 
Summary: Probability in the Engineering and Informational Sciences, 7, 1993, 441464. Printed in the U.S.A.
A TECHNIQUE FOR COMPUTING
SOJOURN TIMES IN
LARGE NETWORKS OF
INTERACTING QUEUES
V. ANANTHARAM AND M. BENCHEKROUN
School of Electrical Engineering
Cornell University
Ithaca, New York 14850
Consider a large number of interacting queues with symmetric interactions. In
the asymptotic limit, the interactions between any fixed finite subcollection
become negligible, and the overall effect of interactions can be replaced by an
empirical rate. The evolution of each queue is given by a time inhomogeneous
Markov process. This may be considered a technique for writing dynamic
Erlang fixedpoint equations. We explore this as a tool to approximate sojourn
time distributions.
1. INTRODUCTION
In this paper we discuss the use of a statistical mechanics technique called prop
agation of chaos for computing the sojourn times of typical customers in large
networks of interacting queues with symmetry. Propagation of chaos is a prop
