Non-Markovian Queueing System, Mx/G/1 with Server Breakdown and Repair Times

This paper deals with the steady state behavior of an MX/G/1 queue with breakdown. It assumed that customers arrive to the system in batches of variable size, but serve one by one. The main new assumption in this paper is that the repair process does not start immediately after a breakdown and there is a delay time waiting for repairs to start. We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average waiting time in the queue

M (X)/G/1 WITH TWO PHASE OF HETEROGENEOUS SERVICE UNDER DIFFERENT VACATION POLICY , RESTRICTED ADMISSIBILITY AND SET UP

In this paper, we consider a batch arrival queueing system with two stage of heterogeneous service with different vacation policy subject to Restricted admissibility  and set up time is considered. Customers arrive in batches according to compound Poisson process with rate  and are served one by one in FIFO basis. After first-stage service the server must provide the second stage service. The service times of two phase of heterogenous services follow arbitrary (general) distribution with different vacation policies. Before providing service to a new customer or a batch of customers that joins the system in the renewed busy period, the server enters into a setup time process such that setup time follows exponential distribution. In addition we assume restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times . The probability generating function for the number of customers in the queue is found using the supplementary variable technique. The mean number of customers in the queue and the system are also found

AN M[X]/G/1M^{[X]}/G/1 QUEUE WITH OPTIONAL SERVICE AND WORKING BREAKDOWN

In this study, a batch arrival single service queue with two stages of service (second stage is optional) and working breakdown is investigated. When the system is in operation, it may breakdown at any time. During breakdown period, instead of terminating the service totally, it continues at a slower rate. We find the time-dependent probability generating functions in terms of their Laplace transforms and derive explicitly the corresponding steady state results. Furthermore, numerous measures indicating system performances, such as the average queue size and the average queue waiting time, has been obtained. Some of the numerical results and graphical representations were also presented

Time Dependent Solution of Batch Arrival Queue with Second Optional Service, Optional Re-Service and Bernoulli Vacation

This paper deals with an M[X]/G/1 queues with second optional service, optional re-service and Bernoulli vacations. Each customer undergoes first phase of service after completion of service, customer has the option to repeat or not to repeat the first phase of service and leave the system without taking the second phase or take the second phase service. Similarly after the second phase service he has yet another option to repeat or not to repeat the second phase service. After each service completion, the server may take a vacation with probability 1-theta or may continue staying in the system with probability . The service and vacation periods are assumed to be general. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Also the average number of customers in the queue and the waiting time are also derived. Keywords: Batch arrival, Second optional service, Optional re-service, Average queue size, Average waiting time

Working Mechanism and Structure of Customer Services Support System

On the basis of analyzing customer services of manufacturing enterprises and these supporting requires, using the method of discrete system simulating, the paper provides the classifications of customer services suitable information technology supporting, brings forward the working mechanisms suitable to the supporting system of different kinds of customer services and the relevant system structure

An optional service Markovian queue with working disasters and customer’s impatience

In this paper, we develop a new class of Markov model with working disasters, second optional service, and reneging of customers. The disasters can occur during regular busy period. Whenever a disaster occurs, server continues to serve the customers with a lower service rate instead of completely stopping the service and after the completion of disaster recovery it switches to the regular busy period. Steady-state solution of the model is obtained by using probability generating function technique and stability condition is derived. Further, some important performance measures are presented. A cost model is developed in order to obtain the optimal service rates during first essential service, second optional service and during disaster period using quadratic fit search method. At the end, we provide some numerical examples to visualize the applicability of the model in practical situations.Publisher's Versio

On some queueing systems with server vacations, extended vacations, breakdowns, delayed repairs and stand-bys

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This research investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process. The service times, vacation times, repair times, delay times and extended vacation times are assumed to follow different general distributions while the breakdown times and the service times of the stand-by server follow an exponential distribution. By introducing a supplementary variable we are able to obtain steady state results in an explicit closed form in terms of the probability generating functions. Some important performance measures including; the average length of the queue, the average number of customers in the system, the mean response time, and the value of the traffic intensity are presented. The professional MathCad 2001 software has been used to illustrate the numerical results in this study