Priority Queueing System with a Single Server Serving Two Queues M[X1],M[X2]/G1,G2/1 with Balking and Optional Server Vacation

In this paper we study a vacation queueing system with a single server simultaneously dealing with an M[x1] /G1/1 and an M[x2] /G2/1 queues. Two classes of units, priority and non-priority, arrive at the system in two independent compound Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority and non-priority units. We further assume that the server may take a vacation of random length just after serving the last customer in the priority unit present in the system. If the server is busy or on vacation, an arriving non-priority customer either join the queue with probability b or balks(does not join the queue) with probability (1 - b). The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained explicitly. Also the average number of customer in the priority and the non-priority queue and the average waiting time are derived. Numerical results are computed

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

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

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

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of service 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 join into the orbit. The negative customer, arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters into 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. The busy server may breakdown at any instant and the service channel will 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 system parameters

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

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 an M/M/ c

We consider an M/M/c queueing system with impatient customers and a synchronous vacation policy, where customer impatience is due to the servers’ vacation. Whenever a system becomes empty, all the servers take a vacation. If the system is still empty, when the vacation ends, all the servers take another vacation; otherwise, they return to serve the queue. We develop the balance equations for the steady-state probabilities and solve the equations by using the probability generating function method. We obtain explicit expressions of some important performance measures by means of the two indexes. Based on these, we obtain some results about limiting behavior for some performance measures. We derive closed-form expressions of some important performance measures for two special cases. Finally, some numerical results are also presented

A Discrete-Time G

This paper is concerned with a discrete-time Geo/G/1 retrial queueing model with J vacations and two types of breakdowns. If the orbit is empty, the server takes at most J vacations repeatedly until at least one customer appears in the orbit upon returning from a vacation. It is assumed that the server is subject to two types of different breakdowns and is sent immediately for repair. We analyze the Markov chain underlying the considered queueing system and derive the system state distribution as well as the orbit size and the system size distributions in terms of their generating functions. Then, we obtain some performance measures through the generating functions. Moreover, the stochastic decomposition property and the corresponding continuous-time queueing system are investigated. Finally, some numerical examples are provided to illustrate the effect of vacations and breakdowns on several performance measures of the system

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

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