Jesus R. Artalejo

Accessible bibliography on retrial queues: Progress in 2000-2009

In this work, we present a bibliography on retrial queues which updates the bibliography published in this journal in Artalejo (1999) [7]. The bibliography is focused on the progress made during the last decade 2000-2009. For the sake of completeness, a few papers published in 1999, and non-cited in Artalejo (1999) [7], have also been included. To keep the length manageable we have excluded conference proceedings, theses, unpublished reports, and works in languages other than English. The bibliography is structured in the following way: Section 1 lists the recent specific book (Artalejo and Gomez-Corral (2008)) [1] and other monographs including any chapter or section devoted to retrial queues. Section 2 lists survey papers and bibliographic works. Section 3 lists papers published in scientific journals. Section 4 includes a few forthcoming papers already in press. The author hopes that this bibliography could be of help to anyone contemplating research on retrial queues.

G-networks: A versatile approach for work removal in queueing networks

Abstract G-networks (or queueing networks with negative customers, signals, triggers, etc.) are characterized by the following feature: in contrast with the normal positive customers, negative customers arriving to a non-empty queue remove an amount of work from the queue. In its simplest version, a negative customer deletes an ordinary positive customer according to some strategy. Extensions of the model result when a negative customer removes a random batch of customers, all the work from the queue or indeed a random amount of work that does not necessarily correspond to an integer number of positive customers. Since Gelenbe (E. Gelenbe, Neural Computation 1 (1989) 502–510; E. Gelenbe, Journal of Applied Probability 28 (1991) 656–663) introduced the notion of negative customers, there has been an increasing interest not only in queueing networks but also in the single server node case. Significant progress in the analysis of this versatile class of networks has enriched queueing theory as well as contributed to the development of real applications in fields such as computers, communications and manufacturing. This paper presents a survey of the main results and methods of the theory of G-networks.

On the single server retrial queue subject to breakdowns

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 [1] and Kulkarni and Choi [15]. 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.

Analysis of an M/G/1 queue with constant repeated attempts and server vacations

We consider an M/G/1 queue with repeated attempts in which the server operates under a general exhaustive service vacation policy. We develop a comprehensive analysis of the system including ergodicity, limiting behaviour, stochastic decomposition and optimal control. We would like to point out that the system size distribution decomposes into three random variables which are respectively associated with the vacation time, the retrial policy and the ordinary M/G/1 queue without vacations and repeated attempts.

Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue

We are concerned with the main multiserver retrial queue of M/M/c type with exponential repeated attempts. It is known that an analytical solution of this queueing model is difficult and does not lead to numerical implementation. Based on appropriate understanding of the physical behavior, an efficient and numerically stable algorithm for computing the stationary distribution of the system state is developed. Numerical calculations are done to compare our approach with the existing approximations.

On the single server retrial queue with priority customers

We consider anM2/G2/1 type queueing system which serves two types of calls. In the case of blocking the first type customers can be queued whereas the second type customers must leave the service area but return after some random period of time to try their luck again. This model is a natural generalization of the classicM2/G2/1 priority queue with the head-of-theline priority discipline and the classicM/G/1 retrial queue. We carry out an extensive analysis of the system, including existence of the stationary regime, embedded Markov chain, stochastic decomposition, limit theorems under high and low rates of retrials and heavy traffic analysis.

A finite source retrial queue

This paper deals with a single-server retrial queue with a finite number of sources. Our analysis extends previous work on this topic and includes the analysis of the arriving customers distribution, the busy period and the waiting time process. This queuing system and its variants are widely used to model magnetic disk memory systems, star-like local area networks and other communication systems.

Stochastic Decomposition for Retrial Queues

SummaryThis paper deals with the stochastic decomposition property for retrial queues. This property is connected with similar results for vacation models. As applications, the moments of the number of customers in orbit and the rate of convergence under high retrial intensity can be obtained.

Analysis of Markov Multiserver Retrial Queues with Negative Arrivals

Negative arrivals are used as a control mechanism in many telecommunication and computer networks. In the paper we analyze multiserver retrial queues; i.e., any customer finding all servers busy upon arrival must leave the service area and re-apply for service after some random time. The control mechanism is such that, whenever the service facility is full occupied, an exponential timer is activated. If the timer expires and the service facility remains full, then a random batch of customers, which are stored at the retrial pool, are automatically removed. This model extends the existing literature, which only deals with a single server case and individual removals. Two different approaches are considered. For the stable case, the matrix–analytic formalism is used to study the joint distribution of the service facility and the retrial pool. The approximation by more simple infinite retrial model is also proved. In the overloading case we study the transient behaviour of the trajectory of the suitably normalized retrial queue and the long-run behaviour of the number of busy servers. The method of investigation in this case is based on the averaging principle for switching processes.

Steady State Analysis of an M/G/1 Queue with Repeated Attempts and Two-Phase Service

Abstract This paper examines the steady state behavior of an M/G/1 queue with repeated attempts in which the server may provide an additional second phase of service. This model generalizes both the classical M/G/1 retrial queue and the M/G/1 queue with classical waiting line and second optional service. We carry out an extensive stationary analysis of the system, including existence of stationary regime, embedded Markov chain, steady state distribution of the server state and the number of customers in the retrial group, stochastic decomposition and calculation of the first moments.