Retrial queue

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

Optimum alternatives of tandem G/G/K queues with disaster customers and retrial phenomenon: interactive voice response systems

Abstract: In this paper, we study a tandem queue with retrials where the queue experiences disasters. The probability of system failure depends on the strength of equipment, which makes servers idle and causes the removal of all customers in queues and service areas at once. The customers in the queue are forced to orbit in a retrial queue during the system failure where they decide whether or not to come back to the system. Reducing the disaster arrival rate (the probability of system failure) by employing more servers and reducing the number of lost customers is very costly. Moreover, it is important to service the customers with no interruption and reduce the time in system. The developed scenarios are compared in five dimensions including time in system, cost of lost customer, operator cost, the number of uninterrupted service customers and cost of reducing disaster arrival rate (or empowering system cost). The scenarios are modeled by computer simulation. Then, the optimal scenario is chosen using data envelopment analysis. The optimal scenario maximizes system efficiency in terms of disaster arrival rate, cost of lost customers and the number of satisfied customers. In the main problem, the disasters arrive at the system according to Poisson process; the effect of changing the distribution function of disaster arrival has been investigated finally. We are among the first ones to study and optimize G/G/K tandem queuing systems with system failures and retrial phenomena in interactive voice response systems.

An M/G/1 retrial queue with single working vacation under Bernoulli schedule

Abstract: In this paper, an M/G/1 retrial queue with general retrial times and single working vacation is considered. We assume that the customers who find the server busy are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline and only the customer at the head of the queue is allowed access to the server. During the normal period, if the orbit queue is not empty at a service completion instant, the server begins a working vacation with specified probability q (0 ≤ q ≤ 1), and with probability 1 − q , he waits for serving the next customer. During the working vacation period, customers can be served at a lower service rate. We first present the necessary and sufficient condition for the system to be stable. Using the supplementary variable method, we deal with the generating functions of the server state and the number of customers in the orbit. Various interesting performance measures are also derived. Finally, some numerical examples and cost optimization analysis are presented.

Analysis of a preemptive priority retrial queue with negative customers, starting failure and at most J vacations

Abstract: An analysis of single server preemptive priority retrial queue with at most J vacations where two types of customers called (priority customers and ordinary customers) are considered in this paper The priority customers do not have queue and they have higher priority to receive their services over ordinary customers If negative customer is arriving during the service time of any positive customer (priority customer or ordinary customer), it will remove the positive customer from the service If the interrupted customer is an ordinary customer, he may join the orbit and the priority customer will leave the system As soon as the system is empty, the server takes at most J vacations The probability generating functions for the system/orbit size in steady state is obtained using supplementary variable method Some important system measures and the stochastic decomposition are discussed Numerical examples are presented to picturise the effect of parameters on system performance measures

Two-Way Communication M/M/1/1 Queue with Server-Orbit Interaction and Feedback of Outgoing Retrial Calls

Abstract: The paper deals with two-way communication M/M/1/1 retrial queue where the server during its idle time makes outgoing calls of two types - to the customers in orbit and to the customers outside it. Durations of these calls follow two distinct exponential distributions. After completion of the outgoing call to a customer from orbit, this customer with probability p rejoins the orbit, and with its complementary probability leaves the service area. Using generating functions approach we derive explicit and recursive formulas for the stationary system state distribution and its factorial moments.

Performance analysis of a batch arrival retrial queue with Bernoulli feedback

Abstract: This paper facilitates the performance prediction of an M X /G/1 retrial queue wherein the single server follows a modified vacation policy . We assume that the job who finds the server busy joins the retrial group (orbit) to get its service in random order and only the job at the head of the queue is allowed to receive service from the server first. As soon as the system becomes empty, the server leaves for at most J vacations of random length V each. When the server returns from the vacation and finds at least one job in the orbit, it renders service to these jobs otherwise it goes for next vacation. We assume that the service time, retrial time and vacation times are general distributed. The balking behaviour of the jobs is also taken into consideration. By using supplementary variable technique, we derive the formulas for system size distribution and mean system size at departure points and other performance measures. Numerical illustrations have been provided to validate the analytical results. In addition, by setting appropriate parameters, some special cases are deduced which tally with existing results. Tables and figures have been facilitated to examine the system behaviour with regard to different parameters.