Asymptotics of the Partition Function in Large Closed BCMP Networks with Bottlenecks

Authors:
Yaakov Kogan;Andrei Yakovlev
Affiliations:
-;-
Venue:
MASCOTS '95 Proceedings of the 3rd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems
Year:
1995

Citing 3
Cited 0

Multidimensional residues, generating functions, and their application to queueing networks

SIAM Review
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers

Journal of the ACM (JACM)
Asymptotic analysis of closed queueing networks with bottlenecks

Proceedings of the IFIP WG 7.3 International Conference on Performance of Distributed Systems and Integrated Communication Networks

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Abstract

We consider a two-chain exponential queueing network with a large number of customers, which consists of one infinite-server (lS) station and two processor-sharing (PS) or FCFS single-server stations. Asymptotic behavior of the partition function is studied for such a network when one or both PS (FCFS) nodes are heavily loaded. The results are derived using methods of multidimensional complex analysis (the theory of homologies and residues) and the saddle-point method.