Retrial queue

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

A discrete-time retrial queueing system with starting failures, Bernoulli feedback and general retrial times

Abstract: It is well known that discrete-time queues are more appropiate than their continuous-time counterparts for modelling computer and telecommunication systems. We present a discrete-time Geo/G/1 retrial queue with general retrial times, Bernoulli feedback and the server subjected to starting failures. We gene- ralize the previous works in discrete{time retrial queue with unrealiable server due to starting failures in the sense that we consider general service and ge- neral retrial times. Also we consider the realistic phenomenon of feedback. We analyse the Markov chain underlying the considered queueing system and pre- sent some performance measures of the system in steady-state. We provide two stochastic decomposition laws. Besides, we prove that the M/G/1 retrial queue with feedback and starting failures can be approximated by our corresponding discrete-time system. Some numerical results are given to illustrate the impact of the unreability and the feedback on the performance of the syste

The M/G/1 retrial queue: An information theoretic approach

Abstract: In this paper, we give a survey of the use of information theoretic techniques for the estimation of the main performance characteristics of the M/G/1 retrial queue. We focus on the limiting distribution of the system state, the length of a busy period and the waiting time. Numerical examples are given to illustrate the accuracy of the maximum entropy estimations when they are compared versus the classical solutions.

Analysis of a Retrial Queue With Two-Type Breakdowns and Delayed Repairs

Abstract: This article studies an M/G/1 retrial queue with two types of breakdowns. When the server is idle, it is subject to breakdowns according to a Poisson process with rate $\delta $ and it cannot be repaired immediately. While when the server is busy, it may break down according to a Poisson process with rate $\theta $ and can be immediately repaired. Firstly, based on embedded Markov chain technique and probability generating function (PGF) method, we present the necessary and sufficient condition for the system to be stable and the PGF of the orbit size at the departure epochs. Secondly, we give the steady-state joint queue length distribution by supplementary variable method, and present some important performance measures and reliability indices. Thirdly, we provide the analysis of sojourn time of an arbitrary customer in the system when the system is in stable state. Finally, some numerical examples are presented to illustrate the effect of the some system parameters on important performance measures and reliability indices.

A retrial queueing system with two types of calls and geometric loss

Abstract: A retrial queueing system with two types of calls are considered. Type I calls arrive in a batch of size k with probability c k and type II calls arrive singly according to Poisson processes with rates λ 1 c and λ 2 . Service time distributions are independent and identically distributed and are different for both types of calls. If arriving calls are blocked due to server being busy, type I calls are queued in a priority queue of infinite capacity whereas type II calls are entered into the retrial group in order to seek service again after a random amount of time. For this system the joint distribution of the number of calls in the priority queue and in the retrial group in closed form is obtained. The operating characteristics and numerical results are also presented.