Retrial queue

About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.

The M/G/1 Vacation Queue with General Retrial Times and Repairable Server

Abstract: This paper considers an M/G/1 retrial queue system with single vacation and server breakdowns. The necessary and sufficient condition for the system stability is obtained. The queue indices of server are also derived with the supplementary variable method. Besides, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.

A single server non-Markovian retrial queue with two types of service and Bernoulli vacation

Abstract: A single server retrial queueing system with two types of service and Bernoulli vacation is analysed in this paper. It is assumed that the arriving job finds the server busy by providing either type of service is said to be in orbit with an FCFS discipline and repeat its request (demand) for service after some random time. The customer at the head of the orbit is allowed to access the server. For such queueing model, the system size probabilities are investigated in steady state by using supplementary variable technique. The effects of various parameters on the system performance are analysed numerically. Stochastic decomposition and some special cases of interest are also discussed.

Анализ системы обслуживания с повторными вызовами, неоднородными приборами и марковским процессом поступления

Abstract: Multi-server retrial queueing system with heterogeneous servers is analyzed. Requests arrive to the system according to the Markovian arrival process. Arriving primary requests and requests retrying from orbit occupy an available server with the highest service rate, if there is any available server. Otherwise, the requests move to the orbit having an infinite capacity. The total retrial rate infinitely increases when the number of requests in orbit increases. Service periods have exponential distribution. Behavior of the system is described by multi-dimensional continuous-time Markov chain which belongs to the class of asymptotically quasi-toeplitz Markov chains. This allows to derive simple and transparent ergodicity condition and compute the stationary probabilities distribution of chain states. Presented numerical results illustrate the dynamics of some system effectiveness indicators and the importance of considering of correlation in the requests arrival process.

Approximation of the steady state system state distribution of the m/g/1 retrial queue with impatient customers

Abstract: For M/G/1 retrial queues with impatient customers, we review the results, concerning the steady state distribution of the system state, presented in the literature. Since the existing formulas are cumbersome (so their utilization in practice becomes delicate) or the obtaining of these formulas is impossible, we apply the information theoretic techniques for estimating the above mentioned distribution. More concretely, we use the principle of maximum entropy which provides an adequate methodology for computing a unique estimate for an unknown probability distribution based on information expressed in terms of some given mean value constraints. Keywords: Retrial queue, steady state distribution, estimation, principle of maximum entropy, impatient customer.