueing networks with many stations. Communications in Statistics. Stochastic Models 8, 543-563.
Provides asymptotic evaluation of closed networks as the number of stations grows large.
C. Knessl, C. Tier. (1992). Asymptotic expansions for large closed queueing networks with multiple job classes. IEEE Transactions on Computers 41, 480-488.
Extends the asymptotic-expansion approach to large closed networks with multiple job classes.
Yaakov Kogan. (1992). Another approach to asymptotic expansions for large closed queueing networks. Operations Research Letters 11, 317-321.
Derives singular-perturbation asymptotic expansions of the stationary distribution of large closed networks.
Yaakov Kogan, Robert Sh. Liptser. (1993). Limit non-stationary behavior of large closed queueing networks with bottlenecks. Queueing Systems 14, 33-55.
Analyzes the transient (non-stationary) limiting behaviour of large closed networks with bottlenecks.
Jing-Dong Mei, Charles Tier. (1994). Asymptotic Approximations for a Queueing Network with Multiple Classes. SIAM Journal on Applied Mathematics 54, 1147-1180.
Derives asymptotic approximations for the performance of a multiclass queueing network.
Jing-Dong Mei, Charles Tier. (1994). Asymptotic Approximations for a Queueing Network with Multiple Classes. SIAM Journal on Applied Mathematics 54, 1147-1180.
Constructs ray-method asymptotic approximations for the normalization constant of large closed multiclass networks with an infinite-server node and many fixed-rate single-server nodes.
Jing-Dong Mei, Charles Tier. (1994). Asymptotic Approximations for a Queueing Network with Multiple Classes. SIAM Journal on Applied Mathematics 54, 1147-1180.
Constructs ray-method asymptotic approximations for the normalization constant of large closed multiclass networks with an infinite-server node and many fixed-rate single-server nodes.
Jie Wang, Keith W. Ross. (1994). Asymptotic analysis for closed multiclass queueing networks in critical usage. Queueing Systems 16-16, 167-191.
Analyzes closed multiclass networks in the critical-usage regime where several stations approach saturation together.
G. Fayolle, J.-M. Lasgouttes. (1995). Asymptotics and Scalings for Large Closed Product-Form Networks via the Central Limit Theorem.
Applies central-limit-theorem scaling to derive asymptotics of large closed product-form networks.
Gianfranco Balbo, Giuseppe Serazzi. (1996). Asymptotic analysis of multiclass closed queueing networks: Common bottleneck. Performance Evaluation 26, 51-72.
Derives the asymptotic performance of multiclass closed networks that share a single common bottleneck as population grows.
G. Fayolle, J.-M. Lasgouttes. (1996). Asymptotics and Scalings for Large Closed Product-Form Networks via the Central Limit Theorem.
Journal version of the CLT-based asymptotic and scaling analysis of large closed product-form networks.
Yaakov Kogan, Andrei Yakovlev. (1996). Asymptotic analysis for closed multichain queueing networks with bottlenecks. Queueing Systems 23, 235-258.
Performs asymptotic analysis of closed multichain networks with bottleneck stations.
Vadim A. Malyshev, Andrei V. Yakovlev. (1996). Condensation in large closed Jackson networks. The Annals of Applied Probability 6.
Establishes a condensation phenomenon in which jobs accumulate at the bottleneck of large closed Jackson networks.
Gianfranco Balbo, Giuseppe Serazzi. (1997). Asymptotic analysis of multiclass closed queueing networks: Multiple bottlenecks. Performance Evaluation 30, 115-152.
Extends the asymptotic analysis to multiclass closed networks with multiple simultaneous bottlenecks.
S. Coury, P.G. Harrison. (1997). Asymptotic properties of queuing networks. IEE Proceedings - Computers and Digital Techniques 144, 249.
Studies asymptotic properties, including limiting distributions and bottleneck structure, of closed queueing networks.
A. I. Lyakhov. (1997). Closed Queueing Networks with Load-Dependent Servers: An Asymptotic Analysis.
Provides asymptotic analysis of large closed networks with load-dependent servers.
K. A. Borovkov. (1998). Propagation of Chaos for Queueing Networks. Theory of Probability & Its Applications 42, 385-394.
Proves propagation-of-chaos (mean-field) limits establishing asymptotic independence of queues in large networks.
Charles Knessl, Charles Tier. (1998). Asymptotic approximations and bottleneck analysis in product form queueing networks with large populations. Performance Evaluation 33, 219-248.
Combines asymptotic approximations with bottleneck analysis for product-form networks at large populations.
Vyacheslav M. Abramov. (2000). A large closed queueing network with autonomous service and bottleneck. Queueing Systems 35, 23-54.
Analyzes the asymptotic behavior of a large closed network with autonomous service and a single bottleneck station.
Arthur Berger, Yaakov Kogan. (2000). Distribution of Processor-Sharing Customers for a Large Closed System with Multiple Classes. SIAM Journal on Applied Mathematics 60, 1330-1339.
Characterizes the limiting distribution of processor-sharing customers in large multiclass closed systems.
Yaakov Kogan. (2001). Asymptotic expansions for probability distributions in large loss and closed queueing networks. ACM SIGMETRICS Performance Evaluation Review 29, 25-27.
Provides unified asymptotic expansions for probability distributions in large loss and closed networks.
Peter G. Harrison, Sérgio Coury. (2002). On the asymptotic behaviour of closed multiclass queueing networks. Performance Evaluation 47, 131-138.
Characterizes the large-population asymptotic behaviour of closed multiclass networks and their bottlenecks.
Jonatha Anselmi, Giuliano Casale. (2013). Heavy-traffic revenue maximization in parallel multiclass queues. Performance Evaluation 70, 806-821.
Solves revenue maximization in parallel multiclass queues under heavy traffic using an asymptotic characterization of the optimum.
Giuliano Casale. (2017). Accelerating Performance Inference over Closed Systems by Asymptotic Methods. ACM SIGMETRICS Performance Evaluation Review 45, 64-64.
Uses asymptotic (integral-expansion) methods to accelerate Bayesian performance inference over closed queueing systems.
L.R. van Kreveld, O.J. Boxma, J.L. Dorsman, M.R.H. Mandjes. (2021). Scaling limits for closed product-form queueing networks. Performance Evaluation 151, 102220.
Establishes scaling limits (functional CLT / fluid) for closed product-form networks as population and size grow.
Johan Ruuskanen, Tommi Berner, Karl-Erik Årzén, Anton Cervin. (2021). Improving the mean-field fluid model of processor sharing queueing networks for dynamic performance models in cloud computing. Performance Evaluation 151, 102231.
Improves the mean-field fluid model of processor-sharing networks for accurate dynamic (transient) performance prediction.
D. K. George, C. H. Xia, M. S. Squillante. (n.d.). Exact-Order Asymptotic Analysis for Closed Queueing Networks.
Provides exact-order asymptotic estimates of performance measures for closed queueing networks.
Y. Kogan. (n.d.). Asymptotic Expansions for Large Closed and Loss Queueing Networks.
Derives asymptotic expansions for normalizing constants of large closed and loss networks from a contour-integral (saddle-point and residue) representation of the partition function.

