Showing papers on "Retrial queue published in 1994"
TL;DR: An approximation method for the calculation of the steady-state queue size distribution is proposed and it is demonstrated through numerical results that the approximation works very well for models of practical interest.
63 citations
TL;DR: This paper studies a version of the retrial queue with variable service and obtains the analogue of the Pollaczek-Khintchine formula for such retrial queues, which is useful for operations researchers to obtain performance measures of interest.
Abstract: Retrial queues are useful in the stochastic modelling of computer and telecommunication systems amongst others. In this paper we study a version of the retrial queue with variable service. Such a point of view gives another look at the unreliable retrial queueing problem which includes the redundancy model.
56 citations
TL;DR: In this paper, the authors consider retrial queues with servers that are subject to active breakdowns and give an algorithm to compute the steady-state probabilities for the M/G/l retrial queue with breakdowns.
Abstract: We consider retrial queues with servers that are subject to active breakdowns. First, we concentrate on Markovian queueing models. For the multiserver case we obtain sufficient conditions for ergodicity. For the singleserver case we introduce new performance measures: the “orbit” idle period and the “orbit” busy period. Further, we investigate the asymptotic behaviour under high intensity of retrials. We also give an algorithm to compute the steady-state probabilities for the M/G/l retrial queue with breakdowns. The algorithm is based on a regenerative approach.
56 citations
TL;DR: It is demonstrated that a few well known queueing models are special cases of the present model and various interpretations of the stochastic decomposition law when applied to each of these special cases.
Abstract: In this paper, we study a retrial queueing model with the server subject to starting failures. We first present the necessary and sufficient condition for the system to be stable and derive analytical results for the queue length distribution as well as some performance measures of the system in steady state. We show that the general stochastic decomposition law forM/G/1 vacation models also holds for the present system. Finally, we demonstrate that a few well known queueing models are special cases of the present model and discuss various interpretations of the stochastic decomposition law when applied to each of these special cases.
49 citations
TL;DR: Information theoretic approximations for the M/G/1 queue with retrials are presented according to the available information about the service time probability density and the steady-state distribution of the system state.
Abstract: In this paper we present information theoretic approximations for theM/G/1 queue with retrials. Various approximations for this model are obtained according to the available information about the service time probability density and the steady-state distribution of the system state. The results are well-suited for numerical computation.
19 citations
TL;DR: The general theory of stochastic orderings is used to investigate the monotonicity properties of the system relative to the strong Stochastic ordering, convex ordering and Laplace ordering and results imply simple insensitive bounds for the stationary distribution of the number of customers in the system and the mean number ofcustomers served during a busy period.
12 citations