Asymptotic expansions for closed Markovian networks with state-dependent service rates
Journal of the ACM (JACM)
Asymptotic expansion for large closed queuing networks
Journal of the ACM (JACM)
Elements of information theory
Elements of information theory
Asymptotic Expansions for Large Closed Queueing Networks with Multiple Job Classes
IEEE Transactions on Computers
Asymptotic analysis of multiclass closed queueing networks: multiple bottlenecks
Performance Evaluation
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)
Linearizer: a heuristic algorithm for queueing network models of computing systems
Communications of the ACM
On the asymptotic behavior of time-sharing systems
Communications of the ACM
On the asymptotic behaviour of closed multiclass queueing networks
Performance Evaluation
Bottleneck analysis in multiclass closed queueing networks and its application
Queueing Systems: Theory and Applications
A Survey of Bottleneck Analysis in Closed Networks of Queues
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
Bottlenecks Identification in Multiclass Queueing Networks Using Convex Polytopes
MASCOTS '04 Proceedings of the The IEEE Computer Society's 12th Annual International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
An analytical model for multi-tier internet services and its applications
SIGMETRICS '05 Proceedings of the 2005 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Service Consolidation with End-to-End Response Time Constraints
SEAA '08 Proceedings of the 2008 34th Euromicro Conference Software Engineering and Advanced Applications
Queuing networks with multiple closed chains: theory and computational algorithms
IBM Journal of Research and Development
Resource pooling in congested networks: proportional fairness and product form
Queueing Systems: Theory and Applications
A unified framework for the bottleneck analysis of multiclass queueing networks
Performance Evaluation
A generalized method of moments for closed queueing networks
Performance Evaluation
Heavy-traffic revenue maximization in parallel multiclass queues
Performance Evaluation
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We analyze the behavior of closed multiclass product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route or class. First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at nonbottleneck queues converges weakly to the stationary distribution of an ergodic, open product-form queueing network, which is geometric. This open network is obtained by replacing bottleneck queues with per-route Poissonian sources whose rates are uniquely determined by the solution of a strictly concave optimization problem. We strengthen such results by also proving convergence of the first moment of the queue lengths of nonbottleneck stations. Then we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid, or customers, on each route eventually concentrates on the bottleneck queues only and that the long-term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network.