Optimal arrival rate and service rate control of multi-server queues

Authors:
Nelson Lee;Vidyadhar G. Kulkarni
Affiliations:
Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, USA;Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, USA
Venue:
Queueing Systems: Theory and Applications
Year:
2014

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Abstract

We consider the problem of optimal control of a multi-server queue with controllable arrival and service rates. This study is motivated by its potential application to the design and control of data centers. The cost structure includes customer holding cost which is a non-decreasing convex function of the number of customers in the system, server operating cost which is a non-decreasing convex function of the chosen service rate, and system operating reward which is a non-decreasing concave function of the chosen arrival rate. We formulate the problem as a continuous-time Markov decision process and derive structural properties of the optimal control policies under both discounted cost and average cost criterions.