Efficient simulation of tail probabilities in a queueing model with heterogeneous servers

This paper considers a multi-server queue with Markov-modulated Poisson input and server-dependent phase-type service times. We develop an efficient rare-event simulation technique to estimate the probability that the number of customers in this system reaches a high value. Relying on explicit bounds on the probability under consideration as well as the associated likelihood ratio, we succeed in proving that the proposed estimator is of bounded relative error. Simulation experiments illustrate the significant speed-up that can be achieved by the proposed algorithm.     

Transient analysis of a finite source discrete-time queueing system using homogeneous Markov system with state size capacities (HMS/c)

Abstract

In this article, a finite source discrete-time queueing system is modeled as a discrete-time homogeneous Markov system with finite state size capacities (HMS/c) and transition priorities. This Markov system is comprised of three states. The first state of the HMS/c corresponds to the source and the second one to the state with the servers. The second state has a finite capacity which corresponds to the number of servers. The members of the system which can not enter the second state, due to its finite capacity, enter the third state which represents the system's queue. In order to examine the variability of the state sizes recursive formulae for their factorial and mixed factorial moments are derived in matrix form. As a consequence the probability mass function of each state size can be evaluated. Also the expected time in queue is computed by means of the interval transition probabilities. The theoretical results are illustrated by a numerical example.     

A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy

This paper deals with a single server Poisson arrival queue with two phases of heterogeneous service along with a Bernoulli schedule vacation model, where after two successive phases service the server either goes for a vacation with probability p (0≤p≤1) or may continue to serve the next unit, if any, with probability q(=1−p). Further the concept of multiple vacation policy is also introduced here. We obtained the queue size distributions at a departure epoch and at a random epoch, Laplace Stieltjes Transform of the waiting time distribution and busy period distribution along with some mean performance measures. Finally we discuss some statistical inference related issues.     

A geometric process repair model for a cold standby repairable system with imperfect delay repair and priority in use

In this article, a two-dissimilar-component cold standby repairable system with one repairman is studied. Assume that the repair after failure for each component is delayed or undelayed. Component 2 after repair is “as good as new” while Component 1 after repair is not, but Component 1 has priority in use. Under these assumptions, using a geometric process, we consider a replacement policy N based on the failure number of Component 1. An optimal replacement policy N* is determined by minimizing the average cost rate C(N) of the system. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.