Operational Analysis (8)top

Peter J. Denning, Jeffrey P. Buzen. (1978). The Operational Analysis of Queueing Network Models. ACM Computing Surveys 10, 225-261.
Foundational paper establishing operational analysis, deriving performance laws from directly measurable operational quantities.
Y. Bard. (1979). Surveyors' Forum: Stochastic or Operational?.
Contrasts the stochastic and operational viewpoints of queueing-network analysis and their assumptions.
H. D. Schwetman. (1980). Operational Analysis: An Aid to Interpretation of Measurement Data.
Shows how operational analysis aids the interpretation of measured system performance data.
Y. Dallery. (1984). Some New Results on Operational Analysis.
Presents new operational-analysis results relating measurable quantities to performance without stochastic assumptions (part a).
Y. Dallery. (1984). Some New Results on Operational Analysis.
Continuation presenting further operational-analysis results (part b).
Yves Dallery, Xi-Ren Cao. (1992). Operational analysis of stochastic closed queueing networks. Performance Evaluation 14, 43-61.
Connects operational analysis with the stochastic theory of closed networks, reconciling the two frameworks.
Peter J. Denning. (2006). Operational Analysis. Advances in Computer Science and Engineering: Texts, 21-33.
Retrospective tutorial on operational analysis of computer-system performance.
B. Bengtson. (2013). Operational Analysis Revisited.
Revisits operational analysis, re-examining its assumptions and relation to stochastic queueing theory.

Response-Time / Passage-Time Distributions (19)top

S. S. Lavenberg, M. Reiser. (1980). Stationary state probabilities at arrival instants for closed queueing networks with multiple types of customers. Journal of Applied Probability 17, 1048-1061.
Proves the arrival theorem for closed multiclass networks: an arriving customer sees the network in its stationary state with one fewer customer.
Simon S. Lam, A.Udaya Shankar. (1981). A derivation of response time distributions for a multi-class feedback queueing systems. Performance Evaluation 1, 48-61.
Derives response-time distributions for a multiclass feedback queue.
K. C. Sevcik, I. Mitrani. (1981). The Distribution of Queuing Network States at Input and Output Instants. Journal of the ACM 28, 358-371.
Characterizes the network state seen at customer arrival and departure instants, formalizing the arrival theorem.
Jeffrey A. Brumfield, Peter J. Denning. (1982). Error analysis of homogeneous mean queue and response time estimators. ACM SIGMETRICS Performance Evaluation Review 11, 215-221.
Analyzes the error of homogeneous estimators of mean queue length and response time in queueing networks.
P G Harrison. (1983). An exact analysis of the distribution of cycle times in a class of queueing networks. Proceedings of the 1983 ACM SIGMETRICS conference on Measurement and modeling of computer systems - SIGMETRICS '83, 224-242.
Derives exact cycle-time (passage-time) distributions for a class of closed queueing networks.
F. P. Kelly, P. K. Pollett. (1983). Sojourn times in closed queueing networks. Advances in Applied Probability 15, 638-656.
Analyzes sojourn-time distributions along overtake-free paths in closed queueing networks.
O. J. Boxma, F. P. Kelly, A. G. Konheim. (1984). The Product Form for Sojourn Time Distributions in Cyclic Exponential Queues. Journal of the ACM 31, 128-133.
Establishes product-form results for sojourn-time distributions in cyclic (tandem) exponential queues.
Lawrence W. Dowdy, Derek L. Eager, Karen D. Gordon, Lawrence V. Saxton. (1984). Throughput concavity and response time convexity. Information Processing Letters 19, 209-212.
Proves that throughput is concave and response time convex in population for product-form closed networks.
Lawrence W. Dowdy, Derek L. Eager, Karen D. Gordon, Lawrence V. Saxton. (1984). Throughput concavity and response time convexity. Information Processing Letters 19, 209-212.
Journal version establishing throughput concavity and response-time convexity in closed networks.
C.M. Woodside. (1984). Response time sensitivity measurement for computer systems and general closed queuing networks. Performance Evaluation 4, 199-210.
Develops response-time sensitivity measures for computer systems modeled as general closed networks.
John Zahorjan. (1984). The distribution of network states during residence times in product form queueing networks. Performance Evaluation 4, 99-104.
Characterizes the distribution of network states observed during a customer's residence time in product-form networks.
K. E. E. Raatikainen. (1989). Approximating response time distributions. ACM SIGMETRICS Performance Evaluation Review 17, 190-199.
Presents approximations for response-time distributions in queueing networks.
K. E. E. Raatikainen. (1989). Approximating response time distributions. ACM SIGMETRICS Performance Evaluation Review 17, 190-199.
Proposes a method to approximate response-time distributions in queueing networks that accounts for service-time distributions and routing behaviour.
A.E. Conway, D.E. O'Brien. (1993). Hybrid analysis of response time distributions in queueing networks. IEEE Transactions on Communications 41, 1091-1101.
Combines analytic and numerical techniques to compute response-time distributions in queueing networks.
Giuliano Casale. (2010). Approximating passage time distributions in queueing models by Bayesian expansion. Performance Evaluation 67, 1076-1091.
Approximates passage-time (response-time) distributions in queueing models using a Bayesian moment-matching approach.
P. J. Denning. (n.d.). Error Analysis of Homogeneous Mean Queue and Response Time Estimators.
Relates flow-balance and homogeneity assumption errors to errors in operational queue-length and response-time estimators, deriving and empirically validating error bounds.
Peter G. Harrison. (n.d.). Response time distributions in queueing network models. Lecture Notes in Computer Science, 147-164.
Provides methods and results for computing full response-time distributions in queueing network models.
James McKenna. (n.d.). A generalization of little's law to moments of queue lengths and waiting times in closed, product form queueing networks. Lecture Notes in Control and Information Sciences, 1000-1011.
Generalizes Little's law to relate higher moments of queue lengths and waiting times in closed product-form networks.
O. K. Yu. (n.d.). Passage Time Distributions for a Class of Queueing Networks.
Derives passage-time (response-time) distributions for a class of queueing networks.

