Optimal control of arrivals to multiserver queues in a random environment

Abstract

We study the problem of optimal customer admission to multiserver queues. These queues are assumed to live in an extraneous environment which changes in a semi-Markovian way. Arrivals, service mechanism and random reward/cost structure may all depend on these surroundings. Included as special cases are SM/M/c queues, in particular G/M/c queues, in a random environment. By a direct inductive approach we establish optimality of a generalized control-limit rule depending on the actual environment. Particular emphasis is laid on different applications that show the versatility of the proposed setup.

Generalized product-form stationary distributions for Markov chains in random environments with queueing applications

“…Hambly (1992)), mathematical programming (e.g. Helm and Waldmann (1984) and Posner and Zuckerman (1990)), and queueing theory (see below). The majority of such models in the applied probability literature are described by Markov processes evolving in a random environment.…”

Distribution sensitivity in a highway flow model

“…This does not fit a model of traffic flow subject to random incidents; such a model is commonly called a 'random environment' model. Queues in random environments are discussed in, for example, [9][10][11][12][13][14][15][16][17][18], though almost all of these are for the single-server case.…”

Access control of parallel multiserver loss queues

“…Although there is a rich literature on control of single multiserver queues (see e.g. [14][24] [35] [36]), again there are very few results either on control of networks of more than two queues or on control of networks of loss queues.…”