HEAVY TRAFFIC APPROXIMATIONS FOR A SYSTEM OF INFINITE SERVERS WITH LOAD BALANCING

Authors:
Philip J. Fleming;Burton Simon
Affiliations:
Motorola, Inc., 1501 West Shure Drive, Arlington Heights, Illinois 60004, e-mail: fleming@cig.mot.com;Department of Mathematics, University of Colorado at Denver, Denver, Colorado 80217, e-mail: bsimon@math.cudenver.edu
Venue:
Probability in the Engineering and Informational Sciences
Year:
1999

Citing 2
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Abstract

We consider an exponential queueing system with multiple stations, each of which has an infinite number of servers and a dedicated arrival stream of jobs. In addition, there is an arrival stream of jobs that choose a station based on the state of the system. In this paper we describe two heavy traffic approximations for the stationary joint probability mass function of the number of busy servers at each station. One of the approximations involves state-space collapse and is accurate for large traffic loads. The state-space in the second approximation does not collapse. It provides an accurate estimate of the stationary behavior of the system over a wide range of traffic loads.