Retrial queue

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

Performance analysis of call center based on M/M/s/k+M retrial queue with feedback and negative customers

Abstract: The M/M/s/k+M retrial queuing models with negative customer arrival and abandon of wait with impatience in the ACD queuing are studied.The matrix geometrical method is used to obtain the analytic solution system stability index for the feedback queue model.A numerical example and some conclusions are given such as more customers can be served by using quicker service rate.

Asymptotic and Numerical Analysis of Multiserver Retrial Queue with Guard Channel for Cellular Networks

Abstract: This paper considers a retrial queueing model for a base station in cellular networks where fresh calls and handover calls are available. Fresh calls are initiated from the cell of the base station. On the other hand, a handover call has been connecting to a base station and moves to another one. In order to keep the continuation of the communication, it is desired that an available channel in the new base station is immediately assigned to the handover call. To this end, a channel is reserved as the guard channel for handover calls in base stations. Blocked fresh and handover calls join a virtual orbit and repeat their attempts in a later time. We assume that a base station can recognize retrial calls and give them the same priority as that of handover calls. We model a base station by a multiserver retrial queue with priority customers for which a level-dependent QBD process is formulated. We obtain Taylor series expansion for the nonzero elements of the rate matrices of the level-dependent QBD. Using the expansion results, we obtain an asymptotic upper bound for the joint stationary distribution of the number of busy channels and that of customers in the orbit. Furthermore, we derive an efficient numerical algorithm to calculate the joint stationary distribution.

The Simulation of Finite-Source Retrial Queueing Systems with Two-Way Communications to the Orbit and Blocking

Abstract: A two-way communication, retrial queueing system is considered with a single server which from time to time is subject to random breakdowns. The investigated model is a M/M/1//N type of system where the number of sources is finite. After the service unit becomes idle it is able to call in customers residing in the orbit (outgoing call or secondary customers). Distribution of the service time of primary and secondary customers is exponential with rates \(\mu _1\) and \(\mu _2\), respectively. Every used random variable is assumed to be totally independent of each other in the model. Each time the server becoming in faulty state the operation of the system is blocked resulting that throughout this period customers can not enter the system. The novelty of this analysis is to study the effect of blocking in such system on the main performance measures using different distributions of failure time. Results are illustrated graphically with the help of a simulation program developed by the authors.

A heuristic algorithm for the optimization of a retrial system with Bernoulli vacation

Abstract: In this study, we consider an M/M/c retrial queue with Bernoulli vacation under a single vacation policy. When an arrived customer finds a free server, the customer receives the service immediately; otherwise the customer would enter into an orbit. After the server completes the service, the server may go on a vacation or become idle (waiting for the next arriving, retrying customer). The retrial system is analysed as a quasi-birth-and-death process. The sufficient and necessary condition of system equilibrium is obtained. The formulae for computing the rate matrix and stationary probabilities are derived. The explicit close forms for system performance measures are developed. A cost model is constructed to determine the optimal values of the number of servers, service rate, and vacation rate for minimizing the total expected cost per unit time. Numerical examples are given to demonstrate this optimization approach. The effects of various parameters in the cost model on system performance are investigated.

The Two-Dimensional Output Process of Retrial Queue with Two-Way Communication

Abstract: In this paper, we review a two-dimensional output process of the system with repeated calls and called applications. In a system with repeated calls, incoming applications, which found serving unit busy, move to the source of repeated calls, where carry out random exponentially distributed delay, after which try to receive serving again. While serving unit is free, it can call applications itself with exponentially distributed intensity, which will serve with their serving time parameter. This feature characterises a system as one with called applications. An asymptotic approximation of the two-dimensional characteristic function is obtained under the condition of a large delay of applications in the orbit. Using integral transformations, the asymptotic two-dimensional distribution of the probabilities of the number of applications of different types that have finished serving in the system is found. A numerical analysis of the values of the correlation coefficient of the components of the considered two-dimensional output is carried out.