Dynamic Service Rate Control for a Single

Server Queue with Markov Modulated Arrivals

Ravi Kumar, Mark E. Lewis and Huseyin Topaloglu
Cornell University
School of Operations Research and Information Engineering
226 Rhodes Hall
Ithaca, New York 14853


    We consider the problem of service rate control of a single server queueing system

    when the arrival process is governed by a finite-state Markov-modulated Poisson

    process. There are two main technical contributions. First, in keeping with

    intuition, we show that the optimal service rate is non-decreasing

    in the number of customers in the system. That is, higher congestion rates

    warrant higher service rates. On the contrary, however, we show that

    the optimal service rate is \textbf{not} necessarily monotone in the current arrival rate.

    If the modulating process satisfies a stochastic monotonicity property we show that

    the monotonicity is recovered. Together these results imply that we have reasonable conditions for the

    optimal control to follow a monotone switching curve in the current state of the system.


    Our numerical study also has two components. We examine several heuristics

    and show where those heuristics can be reasonable substitutes for the optimal

    control. None of the heuristics perform well in all the regimes we consider.

    Secondly, we discuss when the Markov-modulated Poisson process with

    service rate control can act as a heuristic itself. In particular, we show that it can

    approximate the optimal control of a system with a periodic non-homogeneous

    Poisson arrival process. Thus, not only is the current model of interest in the control

    of Internet or mobile networks with bursty traffic, but it is also useful in providing a

    tractable alternative for the control of service centers with non-stationary arrival rates.