Bottleneck Analysis (7)top

J. Luthi. (1997). Bottleneck Analysis for Computer and Communication Systems with Variabilities and Uncertainties.
Extends bottleneck analysis to systems with workload variabilities and parameter uncertainty.
Arthur Berger, Lev Bregman, Yaakov Kogan. (1999). Bottleneck analysis in multiclass closed queueing networks and its application. Queueing Systems 31, 217-237.
Analyzes bottleneck structure in multiclass closed networks and applies it to system design.
G. Casale, Giuseppe Serazzi. (2004). Bottlenecks identification in multiclass queueing networks using convex polytopes. The IEEE Computer Society's 12th Annual International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems, 2004. (MASCOTS 2004). Proceedings., 223-230.
Identifies bottlenecks and their population mixes in multiclass networks via convex-polytope analysis of the saturation sectors.
Jonatha Anselmi. (2008). A new framework supporting the bottleneck analysis of multiclass queueing networks. Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools.
Introduces a geometric/convex framework for identifying bottlenecks and saturation sectors in multiclass closed networks.
Pollett. (n.d.). Markovian Queueing Networks. An Introduction to Queueing Theory and Matrix-Analytic Methods, 63-109.
Studies bottleneck behaviour and limiting queue distribution in Markovian queueing networks.
G. Serazzi. (n.d.). A Survey of Bottleneck Analysis in Closed Networks of Queues.
Survey of bottleneck-analysis concepts and methods in closed queueing networks.
G. Serazzi. (n.d.). A Survey of Bottleneck Analysis in Closed Networks of Queues.
Surveys methods for identifying and analyzing bottlenecks in closed queueing networks and their use in performance evaluation.

Load-Dependent / State-Dependent Stations (11)top

Don Towsley. (1980). Queuing Network Models with State-Dependent Routing. Journal of the ACM 27, 323-337.
Identifies conditions under which networks with state-dependent routing retain product form.
Charles H. Sauer. (1983). Computational algorithms for state-dependent queueing networks. ACM Transactions on Computer Systems 1, 67-92.
Presents computational algorithms for networks with state-dependent (load-dependent) service and routing.
Charles H. Sauer. (1983). Computational algorithms for state-dependent queueing networks. ACM Transactions on Computer Systems 1, 67-92.
Develops computational algorithms for product-form queueing networks with several forms of state-dependent behavior that lacked efficient prior methods.
A.E. Krzesinski. (1987). Multiclass Queueing Networks with State-Dependent Routing. Performance Evaluation 7, 125-143.
Extends product-form theory to multiclass networks with state-dependent routing.
A.E. Krzesinski. (1987). Multiclass Queueing Networks with State-Dependent Routing. Performance Evaluation 7, 125-143.
Analyzes multiclass BCMP networks with state-dependent routing by partitioning centers into groups, extending product-form results to state-dependent routing.
I.F. Akyildiz, A. Sieber. (1988). Approximate analysis of load dependent general queueing networks. IEEE Transactions on Software Engineering 14, 1537-1545.
Provides approximate analysis of general (non-product-form) queueing networks containing load-dependent stations.
Edmundo de Souza e Silva, S. S. Lavenberg. (1989). Calculating joint queue-length distributions in product-form queuing networks. Journal of the ACM 36, 194-207.
Gives algorithms to compute joint queue-length distributions across stations in product-form networks.
Edmundo de Souza e Silva, S. S. Lavenberg. (1989). Calculating joint queue-length distributions in product-form queuing networks. Journal of the ACM 36, 194-207.
Technical-report version on computing joint queue-length distributions in product-form networks.
I.F. Akyildiz, J.C. Strelen. (1991). Moment analysis for load-dependent mixed product form queueing networks. IEEE Transactions on Communications 39, 828-832.
Derives moment formulas for mixed product-form networks with load-dependent stations.
J.-Y. Le Boudec. (n.d.). A BCMP Extension to Multiserver Stations with Concurrent Classes of Customers.
Extends BCMP product form to multiserver stations serving concurrent classes of customers.
W. J. Stewart. (n.d.). Some Equivalent Results for Load-Dependent Exponential Queueing Networks.
Establishes equivalence results relating load-dependent exponential networks to simpler forms.

