M.C. Saravanarajan

Bio: M.C. Saravanarajan is an academic researcher from VIT University. The author has contributed to research in topic(s): Retrial queue & Queue. The author has an hindex of 6, co-authored 20 publication(s) receiving 116 citation(s).

A study on M/G/1 feedback retrial queue with subject to server breakdown and repair under multiple working vacation policy

Abstract: In this paper, we consider a single server feedback retrial queueing system with multiple working vacations and vacation interruption. An arriving customer may balk the system at some particular times. As soon as orbit becomes empty at regular service completion instant, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. After completion of regular service, the unsatisfied customer may rejoin into the orbit to get another service as feedback customer. The normal busy server may get to breakdown 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. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented.

Analysis of M[X]/G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown

Abstract: This paper investigates the steady state behaviour of an M[x]/G/1 retrial queue with two phases of service under Bernoulli vacation schedule and breakdown. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters the service immediately while the rest join the orbit. After completion of each two phases of service, the server either goes for a vacation with probability p or may wait for serving the next customer with probability (1-p). 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. We construct the mathematical model and derive the probability generating functions of number of customers in the system when it is idle, busy, on vacation and under repair. Some system performances are obtained.

Analysis of an M[X]/(G1, G2)/1 retrial queueing system with balking, optional re-service under modified vacation policy and service interruption

Abstract: This paper deals with the steady state analysis of batch arrival retrial queueing system with two types of service under modified vacation policy, where each type consists of an optional re-service. An arriving batch may balk the system at some particular times. After the completion of each types of service the customers may re-service of the same type without joining the orbit or may leave the system. If the orbit is empty at the service completion of each types 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. Busy server may breakdown at any instance and the service channel will fail for a short interval of time. The steady state probability generating function for system/orbit size is obtained by using the supplementary variable method. Some system performance measures and numerical illustrations are discussed.

Analysis of an M [X] /G/1 unreliable retrial G -queue with orbital search and feedback under Bernoulli vacation schedule

Abstract: In this paper, we consider a batch arrival retrial queue with feedback under Bernoulli vacation schedule, where the busy server is subjected to breakdown due to the arrival of negative customers. Any arriving batch of positive customers finds the server free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. Arriving positive customers may balk (or renege) the system at particular times. After completion of service the unsatisfied positive customer may rejoin into the orbit to get another regular service as feedback customer. The server takes Bernoulli vacation after service completion of positive customers. After completion of service (if the server is not taking vacation), repair or vacation the server searches for the customers in the orbit or remains idle. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some system performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented.

Analysis of an unreliable retrial G-queue with working vacations and vacation interruption under Bernoulli schedule

Abstract: In this paper, we consider a single server retrial queueing system with working vacations. Further vacation interruption is considering with the regular busy server is subjected to breakdown due to the arrival of negative customers. When the orbit becomes empty at the time of service completion for a positive customer, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. If there are customers in the system at the end of each vacation, the server becomes idle and ready for serving new arrivals with probability p (single WV) or it remains on vacation with probability q (multiple WVs). By using the supplementary variable technique, we found out the steady state probability generating function for the system and its orbit. System performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented.

On an unreliable-server retrial queue with customer feedback and impatience

Abstract: Analysis of an unreliable-server retrial queue with customer's feedback and impatience is presented. Truncated classical and constant retrial policies are taken into account. This system is analyzed as a process of quasi-birth-and-death (QBD). The quasi-progression algorithm is applied to compute the rate matrix of QBD model. A recursive solver algorithm for computing the stationary probabilities is also developed. To make the investigated system viable economically, a cost function is developed to decide the optimum values of servers, mean service rate and mean repair rate. Quasi-Newton method, pattern search method and Nelder–Mead simplex direct search method are employed to implement the optimization tasks. Under optimum operating conditions, numerical results are provided for a comparison of retrial policies. We also give a potential application to illustrate the system's applicability.

A study on M/G/1 feedback retrial queue with subject to server breakdown and repair under multiple working vacation policy

Abstract: In this paper, we consider a single server feedback retrial queueing system with multiple working vacations and vacation interruption. An arriving customer may balk the system at some particular times. As soon as orbit becomes empty at regular service completion instant, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. After completion of regular service, the unsatisfied customer may rejoin into the orbit to get another service as feedback customer. The normal busy server may get to breakdown 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. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented.

On an unreliable retrial queue with general repeated attempts and J optional vacations

Abstract: In this paper, we consider a single-server retrial queue with constant retrial rate and batch arrivals, in which the unreliable server has the option to take an additional vacation after the first essential vacation. Customers arriving at the system according to a compound Poisson process are served immediately as long as the server is available; otherwise, they enter a retrial orbit and form a single queue. When the orbit becomes empty, the server leaves for the first essential vacation, after which he may either remain idle within the system or take one of J optional vacations. When the server is busy, he is subject to random breakdowns and repairs. It is assumed that the service times, repair times and customer retrial times are arbitrarily distributed. The implementation of the supplementary variable technique makes it possible to derive the probability generating functions of the system size distribution at a random epoch. We also develop a variety of system performance measures as well as two reliability indices. Finally, we deal with the problem of cost optimization and provide a number of numerical examples.

Analysis of a single server batch arrival unreliable queue with balking and general retrial time

Abstract: This paper deals with a batch arrivals queue with general retrial time, breakdowns, repairs and reserved time Here we assume that customers arrive according to compound Poisson processes Any arri

An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns

Abstract: This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs. If the system is not empty during a normal service period, the arrival of a negative customer can cause the server breakdown, and the failed server still works at a lower service rate rather than stopping the service completely. Applying the embedded Markov chain, we obtain the necessary and sufficient condition for the stability of the system. Using the supplementary variable method, we deal with the generating functions of the number of customers in the orbit. Various system performance measures are also developed. Finally, some numerical examples and a cost optimization analysis are presented.