Topic
Retrial queue
About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.
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TL;DR: The M/M/1 retrial queue with working vacations and negative customers is introduced and efficient methodology to compute the stationary distribution for this new queue is developed and presented.
Abstract: The M/M/1 retrial queue with working vacations and negative customers is introduced. The arrival processes of positive customers and negative customers are Poisson. Upon the arrival of a positive customer, if the server is busy the customer would enter an orbit of infinite size and the orbital customers send their requests for service with a constant retrial rate. The single server takes an exponential working vacation once customers being served depart from the system and no customers are in the orbit. Arriving negative customers kill a batch of the positive customers waiting in the orbit randomly. Efficient methodology to compute the stationary distribution for this new queue is developed and presented.
11 citations
TL;DR: It is proved that the M/G/1 retrial queue with service interruptions can be approximated by the corresponding discrete-time system, and the stochastic decomposition law has been derived and bounds for the proximity between the steady-state distributions for the considered queueing system and its corresponding standard system are obtained.
11 citations
TL;DR: This paper considers a repairable M/G/1 retrial queue with Bernoulli schedule and a general retrial policy, which is motivated by a contention problem in the downlink direction of wireless base stations in cognitive radio networks.
Abstract: This paper considers a repairable M/G/1 retrial queue with Bernoulli schedule and a general retrial policy, which is motivated by a contention problem in the downlink direction of wireless base stations in cognitive radio networks. Arriving Customers (called primary arrivals) who cannot receive service upon arrival either join the infinite waiting space in front of the server (called as the normal queue) with probability $$q$$
, or enter the orbit with probability $$1-q$$
according to the FCFS discipline. If the server breaks down in the process of the service of a customer, the customer in service either joins the orbit queue or leaves the system forever. First, we study the ergodicity of two related embedded Markov chains and derive stationary distributions. Second, we find the steady-state joint generating function of the number of customers in both queues. Some important performance measures of the system are obtained. Third, the reliability analysis of the system is also given. Finally, numerical examples are given to illustrate the impact of system parameters on the system performance measures.
11 citations
TL;DR: In this article, the authors considered the M/M/c retrial queues with multiclass of customers and showed that the stationary joint distribution for the number of customers in service facility and orbit converges to those of the ordinary M/m/c with discriminatory random order service (DROS) policy as retrial rate tends to infinity.
Abstract: We consider the M/M/c retrial queues with multiclass of customers. We show that the stationary joint distribution for the number of customers in service facility and orbit converges to those of the ordinary M/M/c with discriminatory random order service (DROS) policy as retrial rate tends to infinity. Approximation formulae for the distributions of the number of customers in service facility, the mean number of customers in orbit and the sojourn time distribution of a customer are presented. The approximations are compared with exact and simulation results.
11 citations
25 Sep 2017
TL;DR: The main steady-state performance measures of the single-server retrial queueing system with collision of the customer and an unreliable server are computed by the help of the MOSEL tool.
Abstract: In this paper we investigate a single-server retrial queueing system with collision of the customer and an unreliable server. If a customer finds the server idle, he enters into service immediately. The service times are independent exponentially distributed random variables. During the service time the source cannot generate a new primary call. Otherwise, if the server is busy, an arriving (primary or repeated) customer involves into collision with customer under service and they both moves into the orbit. The retrial time of requests are exponentially distributed. We assume that the server is unreliable and could be break down. When the server is interrupted, the call being served just before server interruption goes to the orbit. Our interest is to give the main steady-state performance measures of the system computed by the help of the MOSEL tool. Several Figures illustrate the effect of input parameters on the mean response time.
11 citations