Aggregation, Decomposition, Norton's Theorem (11)top

Hendrik Vantilborgh. (1978). Exact Aggregation in Exponential Queueing Networks. Journal of the ACM 25, 620-629.
Establishes conditions for exact aggregation (Norton reduction) in exponential queueing networks.
William J. Stewart, Gerald A. Zeiszler. (1980). On the existence of composite flow equivalent markovian servers. ACM SIGMETRICS Performance Evaluation Review 9, 105-116.
Studies conditions for the existence of composite flow-equivalent servers used in aggregation.
Alexander Thomasian, Behzad Nadji. (1981). Aggregation of stations in queueing network models of multiprogrammed computers. ACM SIGMETRICS Performance Evaluation Review 10, 86-104.
Applies station aggregation to reduce queueing network models of multiprogrammed computers.
P.S Kritzinger, S van Wyk, A.E Krzesinski. (1982). A generalisation of Norton's theorem for multiclass queueing networks. Performance Evaluation 2, 98-107.
Generalizes Norton's flow-equivalent theorem to multiclass queueing networks.
G Balbo, S.C Bruell. (1983). Computational aspects of aggregation in multiple class queueing networks. Performance Evaluation 3, 177-185.
Examines the computational aspects and accuracy of aggregating stations in multiclass networks.
Alexandre Brandwajn. (1985). Equivalence and decomposition in queueing systems-A unified approach. Performance Evaluation 5, 175-186.
Offers a unified approach to equivalence and decomposition (aggregation) in queueing systems.
Adrian E. Conway, Nicolas D. Georganas. (1986). Decomposition and aggregation by class in closed queueing networks. IEEE Transactions on Software Engineering SE-12, 1025-1040.
Part I developing exact decomposition and aggregation by class in closed networks.
Adrian E. Conway, Nicolas D. Georganas. (1986). Decomposition and aggregation by class in closed queueing networks. IEEE Transactions on Software Engineering SE-12, 1025-1040.
Part II continuing class-based decomposition and aggregation in closed networks.
Bruno Baynat, Yves Dallery, Keith Ross. (1994). A decomposition approximation method for multiclass BCMP queueing networks with multiple-server stations. Annals of Operations Research 48, 273-294.
Presents a decomposition approximation for multiclass BCMP networks with non-product-form features.
S. Balsamo, G. Iazeolla. (n.d.). An Extension of Norton's Theorem for Queueing Networks.
Extends Norton's theorem (flow-equivalent aggregation) to broader classes of queueing networks (part a).
S. Balsamo, G. Iazeolla. (n.d.). An Extension of Norton's Theorem for Queueing Networks.
Continuation extending Norton's theorem for queueing networks (part b).

Multichain / Class-Switching / Tree Algorithms (10)top

M. Reiser, H. Kobayashi. (1975). Queuing Networks with Multiple Closed Chains: Theory and Computational Algorithms. IBM Journal of Research and Development 19, 283-294.
Establishes product-form solution and computation for closed networks with multiple routing chains.
John Zahorjan. (1979). An exact solution method for the general class of closed separable queueing networks. ACM SIGSIM Simulation Digest 11, 107-112.
Gives an exact solution method for closed separable networks with class switching (routing chains).
G. Balbo, S.C. Bruell, S. Ghanta. (1986). The solution of homogeneous queueing networks with many job classes. Journal of Systems and Software 6, 41-53.
Exploits class homogeneity to reduce the cost of solving networks with many job classes.
B. Bahadori. (1987). A Hierarchical Approximation Algorithm for Large Multichain Product-Form Queueing Networks.
Introduces a hierarchical approximation for large multichain product-form networks by merging delay stations.
F.B Hanson, Jing-Dong Mei, Charles Tier, Huihuang Xu. (1993). PDAC: A data parallel algorithm for the performance analysis of closed queueing networks. Parallel Computing 19, 1345-1358.
Introduces PDAC, a data-parallel algorithm for performance analysis of closed networks.
PDAC. (1993). PDAC: A Data-Parallel Algorithm for the Solution of Queueing Network Models.
Presents PDAC, a data-parallel distribution-analysis-by-chain algorithm for closed multiclass networks whose polynomial cost has lower degree than the serial DAC algorithm.
Bruno Tuffin. (1997). Variance reduction applied to product form multiclass queuing networks. ACM Transactions on Modeling and Computer Simulation 7, 478-500.
Develops variance-reduction techniques for Monte Carlo estimation of product-form multiclass network measures.
P. Cremonesi, P.J. Schweitzer, G. Serazzi. (2002). A unifying framework for the approximate solution of closed multiclass queuing networks. IEEE Transactions on Computers 51, 1423-1434.
Provides a unifying framework relating the main approximate solution methods for closed multiclass networks.
Giuliano Casale. (2006). An efficient algorithm for the exact analysis of multiclass queueing networks with large population sizes. Proceedings of the joint international conference on Measurement and modeling of computer systems, 169-180.
Presents an efficient exact algorithm (CoMoM precursor) for multiclass closed networks reducing the cost of normalizing-constant evaluation.
N. S. Walton. (2009). Proportional fairness and its relationship with multi-class queueing networks. The Annals of Applied Probability 19.
Relates proportional-fairness bandwidth allocation to the stationary behaviour of multiclass queueing networks.

