An M/G/1 clearing queueing system with setup time and multiple vacations for an unreliable server

This paper studies an M/G/1 clearing queueing system with setup time and multiple vacations, in which all present customers in the system are served simultaneously and breakdowns may occur in busy or setup period. We investigate the stationary distribution of system size and the Laplace–Stieltjes transform of sojourn time. In addition, various performance measures are discussed, such as the mean system size at arbitrary time and the mean length of a vacation circle. Moreover, a cost analysis is carried out for this queueing system. Numerical results are presented to study the sensitivity of the system parameters on the expected cost function and system performances.     

Performance measures of M/G/1 retrial queues with recurrent customers,breakdowns, and general delays

In this paper, an M/G/1 retrial system with two classes of customers: transit and recurrent customers is studied. After service completion, recurrent customers always return to the orbit and transit customers leave the system forever. The server is subject to breakdowns and delayed repairs. The customer whose service is interrupted stays in the service, waiting for delay and repair of the server. After repair this customer completes his service. The study of the system concerns the joint generating function of the server state and the queue length in steady state. Some performance measures of the system are then derived and some numerical results are presented to illustrate the effect of the system parameters on the developed performance measures.     

The analysis of MX/M/1 queue with two-stage vacations policy

Abstract

In this article, we consider a batch arrival M^X/M/1 queue with two-stage vacations policy that comprises of single working vacation and multiple vacations, denoted by M^X/M/1/SWV?+?MV. Using the matrix analytic method, we derive the probability generating function (PGF) of the stationary system size and investigate the stochastic decomposition structure of stationary system size. Further, we obtain the Laplace–Stieltjes transform (LST) of stationary sojourn time of a customer by the first passage time analysis. At last, we illustrate the effects of various parameters on the performance measures numerically and graphically by some numerical examples.     

Analysis of a two incongruent arrivals and services M/G/1 queue with random feedback

A queuing system with two incongruent arrivals and services is considered. Two kinds of customers enter the system by Poisson process and the service times are assumed to have general distribution. After first kind service completion, it may feedback to repeat the first service, leave the system or go to give second service. The same policy is applied for the other kind of customer. All stochastic processes involved in this system are independent. We derive the probability generating function for each kind and for the system that yield the performance measures. Some numerical approaches examined the validity of the results.