Retrial queue

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

Analysis of Retrial Queueing System M/G/1 with Impatient Customers, Collisions and Unreliable Server Using Simulation

Abstract: In this paper, we consider a retrial queueing system of M/G/1 type with an unreliable server, collisions, and impatient customers. The novelty of our work is to carry out a sensitivity analysis applying different distributions of service time of customers on significant performance measures for example on the probability of abandonment, the mean waiting time of an arbitrary, successfully served, impatient customer, etc. A customer is able to depart from the system in the orbit if it does not get its appropriate service after a definite random waiting time so these will be the so-called impatient customers. In the case of server failure, requests are allowed to enter the system but these will be forwarded immediately towards the orbit. The service, retrial, impatience, operation, and repair times are supposed to be independent of each other. Several graphical illustrations demonstrate the comparisons of the investigated distributions and the interesting phenomena which are obtained by our self-developed simulation program. The achieved results are compared to the results of the [2] to check how the system characteristics changes if we use other distributions of service time and to present the advantages of performing simulations in certain scenarios.

Analysis on preemptive priority retrial queue with two types of customers, balking, optional re-service, single vacation and service interruption

Abstract: This paper concerned with performance analysis of single server preemptive priority retrial queue with a single vacation where two types of customers are considered and they are called priority customers and ordinary customers. The ordinary customers arrive in batch into the system. The priority customers do not form any queue. After the completion of regular service, the customers may demand re-service for the previous service without joining the orbit or may leave the system. As soon as the system is empty, the server goes for vacation and the regular busy server can be subjected to breakdown. By using the supplementary variable technique, we obtain the steady-state probability generating functions for the system/orbit size. Some important system performance measures and the stochastic decomposition are discussed. Finally, numerical examples are presented to visualize the effect of parameters on system performance measures.

An Analysis of the M/G/1 Retrial Queue with Negative Arrivals using a Martingale Technique*

Abstract: We consider the M/G/1 retrial queue with negative arrivals. Using the technique of Baccelli and Makowski (1985, 1989) we define a martingale with respect to an embedded process. Using this, an analysis of the stationary behavior of the queue is possible.

The State-Dependent M/G/1 Queue with Orbit: Analysis and Strategic Customer Behavior

Abstract: We consider a state-dependent single server queue with orbit. This is a versatile model for the study of service systems, where the server needs a non-negligible time to retrieve waiting customers every time he completes a service. This situation arises typically when the customers are not physically present at a system, but they have a remote access to it, as in a call center station, a communication node etc. We introduce a probabilistic approach for the performance evaluation of this queueing system, that we refer to as the Queueing Markov Chain Decomposition approach. Then, we use the results to characterize and compute the equilibrium strategies for the customers' joining/balking dilemma under a natural reward-cost structure. Finally, we discuss the applicability of the Queueing Markov Chain Decomposition approach for the performance evaluation and strategic analysis of general non-Markovian service systems.