Optimization, Routing, Structural Properties (12)top

Hiroshi Kobayashi, Mario Gerla. (1983). Optimal routing in closed queuing networks. ACM Transactions on Computer Systems 1, 294-310.
Formulates and solves optimal routing to maximize throughput in closed queueing networks.
J. R. Kenevan. (1984). Convexity and Concavity Properties of Analytic Queueing Models for Computer Systems.
Part I establishing convexity/concavity properties of performance measures in queueing models.
J. R. Kenevan. (1984). Convexity and Concavity Properties of Analytic Queueing Models for Computer Systems.
Part II continuing convexity/concavity properties of queueing performance measures.
Rajan Suri. (1985). A Concept of Monotonicity and Its Characterization for Closed Queueing Networks. Operations Research 33, 606-624.
Introduces and characterizes a monotonicity concept for performance measures in closed networks.
K.E. Stecke. (1986). On the nonconcavity of throughput in certain closed queueing networks. Computer Compacts 4, 183.
Shows that throughput can be nonconcave in load-dependent closed networks, contrary to the product-form case.
J. George Shanthikumar, David D. Yao. (1987). Stochastic Monotonicity of the Queue Lengths in Closed Queueing Networks. Operations Research 35, 583-588.
Proves stochastic monotonicity of queue lengths with respect to population and service parameters in closed networks.
Satish K. Tripathi, C. Murray Woodside. (1988). A vertex-allocation theorem for resources in queuing networks. Journal of the ACM 35, 221-230.
Proves a vertex-allocation theorem showing optimal resource allocations occur at extreme points of the feasible region.
William C. Cheng, Richard R. Muntz. (1991). Optimal routing for closed queueing networks. Performance Evaluation 13, 3-15.
Studies optimal routing policies for throughput maximization in closed networks.
Heungsoon Felix Lee, Mandyam M. Srinivasan, Candace A. Yano. (1991). Characteristics of optimal workload allocation for closed queueing networks. Performance Evaluation 12, 255-268.
Characterizes optimal workload (demand) allocation across stations in closed networks.
F. P. Kelly, L. Massoulié, N. S. Walton. (2009). Resource pooling in congested networks: proportional fairness and product form. Queueing Systems 63, 165-194.
Studies how resource pooling improves performance and stability in congested networks.
Jaron Sanders, Sem Borst, Johan van Leeuwaarden. (2012). Online Optimization of Product-Form Networks. Proceedings of the 6th International Conference on Performance Evaluation Methodologies and Tools.
Develops online (adaptive) optimization of routing/service parameters in product-form networks.
Jonatha Anselmi, Bernardo D'Auria, Neil Walton. (2013). Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence. Mathematics of Operations Research 38, 469-491.
Analyzes closed networks whose service rates degrade under congestion, characterizing performance and optimal load.

Sensitivity, Robustness, Measurement (8)top

A. E. Ferdinand. (1970). A Statistical Mechanical Approach to Systems Analysis. IBM Journal of Research and Development 14, 539-547.
Applies statistical-mechanics (partition-function) reasoning to analyze closed queueing systems.
Clifford A. Rose. (1978). A Measurement Procedure for Queueing Network Models of Computer Systems. ACM Computing Surveys 10, 263-280.
Describes a measurement procedure to parameterize queueing network models from running computer systems.
Yonathan Bard. (1980). Estimation of State Probabilities Using the Maximum Entropy Principle. IBM Journal of Research and Development 24, 563-569.
Uses the maximum-entropy principle to estimate queueing-network state probabilities from limited information.
Karen D. Gordon, Lawrence W. Dowdy. (1980). The impact of certain parameter estimation errors in queueing network models. ACM SIGMETRICS Performance Evaluation Review 9, 3-9.
Quantifies how errors in estimated input parameters propagate to queueing-network performance predictions.
Rajan Suri. (1983). Robustness of queuing network formulas. Journal of the ACM 30, 564-594.
Shows that product-form performance formulas are robust to violations of their underlying assumptions.
Zhen Liu, Philippe Nain. (1991). Sensitivity results in open, closed and mixed product form queueing networks. Performance Evaluation 13, 237-251.
Derives sensitivity results relating performance derivatives to parameters across open, closed, and mixed product-form networks.
Xi-Ren Cao, Dye-Jyun Ma. (1996). Performance sensitivity formulae, algorithms and estimates for closed queueing networks with exponential servers. Performance Evaluation 26, 181-199.
Derives performance-sensitivity formulas and estimation algorithms for closed networks with exponential servers.
T. Bonald, A. Proutière. (2002). Insensitivity in processor-sharing networks. Performance Evaluation 49, 193-209.
Establishes insensitivity of processor-sharing networks: stationary performance depends only on mean service demands, not on their distribution.

Insensitivity and Processor-Sharing Networks (3)top

J.R. Spirn. (1979). Queuing Networks with Random Selection for Service. IEEE Transactions on Software Engineering SE-5, 287-289.
Studies queueing networks under random-selection-for-service scheduling and its product-form/insensitivity properties.
Na Chen, Scott Jordan. (2007). Throughput in Processor-Sharing Queues. IEEE Transactions on Automatic Control 52, 299-305.
Analyzes throughput behaviour of processor-sharing queues and networks.
Céline Comte, Jan-Pieter Dorsman. (2021). Pass-and-swap queues. Queueing Systems 98, 275-331.
Introduces pass-and-swap queues, a class of order-independent queues with product-form stationary distributions generalizing processor sharing.

Little's Law (3)top

John D. C. Little. (1961). A Proof for the Queuing Formula: L = λW. Operations Research 9, 383-387.
Little's seminal paper giving the first general proof of the queueing formula L = lambda W.
J. P. Buzen. (1988). Understanding Little's Law.
Short expository note giving an operational interpretation and understanding of Little's law.
J. D. C. Little. (n.d.). Little's Law: A Personal Account.
Little's personal historical account of the origin and development of the L = lambda W formula.

