Topic
Retrial queue
About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: The generator of this multi-dimensional Markov chain belonging to the class of the asymptotically quasi-Toeplitz Markov chains is constructed, and it is shown that the chain is ergodic for any set of the system parameters.
9 citations
TL;DR: An M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously is considered and the conditional stochastic decomposition for the queue length in the orbit is proved.
Abstract: We consider an M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously. During the working vacation period, customers can be served at a lower rate. Using the matrix-analytic method, we get the necessary and sufficient condition for the system to be stable. Furthermore, the stationary probability distribution and some performance measures are also derived. Moreover, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, we present some numerical examples and use the parabolic method to search the optimum value of service rate in working vacation period.
9 citations
29 Sep 2017
TL;DR: The asymptotics of the number of calls in retrial queue under the conditions of high rate of making outgoing calls and low rate of service time of outgoing calls are derived.
Abstract: In this paper, we consider an MMPP/M/1/1 retrial queue where incoming fresh calls arrive at the server according to a Markov modulated Poisson process. Upon arrival, an incoming call either occupies the server if it is idle or joins an orbit if the server is busy. From the orbit, an incoming call retries to occupy the server and behaves the same as a fresh incoming call. The server makes an outgoing call in its idle time. Our contribution is to derive the asymptotics of the number of calls in retrial queue under the conditions of high rate of making outgoing calls and low rate of service time of outgoing calls.
9 citations
TL;DR: A single server retrial queue with general retrial time and collisions of customers with modified M-vacations is studied and the probability generating function of number of customers in the orbit is derived.
Abstract: In this paper, a single server retrial queue with general retrial time and collisions of customers with modified M-vacations is studied. The primary calls arrive according to Poisson process with rate λ. If the server is free, the arriving customer/the customer from orbit gets served completely and leaves the system. If the server is busy, arriving customer collides with the customer in service resulting in both being shifted to the orbit. After the collision the server becomes idle. If the orbit is empty the server takes at most M vacations until at least one customer is recorded in the orbit when the server returns from a vacation. Whenever the orbit is empty the server leaves for a vacation of random length V. If no customers appear in the orbit when the server returns from vacation he again leaves for another vacation with the same length. This pattern continues until he returns from a vacation to find at least one customer recorded in the orbit or he has already taken M vacations. If the orbit is empty by the end of the Mth vacation, the server remains idle for customers in the system. The time between two successive retrials from the orbit is assumed to be general with arbitrary distribution R(t). By applying the supplementary variables method, the probability generating function of number of customers in the orbit is derived. Some special cases are also discussed. A numerical illustration is also presented.
9 citations
TL;DR: The system with no waiting space in which primary customers arrive according to a Poisson process is considered and the corresponding Nash equilibrium joining strategies and social net benefit maximization problem with respect to the levels of information available to customers upon arrival is derived.
Abstract: We consider the system with no waiting space in which primary customers arrive according to a Poisson process. The arriving customer receives service immediately as the server is idle, otherwise, he will enter a retrial orbit asking for repeated requests. When a negative customer comes, the customer being served is deleted immediately and it also causes the server’s breakdown. Whenever the server breaks down, it is sent for repair immediately. If no customer arrives after every service completion, the server selects the first customer of the orbit to serve. The time required to find the first customer is assumed exponentially distributed with a constant rate referred as constant retrial rate. Based on a natural reward-cost structure, we study the equilibrium behavior of the customers and derive the corresponding Nash equilibrium joining strategies and social net benefit maximization problem with respect to the levels of information available to customers upon arrival.
9 citations