Join Minimum Cost Queue For Multiclass Customers: Stability And Performance Bounds

Authors:
Rahul Tandra;N. Hemachandra;D. Manjunath
Affiliations:
Department of EECS, University of California, Berkeley, CA, tandra@eecs.berkeley.edu;IE and OR Interdisciplinary Programme, Indian Institute of Technology, Bombay, Powai Mumbai, 400 076 India, nh@iitb.ac.in;Department of Electrical Engineering, Indian Institute of Technology, Bombay, Powai Mumbai, 400 076 India, dmanju@ee.iitb.ac.in
Venue:
Probability in the Engineering and Informational Sciences
Year:
2004

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Abstract

We consider a system of K parallel queues providing different grades of service through each of the queues and serving a multiclass customer population. Service differentiation is achieved by specifying different join prices to the queues. Customers of class j define a cost function &psgr;ij(ci,xi) for taking service from queue i when the join price for queue i is ci and congestion in queue i is xi and join the queue that minimizes &psgr;ij(·,·). Such a queuing system will be called the “join minimum cost queue” (JMCQ) and is a generalization of the join shortest queue (JSQ) system. Non-work-conserving (called Paris Metro pricing system) and work-conserving (called the Tirupati system) versions of the JMCQ are analyzed when the cost to an arrival of joining a queue is a convex combination of the join price for that queue and the expected waiting time in that queue at the arrival epoch. Our main results are for a two-queue system.