Showing papers on "Retrial queue published in 1998"
Book•
01 Jun 1998132 citations
TL;DR: This paper introduces the concept of fundamental server period and an auxiliary queueing system with breakdowns and option for leaving the system, and obtains simplified expressions for the partial generating functions of the server state and the number of customers in the retrial group.
Abstract: This paper deals with a single server retrial queueing system subject to active and independent breakdowns. The objective is to extend the results given independently by Aissani l1r and Kulkarni and Choi l15r. To this end, we introduce the concept of fundamental server period and an auxiliary queueing system with breakdowns and option for leaving the system. Then, we concentrate our attention on the limiting distribution of the system state. We obtain simplified expressions for the partial generating functions of the server state and the number of customers in the retrial group, a recursive scheme for computing the limiting probabilities and closed-form formulae for the second order partial moments. Some stochastic decomposition results are also investigated.
108 citations
TL;DR: This analysis extends previous work and includes the analysis of the arriving customer's distribution, the busy period and the waiting time process of the single-server retrial queue with a finite number of sources.
93 citations
TL;DR: In this paper, the authors considered M / M / c retrial queues with geometric loss and feedback when c = 1, 2 and found the joint generating function of the number of busy servers and the queue length by solving Kummer differential equation for 1, and by the method of series solution for 1 2.
Abstract: We consider M / M / c retrial queues with geometric loss and feedback when c = 1,2. We find the joint generating function of the number of busy servers and the queue length by solving Kummer differential equation for c = 1, and by the method of series solution for c = 1,2.
57 citations
TL;DR: It is shown that a stochastic decomposition law holds for the retrial queues under study and recursive formulas developed can be used to compute the marginal steady state probabilities of numbers of customers in the priority and non-priority groups for this case.
43 citations
TL;DR: In this article, a sufficient condition for ergodicity and a numerical method for obtaining the stationary distribution of states and the distribution and moments of the waiting time were derived for the MAP/PH/1 retrial queue.
Abstract: We consider the MAP/PH/1 retrial queue. We obtain a sufficient condition for ergodicity and derive a numerical method for obtaining the stationary distribution of states and the distribution and moments of the waiting time. We derive a method for obtaining a bound on probability lost due to truncation when the service time distribution is a member of a certain class by considering approximations which stochastically dominate the exact queue
37 citations
01 May 1998
TL;DR: An algorithm to find an approximation for the stationary distribution for the general ergodic spatially-inhomogeneous block-partitioned upper Hessenberg form is presented and the numerical results suggest that the method is superior to the ordinary finite-truncation method.
Abstract: We present an algorithm to find an approximation for the stationary distribution for the general ergodic spatially-inhomogeneous block-partitioned upper Hessenberg form. Our approximation makes use of an associated upper block-Hessenberg matrix which is spatially homogeneous except for a finite number of blocks. We treat theMAP/G/1 retrial queue and the retrial queue with two types of customer as specific instances and give some numerical examples. The numerical results suggest that our method is superior to the ordinary finite-truncation method.
12 citations
TL;DR: In this paper, a new Markovian description of the M/G/1 retrial queue was proposed, where M(t) is the total number of arrivals from the last departure until time t and N(t is the number of customers in orbit at time t. They used this process to get an estimator of the parameter of retrial and its variance by solving linear differential equations.
5 citations
Journal Article•
TL;DR: In this article, an M, M/G/1/K retrial queueing system with a finite priority queue for type I calls and infinite retrial group for type II calls was considered.
Abstract: We consider an M, M/G/1/ K retrial queueing system with a finite priority queue for type I calls and infinite retrial group for type II calls where blocked type I calls may join the retrial group. These models, for example, can be applied to cellular mobile communication system where handoff calls have higher priority than originating calls. In this paper we apply the supplementary variable method where supplementary variable is the elapsed service time of the call in service. We find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form and give some performance measures of the system.
2 citations