Showing papers on "Retrial queue published in 2004"

A Discrete-Time Geo /G/1 Retrial Queue with General Retrial Times

Abstract: We consider a discrete-time Geo/G/1 retrial queue in which the retrial time has a general distribution and the server, after each service completion, begins a process of search in order to find the following customer to be served. We study the Markov chain underlying the considered queueing system and its ergodicity condition. We find the generating function of the number of customers in the orbit and in the system. We derive the stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions for our queueing system and its corresponding standard system. Also, we develop recursive formulae for calculating the steady-state distribution of the orbit and system sizes. Besides, we prove that the M/G/1 retrial queue with general retrial times can be approximated by our corresponding discrete-time system. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.

Discrete-time Geo[X]/GH/1 retrial queue with Bernoulli feedback

Abstract: Hreceive a service of type h (h = 1, ..., H) with probability qh, where ~h=l qh 1. We study the Markov chain underlying the considered queueing system and the ergodicity condition too. We find the generating function of the number of calls in the orbit and in the system. We derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions for our queueing system and its corresponding standard system. In the special case of individual arrivals, we develop recursive formulae for calculating the steady-state distribution of the orbit size. Besides, we prove that the MIX]/Gig~1 retrial queue with Bernoulli feedback can be approximated by our corresponding discrete-time system. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics. (~) 2004 Elsevier Ltd. All rights reserved.

On the single server retrial queue with batch arrivals

Abstract: We consider a single server retrial queue with batch arrivals which operates under the so-called linear retrial discipline. In addition, each individual customer is subject to a control admission policy upon arrival. Thismodel generalizes the classical M/G/1 retrial policy with arrivals in batches. We carry out an extensive analysis of the system, including existence of the stationary regime, embedded Markov chain, stochastic decomposition and calculation of the first moments.

Heterogeneous finite-source retrial queues

Abstract: In this paper we investigate a single server retrial queue with a finite number of heterogeneous sources of calls. It is assumed when a given source is idle it will generate a primary call after an exponentially distributed time. If the server is free at the time of the request’ s arrival then the call starts to be served. The service time is also exponentially distributed. During the service time the source cannot generate a new primary call. After service the source moves into free state and can generate a new call again. If the server is busy at the time of the arrival of a primary call, then the source starts generating so called repeated calls with exponentially distributed times until it finds the server free. As before, after service the source becomes free and can generate a new primary call again. We assume that the primary calls, repeated attempts and service times are mutually independent. This queueing system and its variants could be used to model magnetic disk memory systems, local area networks with CSMA/CD protocols and collision avoidance local area networks. The novelty of this model is the heterogeneity of the calls, which means that each call is characterized by its own arrival, repeated and service rates. The aim of the paper is to give the usual steady-state performance measures of the system. To do so, an efficient software tool, MOSEL ( Modeling, Specification and Evaluation Language ) developed at the University of Erlangen, Germany, is used to formulate and solve the problem. Several sample numerical results illustrate the power of the tool showing the effect of different parameters on the system measures.

A retrial queueing system with two types of calls and geometric loss

Abstract: A retrial queueing system with two types of calls are considered. Type I calls arrive in a batch of size k with probability c k and type II calls arrive singly according to Poisson processes with rates λ 1 c and λ 2 . Service time distributions are independent and identically distributed and are different for both types of calls. If arriving calls are blocked due to server being busy, type I calls are queued in a priority queue of infinite capacity whereas type II calls are entered into the retrial group in order to seek service again after a random amount of time. For this system the joint distribution of the number of calls in the priority queue and in the retrial group in closed form is obtained. The operating characteristics and numerical results are also presented.

Mixed loss and delay retrial queueing system with two classes of customers

Abstract: This paper is concerned with the analysis of a single-server batch arrival retrial queue with two classes of customers. In the case of blocking, the class-1 customers leave the system forever whereas the class-2 customers leave the service area and enter the orbit and wait to be served later. The necessary and sufficient condition for the system to be stable is derived and analytic results for the queue length distribution as well as some per-formance measures of the system under steady state condition are obtained. A general decomposition law for the retrial queueing system is established.