100 research outputs found

    Transient behavior of M[x]/G/1 Retrial Queueing Model with Non Persistent Customers, Random break down, Delaying Repair and Bernoulli Vacation

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    In this paper we consider a single server batch arrival non-Markovian retrial queueing model with non persistent customers. In accordance with Poisson process, customers arrive in batches with arrival rate  and are served one by one with first come first served basis. The server is being considered as unreliable that it may encounter break down at any time. In order to resume its service the server has to be sent for repair, but the repair does not start immediately so that there is a waiting time before the repair process. The customer, who finds the server busy upon arrival, can either join the orbit with probability p or he/she can leave the system with probability 1-p. More details can be found in the full paper. Key words: Batch size, break down, delay time, transient solution, steady solution,  reliability indices

    Analysis of M[X1],M[X2]/G1,G2/1 retrial queueing system with priority services, working breakdown, collision, Bernoulli vacation, immediate feedback, starting failure and repair

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    This paper considers an M[X1] , M[X2] /G1,G2/1 general retrial queueing system with priority services. Two types of customers from different classes arrive at the system in different independent compound Poisson processes. The server follows the non-pre-emptive priority rule subject to working breakdown, Bernoulli vacation, starting failure, immediate feedback, collision and repair. After completing each service, the server may go for a vacation or remain idle in the system. The priority customers who find the server busy are queued in the system. If a low-priority customer finds the server busy, he is routed to orbit that attempts to get the service. The system may become defective at any point of time while in operation. However, when the system becomes defective, instead of stopping service completely, the service is continued to the interrupted customer only at a slower rate. Using the supplementary variable technique, the joint distribution of the server state and the number of customers in the queue are derived. Finally, some performance measures are obtained

    Analysis of an M[X]/G/1 Feedback Retrial Queue with Two Phase Service, Bernoulli Vacation, Delaying Repair and Orbit Search

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    In this paper, we considered a batch arrival feedback retrial queue with two phase of service under Bernoulli vacation schedule and orbit search. At the arrival epoch of a batch, if the server is busy, under repair or on vacation then the whole batch joins the orbit. Where as if the server is free, then one of the arriving customers starts his service immediately and the rest join the orbit. At the completion epoch of each service, the server either goes for a vacation or may wait for serving the next customer. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The repair process does not start immediately after a breakdown and there is a delay time for repair to start. After vacation completion, the server searches for the customers in the orbit (i.e. customer in the orbit, if any taken for service immediately) or remains idle. The probability generating function of the number of customers in the system and orbit are found using the supplementary variable technique. The mean numbers of customers in the system/orbit and special cases are analyzed. The effects of various parameters on the performance measure are illustrated numerically. Keywords: Feedback, retrial queue, Bernoulli vacation, delaying repair, orbit searc

    Analysis of repairable M[X]/(G1,G2)/1 - feedback retrial G-queue with balking and starting failures under at most J vacations

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    In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of services and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them get into the orbit. The negative customer, is arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters the orbit or leaves the system. If the orbit is empty at the service completion of each type of service, the server takes at most J vacations until at least one customer is received in the orbit when the server returns from a vacation. While the busy server may breakdown at any instant and the service channel may fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Numerical illustrations are discussed to see the effect of the system parameters

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

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    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

    Transient Analysis of M[X1];M[X2]=G1;G2=1 Queueing Model with Retrial Priority Service, Negative Arrival, Two kinds of Vacations, Breakdown, Delayed Repair, Balking, Reneging and Feedback

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    This paper deals with the analysis of batch arrival retrial queue with two classes non-preemptive priorityunits, negative arrival, balking as well as reneging, feedback, emergency and Bernoulli vacation for anunreliable server. Here we assume that customers arrive according to compound Poisson process inwhich priority customers are assigned to class one and class two customers are of a low-priority type.If the server is free at the time of any batch arrivals, the customers of this batch begins to be servedimmediately. The low-priority customer may join the orbit with feedback if the service is not satisfied(or) may leave the system if the service is satisfied. The priority customers that find the server busyare queued and then served in accordance with FCFS discipline. The priority customers may renegethe queue if the server is not avilable in the system and there is no optional for feedback service tothe priority customers. The arriving low-priority customers on finding the server busy then they arequeued in the orbit in accordance with FCFS retrial policy without balking (or) may balk the orbit.While the server is serving to the customers, it faces two types of break-down there are breakdowns bythe arrival of negative customer and break-down at any instant of service and server will be down for ashort interval of time. Further concept of the delay time of repair is also introduced for breakdowns. Weconsider two different kinds of vacations, one is an emergency and the other one is Bernoulli vacation, theemergency vacation means at the time of the server serving the customer suddenly go for a vacation andthe interrupted customer waits to get the remaining service and after the completion of each service, theserver either goes for a vacation or may continue to serve for the next customer; if any . The retrial time,service time, vacation time, delay time and repair time are all follows general(arbitrary) distribution.Finally, we obtain some important performance measures of this model.Keywords:Batch arrival, priority queue, retrial queue, negative arrival, emergency and Bernoulli vacation, unreliableserver, breakdown and repair.AMSC: 60K25; 60K30; 90B2

    (R1984) Analysis of M^[X1], M^[X2]/G1, G_2^(a,b)/1 Queue with Priority Services, Server Breakdown, Repair, Modified Bernoulli Vacation, Immediate Feedback

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    In this investigation, the steady state analysis of two individualistic batch arrival queues with immediate feedback, modified Bernoulli vacation and server breakdown are introduced. Two different categories of customers like priority and ordinary are to be considered. This model propose nonpreemptive priority discipline. Ordinary and priority customers arrive as per Poisson processes. The server consistently afford single service for priority customers and the general bulk service for the ordinary customers and the service follows general distribution. The ordinary customers to be served only if the batch size should be greater than or equal to a , else the server should not start service until a customers have accumulated. Meanwhile priority queue is empty; the server becomes idle or go for vacation. If server gets breakdown while the priority customers are being served, they may wait in the head of the queue and get fresh service after repair completion, but in case of ordinary customers they may leave the system. After completion of each priority service, customer may rejoin the system as a feedback customer for receiving regular service because of inappropriate quality of service. Supplementary variable technique and probability generating function are generally used to solve the Laplace transforms of time-dependent probabilities of system states. Finally, some performance measures are evaluated and express the numerical results
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