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

Published online by Cambridge University Press:  01 July 1999

Philip J. Fleming  and
Burton Simon
Philip J. Fleming
Affiliation:
Motorola, Inc., 1501 West Shure Drive, Arlington Heights, Illinois 60004, e-mail: fleming@cig.mot.com
Burton Simon
Affiliation:
Department of Mathematics, University of Colorado at Denver, Denver, Colorado 80217, e-mail: bsimon@math.cudenver.edu
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Abstract

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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 13 , Issue 3 , July 1999 , pp. 251 - 273
Copyright
© 1999 Cambridge University Press