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Using Distributed-Event Parallel Simulation to Study Departures from Many Queues in Series

Published online by Cambridge University Press:  27 July 2009

Albert G. Greenberg ,
Otmar Schlunk  and
Ward Whitt
Albert G. Greenberg
Affiliation:
AT&T Bell Laboratories, Murray Hill, New Jersey 07974-0636
Otmar Schlunk
Affiliation:
Coordinated Science Laboratory, University of Illinois, Urbana, Illinois 61801
Ward Whitt
Affiliation:
AT&T Bell Laboratories, Murray Hill, New Jersey 07974-0636
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Abstract

In this paper we describe an application of distributed-event parallel simulation to study the transient behavior of a large non-Markovian network of queues. In particular, we implemented the parallel-prefix-based algorithm of Greenberg, Lubachevsky, and Mitrani [13,14] on the 8,192-processor CM-2 Connection machine and the 16,384-processor MasPar computer to simulate the departure times D(k, n) of the kth customer from the nth queue in a long series of single-server queues. Each queue has unlimited waiting space and uses the first-in first-out discipline. The service times of all the customers at all the queues are i.i.d. with a general distribution, and the system starts out with k customers in the first queue and all other queues empty. Glynn and Whitt [11] established limit theorems for this model, but very little could be said about the limits themselves. The simulation results presented here describe the limits and the quality of the approximations resulting from using the limits for finite k and n. Indeed, the simulations suggest interesting conjectures. For this model speeding up a single long run is far superior to independent replications, because very long runs are required to obtain unbiased estimates of the desired quantities and the variance of the estimator at the end of the run is small. The achieved simulation rate was about 17 billion service completions per hour, which is a speedup by about a factor of 100 compared to simulation on a conventional single-processor machine. This speedup contributed greatly to performing the desired experiments.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 2 , April 1993 , pp. 159 - 186
Copyright
Copyright © Cambridge University Press 1993

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