Asymptotic expansions for closed Markovian networks with state-dependent service rates
Journal of the ACM (JACM)
RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks
Journal of the ACM (JACM)
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
The Operational Analysis of Queueing Network Models
ACM Computing Surveys (CSUR)
Computational algorithms for product form queueing networks
Communications of the ACM
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Computer Performance Modeling Handbook
Computer Performance Modeling Handbook
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Asymptotic Expansions for Large Closed Queueing Networks with Multiple Job Classes
IEEE Transactions on Computers
Asymptotically optimal importance sampling for product-form queuing networks
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the asymptotic behaviour of closed multiclass queueing networks
Performance Evaluation
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Another approach to asymptotic expansions for large closed queueing networks
Operations Research Letters
Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence
Mathematics of Operations Research
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In this paper, a new asymptotic method is developed for analyzing closed BCMP queuing networks with a single class (chain) consisting of a large number of customers, a single infinite server queue, and a large number of single server queues with fixed (state-independent) service rates. Asymptotic approximations are computed for the normalization constant (partition function) starting directly from a recursion relation of Buzen. The approach of the authors employs the ray method of geometrical optics and the method of matched asymptotic expansions. The method is applicable when the servers have nearly equal relative utilizations or can be divided into classes with nearly equal relative utilizations. Numerical comparisons are given that illustrate the accuracy of the asymptotic approximations.