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We consider the problem of service rate control of a single server queueingsystem with a finite-state Markov-modulated Poisson arrival process. We showthat the optimal service rate is non-decreasing in the number of customers inthe system; higher congestion rates warrant higher service rates. On thecontrary, however, we show that the optimal service rate is not necessarilymonotone in the current arrival rate. If the modulating process satisfies astochastic monotonicity property the monotonicity is recovered. We examineseveral heuristics and show where heuristics are reasonable substitutes for theoptimal control. None of the heuristics perform well in all the regimes.Secondly, we discuss when the Markov-modulated Poisson process with servicerate control can act as a heuristic itself to approximate the control of asystem with a periodic non-homogeneous Poisson arrival process. Not only is thecurrent model of interest in the control of Internet or mobile networks withbursty traffic, but it is also useful in providing a tractable alternative forthe control of service centers with non-stationary arrival rates.

Dynamic Service Rate Control for a Single Server Queue with Markov Modulated Arrivals