Foundations and Product-Form Theory (69)top

James R. Jackson. (1957). Networks of Waiting Lines. Operations Research 5, 518-521.
Jackson's foundational paper establishing product form for open networks of exponential queues.
E. Koenigsberg. (1958). On Computational Algorithms for Product-Form Queueing Networks (Letter).
Early letter by Koenigsberg on cyclic-queue analysis, a precursor to closed-network computation.
JAMES R. JACKSON. (1963). JOBSHOP-LIKE QUEUEING SYSTEMS.
Extends Jackson networks to job-shop-like systems with state-dependent arrival and service rates.
William J. Gordon, Gordon F. Newell. (1967). Closed Queuing Systems with Exponential Servers. Operations Research 15, 254-265.
The Gordon-Newell theorem, establishing the product-form stationary distribution of closed exponential networks.
Forest Baskett. (1971). The dependence of computer system queues upon processing time distribution and central processor scheduling. Proceedings of the third symposium on Operating systems principles - SOSP '71, 109-113.
Early precursor to BCMP showing dependence of queue behaviour on service-time distribution and scheduling discipline.
R. R. Muntz. (1972). Poisson Departure Processes and Queueing Networks.
Studies conditions under which departure processes are Poisson, underpinning product form via quasi-reversibility.
F. G. Palacios. (1972). An Analytic Model of a Multiprogramming System Including a Job Mix.
Presents an analytic closed-network model of a multiprogramming system with a mix of jobs.
F. G. Palacios. (1972). On the Steady-State Properties of Networks of Queues.
Studies steady-state properties and product form for networks of queues (Palacios/Muntz).
Jeffrey P. Buzen. (1973). Computational algorithms for closed queueing networks with exponential servers. Communications of the ACM 16, 527-531.
Buzen's convolution algorithm, the first efficient recursion for normalizing constants and measures of closed networks.
Forest Baskett, K. Mani Chandy, Richard R. Muntz, Fernando G. Palacios. (1975). Open, Closed, and Mixed Networks of Queues with Different Classes of Customers. Journal of the ACM 22, 248-260.
The BCMP theorem, establishing product-form stationary distributions for open, closed, and mixed multiclass networks under four service disciplines.
K. M. Chandy, U. Herzog, L. Woo. (1975). Parametric Analysis of Queuing Networks. IBM Journal of Research and Development 19, 36-42.
Introduces flow-equivalent aggregation (Norton's theorem) for parametric analysis of queueing networks.
F. P. Kelly. (1975). Networks of queues with customers of different types. Journal of Applied Probability 12, 542-554.
Establishes product form and reversibility for networks with multiple customer types and general routing.
Andrew D. Barbour. (1976). Networks of queues and the method of stages. Advances in Applied Probability 8, 584-591.
Uses the method of stages (phase-type services) to establish product form for networks with non-exponential services.
Donald P. Gaver, George Humfeld. (1976). Multitype multiprogramming models. Acta Informatica 7, 111-121.
Develops multitype (multiclass) multiprogramming queueing models of computer systems.
S. S. Lam. (1977). Queuing Networks with Population Size Constraints. IBM Journal of Research and Development 21, 370-378.
Analyzes networks with population-size (window/admission) constraints and their product-form-like solution.
S. S. Lam. (1977). An Extension of Moore's Result for Closed Queuing Networks. IBM Journal of Research and Development 21, 384-387.
Extends Moore's asymptotic result on closed-network behaviour.
R. R. Muntz. (1978). Queueing Networks: A Critique of the State of the Art and Directions for the Future.
Tutorial/survey chapter on queueing network theory and computer performance modeling.
Buzen, Denning. (1980). Measuring and Calculating Queue Length Distributions. Computer 13, 33-44.
Relates measurable operational quantities to computed queue-length distributions in queueing network models.
K. Mani Chandy, Charles H. Sauer. (1980). Computational algorithms for product form queueing networks. ACM SIGMETRICS Performance Evaluation Review 9, 1.
Surveys and unifies computational algorithms (convolution, MVA) for product-form networks.
L. Lipsky. (1980). Study of Time-Sharing Systems Considered as Queueing Networks of Exponential Servers.
Models time-sharing systems as closed queueing networks of exponential servers and analyzes their performance.
H. D. Schwetman. (1980). Implementing the Mean Value Algorithm for the Solution of Queueing Network Models.
Discusses practical implementation of the MVA algorithm for queueing network solution.
Ralph L. Disney. (1981). Queueing networks. Proceedings of Symposia in Applied Mathematics, 53-83.
Survey of the mathematical theory of queueing networks, including reversibility, quasi-reversibility, and product form.
P. G. Harrison. (1981). Transient behaviour of queueing networks. Journal of Applied Probability 18, 482-490.
Studies the transient (time-dependent) behaviour of queueing networks.
H. Heffes. (1982). Moment Formulae for a Class of Mixed Multi-Job-Type Queueing Networks. Bell System Technical Journal 61, 709-746.
Derives moment formulae for a class of mixed multi-job-type (multiclass) queueing networks.
Hisao Kameda. (1982). A Finite-Source Queue with Different Customers. Journal of the ACM 29, 478-491.
Analyzes a finite-source (machine-repair) queue serving different customer types.
Herb Schwetman. (1982). Some Computational Aspects of Queueing Network Models. Applied Probability - Computer Science: The Interface, 135-155.
Examines computational aspects and numerical issues in solving queueing network models.
K. M. Chandy, A. J. Martin. (1983). A Characterization of Product-Form Queuing Networks. Journal of the ACM 30, 286-299.
Gives necessary and sufficient (local-balance) conditions characterizing product-form queueing networks.
We-Min Chow. (1983). Approximations for large scale closed queueing networks. Computer Compacts 1, 52.
Proposes approximations for solving very large closed queueing networks.
John Zahorjan. (1983). Workload representations in queueing models of computer systems. Proceedings of the 1983 ACM SIGMETRICS conference on Measurement and modeling of computer systems - SIGMETRICS '83, 70-81.
Studies how workloads are represented and parameterized in queueing models of computer systems.
Lawrence W Dowdy, Karen D Gordon. (1984). Algorithms for nonintegral degrees of multiprogramming in closed queuing networks. Performance Evaluation 4, 19-29.
Extends closed-network solution to non-integral (fractional) degrees of multiprogramming via interpolation.
Derek L Eager, Kenneth C Sevcik. (1984). An analysis of an approximation algorithm for queueing networks. Performance Evaluation 4, 275-284.
Analyzes the accuracy and convergence of an approximate solution algorithm for queueing networks.
E. de Souza e Silva, R. R. Muntz. (1984). A Perspective on Iterative Methods for the Approximate Analysis of Closed Queueing Networks.
Perspective reviewing iterative (fixed-point) methods for approximate analysis of closed networks.
S. Balsamo, G. Iazeolla. (1985). Product-Form Synthesis of Queueing Networks. IEEE Transactions on Software Engineering SE-11, 194-199.
Addresses the synthesis (inverse) problem of constructing networks that exhibit a desired product-form solution.
Lawrence W. Dowdy, Manvinder S. Chopra. (1985). On the applicability of using multiprogramming level distributions. ACM SIGMETRICS Performance Evaluation Review 13, 116-127.
Examines when multiprogramming-level distributions can be used to characterize closed-network workloads.
J. A. Buzacott, D. D. Yao. (1986). On queueing network models of flexible manufacturing systems. Queueing Systems 1, 5-27.
Applies closed queueing network models to the analysis of flexible manufacturing systems.
