Retrial queue

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

• two phase retrial queueing system with impatient customers, additional optional service, server breakdown, elayed repair and reserved time

Abstract: Single server retrial queue with general retrial time is considered. Customers may balk or renege at particular times. The server is subject to breakdowns with repairs. The repair is not immediate and it starts after a random amount of time. While the server is being repaired, the interrupted customer can either remains in the service position or leaves and return by maintaining its rights to the server. The probability generating function is employed to obtain joint distribution of the server state and queue length. The probability of an empty system, availability of the server, failure frequency and the mean number of customers in the retrial queue are derived.

Retrial Queue M/M/1 with Negative Calls Under Heavy Load Condition

Abstract: In the paper, the retrial queueing system of M/M/1 type with negative calls is considered. The system of Kolmogorov equations for the system states process is derived. The method of asymptotic analysis is proposed for the system solving under the heavy load condition. The theorem about the gamma form of the asymptotic characteristic function of the number of calls in the orbit is formulated and proved. During the study, the expression for the system throughput is obtained. Also the exact characteristic function is derived. Numerical examples of comparison asymptotic and exact distributions are presented. The conclusion about the asymptotic method application area is made.

Analysis of adiscrete- time single server retrial queue with general retrial times, multiple vacations and statedependent arrivals

Abstract: This paper analyses a discrete time Geo/G/1 retrial queuing system with general retrial times, multiple vacations and state dependent arrivals. Here the arrival rates are different when the system is idle and busy or on vacation. If the server is busy or on vacation at the arrival epoch, the customers joins the orbit to repeat the request later. On the other hand, if the server is idle, then the arriving customer begins its service immediately. The customers in the orbit try for service when the server is idle. At a service completion epoch, if the number of customers in the orbit is zero, the server goes for vacation repeatedly until at least one customer is found in the orbit. At a vacation completion epoch, if there is at least one customer found in the orbit, then the server remains idle in the system to render service for customers either from the main pool or from the retrial group. The primary arrival rate is p1when the server is idle and the primary arrival rate is p2 when the server is busy or on vacation (p1 > p2). The Steady state probabilities of the considered queueing system are analysed. Performance measures through the generating functions are obtained. Stochastic decompositionof thesystem size is obtained without vacation and the additional system size due to vacation. Numerical results with graphs are provided to study the performance measures of the system.

Numerical optimisation of loss system with retrial phenomenon in cellular networks

Abstract: In this study, we extend upon the model by Haring et al. (2001) by introducing retrial phenomenon in multi-server queueing system. When the most g number of guard channels are available, it allows new calls to join the retrial group. This retrial group is called orbit and can hold a maximum of m retrial calls. The impact of retrial over certain performance measures is numerically investigated. The focus of this work is to construct optimisation problems to determine the optimal number of channels, the optimal number of guard channels and the optimal orbit size. Further, it has been emphasised that the proposed model with retrial phenomenon reduces the blocking probability of new calls in the system.

The stationary analysis of a retrial queue with multiserver in n-limited capacity

Abstract: A retrial queueing system is described by an arriving customer, finds the server busy, joins the retrial group to try again for service after a random amount of time. Retrial queueing systems have been widely used to model many problems in modern telephone switching systems, computer and communication systems. For detailed survey one can see yang and Templeton (1987). Most papers assume that each orbiting customer seeks service independently of each other after a random time exponentially distributed with a fixed rate. Nevertheless, there are other queueing situations in which the retrial rate does not depend on the number of customers in the orbit. Some notable works in this directions are Fayolle (1986) and Martin and Artalejo (1995). Artalejo and Gomez-Corral (1997), in their paper incorporate both possibilities by assuming that time intervals between successive repeated attempts are exponentially distributed with parameter (1-0j)+j, when the orbit size is j.