Departmental Papers (ESE)

Document Type

Conference Paper

Date of this Version

12-2005

Comments

Suggested Citation:
Chaporkar, P. and S. Sarkar. (2005). "Utility Optimal Scheduling for General Reward States and Stability Constraint." Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference 2005. Seville, Spain. December 12-15, 2005.

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Abstract

We consider a queueing system with n parallel queues, which receives a reward for the service it provides. Our aim is to maximize the expected reward obtained per unit time (utility) while ensuring that the mean queue length in each of the queues is bounded (stability). We show that the optimal policy has counter intuitive properties because of the general reward states and stability constraint. For example, the greedy policy of serving a customer that fetches maximum reward need not be optimal. In addition, the optimal policy may belong to a class of non work-conserving policies. We obtain two different policies that attain the above optimality goal. The first policy arbitrates service randomly based on the current reward states and probabilities that depend on system statistics. The second policy arbitrates service deterministically based only on the queue lengths and the current reward states, and does not require any knowledge of the system statistics. The proposed policies are optimal in a large class of policies that includes off-line policies, which use knowledge of past, present and even future arrival and reward states in their decision processes.

Keywords

Queueing theory, utility maximization, stability, randomized algorithms

 

Date Posted: 12 October 2010

This document has been peer reviewed.