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: In this article, the authors considered a finite buffer capacity GI/GI/c/K-type retrial queueing system with constant retrial rate and established sufficient stability conditions for this system.
Abstract: We consider a finite buffer capacity GI/GI/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has \(c\) identical servers and can accommodate up to \(K\) jobs (including \(c\) jobs under service). If a newly arriving job finds the primary queue to be full, it joins the orbit queue. The original primary jobs arrive to the system according to a renewal process. The jobs have i.i.d. service times. The head of line job in the orbit queue retries to enter the primary queue after an exponentially distributed time independent of the length of the orbit queue. Telephone exchange systems, medium access protocols, optical networks with near-zero buffering and TCP short-file transfers are some telecommunication applications of the proposed queueing system. The model is also applicable in logistics. We establish sufficient stability conditions for this system. In addition to the known cases, the proposed model covers a number of new particular cases with the closed-form stability conditions. The stability conditions that we obtained have clear probabilistic interpretation.
21 citations
TL;DR: This paper deals with the maximum number of customers in orbit (and in the system) during a busy period for the M/M/c retrial queue and develops an efficient algorithmic procedure for computation of this distribution by exploiting the special block-tridiagonal structure of the system.
Abstract: This paper deals with the maximum number of customers in orbit (and in the system) during a busy period for the M/M/c retrial queue Determining the distribution for the maximum number of customers in orbit is reduced to computation of certain absorption probabilities By reducing to the single-server case we arrive at a closed analytic formula For the multi-server case we develop an efficient algorithmic procedure for computation of this distribution by exploiting the special block-tridiagonal structure of the system Numerical results illustrate the efficiency of the method and reveal interesting facts concerning the behavior of the M/M/c retrial queue
20 citations
TL;DR: This paper considers a continuous-time retrial queue with two classes of customers: priority customers and ordinary customers, where priority customers don’t queue and have an exclusive preemptive priority to receive their services over ordinary customers.
Abstract: In this paper, we consider a continuous-time retrial queue with two classes of customers: priority customers and ordinary customers, where priority customers don’t queue and have an exclusive preemptive priority to receive their services over ordinary customers. If an arriving ordinary customer finds the server busy, it enters a retrial group (called orbit) according to FCFS discipline. Only the ordinary customer at the head of the retrial queue is allowed to access the server. Firstly, we obtain the necessary and sufficient condition for the system to be stable by embedded Markov chain approach. Secondly, using supplementary variable method, we obtain the stationary probability distribution and some performance measures of interest. Thirdly, we give the analysis of the sojourn time in the system of an arbitrary ordinary customer. Lastly, numerical examples are given to show the effect of system parameters on several performance measures.
20 citations
TL;DR: Two characteristics of the orbit are investigated, namely, the orbit busy period and the orbit idle period, which seem to be very useful from this point of view.
Abstract: In teletraffic applications of retrial queues only the service zone is observable. Another part of a retrial queue, the orbit, which represents the delay before repeated attempts to get service, cannot be observed. Thus, it is very important to get general results about behavior of the orbit. We investigate two characteristics of the orbit, namely, the orbit busy period and the orbit idle period, which seem to be very useful from this point of view.
20 citations
TL;DR: This paper derives the closed form solution for the stationary probabilities of the queue with working vacations and a constant retrial rate and concludes that the social benefit rate is best when customers know all information about the server.
Abstract: In this paper, we investigate the M/M/1 retrial queue with working vacations and a constant retrial rate. In the queue, customers decide about the entry based on the information upon their arrival instants. Scenarios regarding the availability of information (i.e., the server is occupied or not, and the server is on the vacation or not) for customers are compared. We derive the closed form solution for the stationary probabilities of the queue. Social optimizing and Nash equilibrium strategies for joining the system are investigated. Based on numerical results, the social benefit rate is best when customers know all information about the server.
20 citations