2013/07/09 by Ravi Kumar, Kumar, Ravi, Mark Edward Lewis +3 · 1 citation
Business, Management and Accounting · Computer Science · Engineering · #90-XX #90C40 #Advanced Queuing Theory Analysis #Advanced Wireless Network Optimization #FOS: Mathematics #Network Traffic and Congestion Control #Optimization and Control (math.OC) #Wireless Communication Networks Research
paper · pdf · doi:10.48550/arxiv.1307.2601
openalex publication_date 2013/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of service rate control of a single server queueing\nsystem with a finite-state Markov-modulated Poisson arrival process. We show\nthat the optimal service rate is non-decreasing in the number of customers in\nthe system; higher congestion rates warrant higher service rates. On the\ncontrary, however, we show that the optimal service rate is not necessarily\nmonotone in the current arrival rate. If the modulating process satisfies a\nstochastic monotonicity property the monotonicity is recovered. We examine\nseveral heuristics and show where heuristics are reasonable substitutes for the\noptimal control. None of the heuristics perform well in all the regimes.\nSecondly, we discuss when the Markov-modulated Poisson process with service\nrate control can act as a heuristic itself to approximate the control of a\nsystem with a periodic non-homogeneous Poisson arrival process. Not only is the\ncurrent model of interest in the control of Internet or mobile networks with\nbursty traffic, but it is also useful in providing a tractable alternative for\nthe control of service centers with non-stationary arrival rates.\n