Aurel A. Lazar, Thomas G. Robertazzi. (1986). The geometry of lattices for Markovian queueing networks. Performance Evaluation 6, 85-86.
Studies the lattice geometry of the state space of Markovian queueing networks.
C. A. Bannister. (1987). Product-Form Queueing Networks: State Dependence Revisited.
Revisits the conditions on state-dependent rates under which networks retain product form.
L. Seidl. (1987). An Estimate of the Moment of the Regeneration Period in a Closed Central-Server Queueing Network. Theory of Probability & Its Applications 31, 309-313.
Estimates moments of the regeneration period in a closed central-server model.
E. de Souza e Silva. (1987). Distributional Analysis of Product-Form Queueing Networks.
Studies the computation of full queue-length distributions, not only means, in product-form networks.
H. Daduna. (1988). Busy Periods for Subnetworks in Stochastic Networks: Mean Value Analysis.
Analyzes busy-period characteristics of subnetworks embedded in stochastic (product-form) networks.
E. de Souza e Silva, R.R. Muntz. (1988). Simple relationships among moments of queue lengths in product form queueing networks. IEEE Transactions on Computers 37, 1125-1129.
Derives simple recursive relationships among moments of queue lengths in product-form networks.
F. P. Kelly. (1989). On a class of approximations for closed queueing networks. Queueing Systems 4, 69-76.
Introduces a class of approximations for closed networks based on fixed-point/asymptotic arguments.
F. P. Kelly. (1989). On a class of approximations for closed queueing networks. Queueing Systems 4, 69-76.
Analyzes a fixed-point approximation expressing mean sojourn time as a function of queue throughput, deriving throughput equations for closed and non-product-form networks.
Y. C. Tay. (1992). An Approach to Analyzing the Behavior of Some Queueing Networks. Operations Research 40, S300-S311.
Proposes an analytical approach to characterize the behaviour of certain queueing networks.
Randolph D. Nelson. (1993). The mathematics of product form queuing networks. ACM Computing Surveys 25, 339-369.
Comprehensive tutorial on the mathematical foundations (reversibility, quasi-reversibility, partial balance) of product-form networks.
PDAC. (1993). PDAC: A Data-Parallel Algorithm for the Solution of Queueing Network Models.
Presents PDAC, a parallel/data-parallel algorithm for closed-network performance analysis.
PDAC. (1993). PDAC: A Data-Parallel Algorithm for the Solution of Queueing Network Models.
Presents PDAC, a data-parallel distribution-analysis-by-chain algorithm for closed multiclass networks whose polynomial cost has lower degree than the serial DAC algorithm.
Wei-Bo Gong, Hong Yang. (1995). Rational approximants for some performance analysis problems. IEEE Transactions on Computers 44, 1394-1404.
Uses rational (Pade) approximants to estimate performance measures in queueing analysis problems.
M. Mittler. (1995). Moment Approximations in Product-Form Queueing Networks.
Presents moment-based approximations for queue-length distributions in product-form networks.
J. Luthi. (1996). Performance Analysis Using Queueing Network Models with Variabilities and Uncertainties in Workloads.
Analyzes queueing-network performance under workload variabilities and parameter uncertainty.
Michael A. Zazanis. (1997). Formulas and representations for cyclic Markovian networks via Palm calculus. Queueing Systems 26, 151-167.
Derives performance formulas for cyclic Markovian networks using Palm calculus.
Wu-Lin Chen, Colm Art O'Cinneide. (1998). Towards a polynomial-time randomized algorithm for closed product-form networks. ACM Transactions on Modeling and Computer Simulation 8, 227-253.
Works toward a polynomial-time randomized (approximation) algorithm for the partition function of closed product-form networks.
Wu-Lin Chen, Colm Art O'Cinneide. (1998). Towards a polynomial-time randomized algorithm for closed product-form networks. ACM Transactions on Modeling and Computer Simulation 8, 227-253.
Presents a Markov-chain Monte Carlo method for class throughputs in closed multiclass product-form networks by simulating a regularized network with the same steady-state distribution.
Simonetta Balsamo. (2000). Product Form Queueing Networks. Lecture Notes in Computer Science, 377-401.
Survey/chapter presenting the theory and characterizations of product-form queueing networks.
Simonetta Balsamo. (2000). Product Form Queueing Networks. Lecture Notes in Computer Science, 377-401.
Extended survey chapter on product-form queueing networks and their solution algorithms.
P. Cremonesi, E. Rosti, G. Serazzi. (2000). Xaba: Exact, Approximate, and Asymptotic Solvers for Multi-Class Closed Queueing Networks.
Presents XABA, an asymptotic bound analysis tool/method for closed multiclass networks.
Hans Daduna. (2001). Queueing Networks with Discrete Time Scale. Lecture Notes in Computer Science.
Develops product-form theory for discrete-time queueing networks.
J. Anselmi. (n.d.). Bounding the Partition Function of BCMP Queueing Networks (Presentation, BWWQT 2009).
Presentation slides by Anselmi (BWWQT 2009) on product-form network analysis.
K. M. Chandy. (n.d.). The Analysis and Solutions for General Queueing Networks.
Discusses analysis techniques and product-form solutions for general queueing networks.
A. E. Conway, N. D. Georganas. (n.d.). A New Method for Computing the Normalization Constant of Multiple-Chain Queueing Networks.
Gives a computationally efficient formulation of the RECAL recursion for the normalization constant, faster than convolution when the network has many routing chains.
A. I. Gerasimov. (n.d.). Normalizing Constants in Multiclass Queueing Networks (Cybernetics).
Gerasimov paper (Cybernetics) on computation of normalizing constants in multiclass closed networks.
S. Kijima, T. Matsui. (n.d.). Approximate/Perfect Samplers for Closed Jackson Networks. Proceedings of the Winter Simulation Conference, 2005., 862-868.
Develops approximate perfect-sampling (coupling-from-the-past) algorithms for closed Jackson networks.
V. Mathur, V. Apte. (n.d.). A computational complexity-aware model for performance analysis of software servers. The IEEE Computer Society's 12th Annual International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems, 2004. (MASCOTS 2004). Proceedings., 537-544.
Builds a queueing model of software performance that accounts for algorithmic computational complexity.
S. Mizuno. (n.d.). Limitations of Calculating Theoretical Solutions for Closed BCMP Queueing Networks and Verification of Alternative Theoretical Values by Parallel Simulation.
Uses closed BCMP networks and parallel MPI simulation to assess the limits of exact solutions and validate alternative values for large-scale congestion-evaluation models.
R. R. Muntz. (n.d.). Queueing Networks: A Critique of the State of the Art and Directions for the Future.
Critically reviews the state of the art in queueing-network modeling of computer systems and outlines directions for future research.
E. Rosti, F. Schiavoni, G. Serazzi. (n.d.). Queueing network models with two classes of customers. Proceedings Fifth International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, 229-234.
Analyzes queueing network models specialized to two customer classes.
K. Sakurai. (n.d.). Computational Techniques for Solving Stochastic Models (PhD Thesis).
Thesis/monograph on computational techniques (transform inversion) for solving stochastic performance models.
J. G. Shanthikumar. (n.d.). Heuristic Analysis of Closed Queueing Networks.
Presents heuristic approximate analysis methods for closed queueing networks.
J. Zahorjan. (n.d.). The Eager Looping Method (Technical Report TR-360).
Technical report describing the Zahorjan-Eager looping method for approximate closed-network solution.

