Retrial queue

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

Matrix analytic methods for a multi-server retrial queue with buffer

Abstract: We present numerical methods for obtaining the stationary distribution of states for multi-server retrial queues with Markovian arrival process, phase type service time distribution with two states and finite buffer; and moments of the waiting time. The methods are direct extensions of the ones for the single server retrial queues earlier developed by the authors. The queue is modelled as a level dependent Markov process and the generator for the process is approximated with one which is spacially homogeneous above some levelN. The levelN is chosen such that the probability associated with the homogeneous part of the approximated system is bounded by a small tolerance and the generator is eventually truncated above that level. Solutions are obtained by efficient application of block Gaussian elimination.

Unreliable MX/G/1 retrial queue with multi-optional services and impatient customers

Abstract: The present investigation deals with Mx/G/1 retrial queue with unreliable server and general retrial times. The server is subject to breakdowns and takes some setup time before starting the repair. The server renders first essential phase of service (FES) to all the arriving customers whereas second optional phase services (SOS) are provided after FES to only those customers who opt for it. The impatient customers are allowed to balk depending upon server’s status; they may also renege after waiting sometime in the queue. By incorporating the supplementary variables corresponding to service time, repair time, retrial time and setup time and then using generating function method, the queueing analysis has been done to obtain the queue size and orbit size distributions, and some other queueing as well as reliability measures. The effects of several parameters on the system performance are examined numerically by taking an illustration.

Analysis of a single-server retrial queue with quasi-random input and nonpreemptive priority☆

Abstract: In this paper, we model a single-server retrial queue with quasi-random input and two priority classes. In the case of blocking, a high priority unit is queued, whereas a low priority unit joins the orbit to start generating a Poisson flow of repeated attempts until it finds the server free. Since units in orbit will be served only when the high priority queue is empty, high priority units have nonpreemptive priority over low priority units. We present a simple analysis for the outside observer distribution of the system state as well as for the arriving unit distribution in steady state. Besides, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.

An m/g/1 retrial queue with unreliable server for streaming multimedia applications

Abstract: As a model for streaming multimedia applications, we study an unreliable retrial queue with infinite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable. Customers join the retrial orbit if and only if their service is interrupted by a server failure. Interrupted customers do not rejoin the normal queue but repeatedly attempt to access the server at independent and identically distributed intervals until it is found functioning and idle. We provide stability conditions, queue length distributions, stochastic decomposition results, and performance measures. The joint optimization of the retrial and server repair rates is also studied.

The M/G/1 retrial queue with nonpersistent customers

Abstract: We consider anM/G/1 retrial queue in which blocked customers may leave the system forever without service. Basic equations concerning the system in steady state are established in terms of generating functions. An indirect method (the method of moments) is applied to solve the basic equations and expressions for related factorial moments, steady-state probabilities and other system performance measures are derived in terms of server utilization. A numerical algorithm is then developed for the calculation of the server utilization and some numerical results are presented.