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Waiting time distributions for M/M/N processor sharing queues

1994; Taylor & Francis; Volume: 10; Issue: 3 Linguagem: Inglês

10.1080/15326349408807309

2332-4058

Jens Braband,

Advanced Wireless Network Optimization

Abstract We consider a multiple server queue in which arrivals form a Poisson process and each customer's service demand is exponentially distributed. The servers work according to the processor sharing discipline. If there are fewer customers than servers in the system, each customer is served by a single processor, the other servers remaining idle. Otherwise each customer's demand is reduced in proportion to the total service capacity. We calculate implicit representations for the Laplace–Stieltjes transform of conditioned waiting time distributions. In particular we compute the mean and variance of the waiting time of a tagged customer conditioned on the number of customers in the system and the corresponding moments of the equilibrium waiting time. Numerical results are presented †The author's present address is Siemens AG, Bereich Verkehrstechnik, Ackerstrabe 22, D-38126 Braunschweig †The author's present address is Siemens AG, Bereich Verkehrstechnik, Ackerstrabe 22, D-38126 Braunschweig Notes †The author's present address is Siemens AG, Bereich Verkehrstechnik, Ackerstrabe 22, D-38126 Braunschweig