Retrial queue

About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.

Analysis of Customer-Induced Interruption and Retrial of Interrupted Customers

Abstract: SYNOPTIC ABSTRACTWe consider a single-server retrial queue with infinite capacity of the primary buffer and finite capacity of the orbit to which customers arrive according to a Poisson process, and the service time follows phase-type distribution. The customer-induced interruption while in service occurs according to a Poisson, process. The self-interrupted customers enter into orbit. Any interrupted customer, finding the orbit full, is considered lost. The interrupted customers retries for service after the interruption is completed. We investigate the behavior of this queueing system. Several performance measures are evaluated. Numerical illustrations of the system behavior are also provided.

A discrete-time Geo X /G/1 retrial queueing system with starting failures and optional service

Abstract: This paper is concerned with the analysis of a single-server batch arrival retrial queue with starting failures in discrete time in which all the arriving customers need essential service (ES) necessarily whereas only some may require the optional service (OS) after ES. The customers are assumed to arrive at the system according to a geometric process during the consecutive slots. The service times and retrial times are generally distributed. The generating functions of the number of customers in the retrial group and in the system are obtained along with the marginal distributions of the number of customers in the retrial group when the server is idle, busy (in providing ES or OS) or broken down. The explicit formulae for the stationary distribution and other performance measures at equilibrium are obtained. Some special cases are deduced by setting appropriate parameters. The stochastic decomposition property has also been discussed. The numerical examples are facilitated to explore the effect of different parameters on various performance measures.

Dynamic scheduling of a single-server two-class queue with constant retrial policy

Abstract: We analyze the non-preemptive assignment of a single server to two infinite-capacity retrial queues. Customers arrive at both queues according to Poisson processes. They are served on first-come-first-served basis following a cost-optimal routing policy. The customer at the head of a queue generates a Poisson stream of repeated requests for service, that is, we have a constant retrial policy. All service times are exponential, with rates depending on the queues. The costs to be minimized consist of costs per unit time that a customer spends in the system. In case of a scheduling problem that arise when no new customers arrive an explicit condition for server allocation to the first or the second queue is given. The condition presented covers all possible parameter choices. For scheduling that also considers new arrivals, we present the conditions under which server assignment to either queue 1 or queue 2 is cost-optimal.