The M/G/1 queue with instantaneous bernoulli feedback

Abstract

In this paper we are concerned with several random processes that occur in M/G/1 queues with instantaneous feedback in which the feedback decision process is a Bernoulli process. Queue length processes embedded at various times are studied. It is shown that these do not all have the same asymptotic distribution, and that in general none of the output, input, or feedback processes is renewal. These results have implications in the application of certain decomposition results to queueing networks.

Réseaux de files d'attente à forme produit

“…Disney et McNickle [16] montrent que ce processus n'est pas non plus un processus de renouvellement. 322 G. pujoiXE Takacs [14] montre que le processus des départs est un processus de Poisson.…”

“…Juste après un instant de rebouclage, la file est dans l'état i avec la probabilité stationnaire II (i -1) (voir Disney et McNickle [16] pour la démonstration de cette propriété).…”

A queue with a pair of instantaneous independent bernoulli feedback processes

“…For instance these systems occur in computer networks. Disney, McNickle and Simon [5] have studied several random processes that occur in M I C I 1 queues with instantaneous feedback in which the feedback decision process is a Bernoulli process. D'Avignon and Disney [Z] have also considered the same queue with state dependent feedback mechanism.…”

Some results on a generalized M/G/1 feedback queue with negative customers

“…The study of queueing models with Bernoulli feedback goes back to a classical paper by Takacs (1963). Further studies on the queue length, the total sojourn time and waiting time are provided by Disney et al (1980Disney et al ( , 1984. Fontana and Berzosa (1985) have extended some results obtained for the M/G/1 model with Bernoulli feedback to a more general feedback model with priorities.…”