Surveys and Historical Perspectives (12)top

J. P. Buzen. (1976). Fundamental laws of computer system performance. Proceedings of the 1976 ACM SIGMETRICS conference on Computer performance modeling measurement and evaluation - SIGMETRICS '76, 200-210.
Expository article on the fundamental operational laws governing computing-system performance.
Austin J. Lemoine. (1977). State-of-the-Art-Networks of Queues-A Survey of Equilibrium Analysis. Management Science 24, 464-481.
Survey of equilibrium (stationary) analysis methods for networks of queues.
J. W. Wong. (1978). Queueing Network Modeling of Computer Communication Networks. ACM Computing Surveys 10, 343-351.
Applies queueing network modeling to the performance analysis of computer communication networks.
Martin G. Kienzle, K. C. Sevcik. (1979). Survey of analytic queueing network models of computer systems. ACM SIGSIM Simulation Digest 11, 113-129.
Survey of analytic queueing network models used for computer-system performance evaluation.
Yonathan Bard, Charles H. Sauer. (1981). IBM Contributions to Computer Performance Modeling. IBM Journal of Research and Development 25, 562-570.
Historical account of IBM's contributions to computer performance modeling and queueing analysis.
P. J. Denning. (1981). Performance Modeling.
Short overview of performance modeling of computer systems.
Ernest Koenigsberg. (1982). Twenty Five Years of Cyclic Queues and Closed Queue Networks: A Review. Journal of the Operational Research Society 33, 605-619.
Historical survey of twenty-five years of research on cyclic queues and closed queueing networks.
S.S Lavenberg. (1989). A perspective on queueing models of computer performance. Performance Evaluation 10, 53-76.
Reflective perspective on the development and impact of queueing models of computer performance.
E. de Souza e Silva, R. R. Muntz. (1989). Queueing Networks: Solutions and Applications.
Survey of queueing network solution methods and their applications to computer systems.
Martin Reiser. (1991). A quarter century of performance evaluation -where do we stand?. Performance Evaluation 12, 1-4.
Retrospective assessing a quarter century of computer performance evaluation research.
P. J. Schweitzer. (1993). A Tutorial on Mean Value Analysis.
Tutorial on approximate mean value analysis and related solution techniques.
Stephen S. Lavenberg, Mark S. Squillante. (2000). Performance Evaluation in Industry: A Personal Perspective. Lecture Notes in Computer Science, 3-13.
Reviews the application and impact of performance evaluation methods in industry.