Retrial queue

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

N-policy for Mx/G/1 Unreliable Retrial G-Queue with Preemptive Resume and Multi-services

Abstract: Bulk arrival retrial G-queue with impatient customers and multi-services subject to server breakdowns has been analyzed. The system allows the arrival of two types of customers: positive customers and negative customers in the system. The negative customers make the server fail if they find the server in busy state, whereas positive customers are served if the server is idle otherwise they join the virtual pool of customers called orbit. The customers from the retrial orbit try their chance again for the service. The customers have the option of obtaining more than one service. Moreover, the customers are impatient and may renege from the system with probability \((1-r)\). The server is sent for repair as soon as it breakdowns; after repair, the service process starts again. Also, the server has the provision to initiate the service when there are N customers accumulated in the system. Using supplementary variables technique and generating functions, various performance measures like reliability indices and long run probabilities have been obtained.

Retrial Queue M/M/N with Impatient Customer in the Orbit

Abstract: In the paper, the retrial queueing system of M/M/N type with Poisson flow of events and impatient calls is considered. The delay time of calls in the orbit, the calls service time and the impatience time of calls in the system have exponential distribution. Asymptotic analysis method is proposed for the solving problem of finding distribution of the number of calls in the orbit under a system heavy load and long time patience of calls in the orbit condition. The theorem about the Gauss form of the asymptotic probability distribution of the number of calls in the orbit is formulated and proved. Numerical illustrations, results are also given.

F-Policy for M/M/1/K Retrial Queueing Model with State-Dependent Rates

Abstract: In this article, F-policy for the single-server finite capacity Markovian queueing model with retrial attempts is investigated. The system admits the customers to join the system till the system reaches its full capacity and then, the customers are restricted to join the system until the queue size reduces to threshold value ‘F’. To deal with more realistic situations, the concepts of state-dependent arrivals and service process are incorporated while developing a Markov model. On the basis of birth–death process, Chapman–Kolmogorov equations governing the model are developed to analyze the queueing characteristics of the system. The steady-state queue size distributions are obtained by using recursive technique which are further used to establish numerous performance indices to predict the behavior of the studied model. A cost function is framed to compute the optimal service rate and corresponding minimum cost. To investigate the behavior of the system, numerical example, sensitivity analysis of the system, and descriptors for different indices are presented.

On the multi-server retrial queue with geometric loss and feedback: computational algorithm and parameter optimization

Abstract: We consider an M/M/c retrial queue with geometric loss and feedback. An arriving customer finding a free server enters into service immediately; otherwise the customer either enters into an orbit to try again after a random amount of time or leave the system without service. After the completion of service, he decides either to join the retrial orbit or to leave the system. The retrial system is modelled by a quasi-birth-and-death process, and some system performance measures are derived. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of matrix-analytical approach. A cost model is derived to determine the optimal values of the number of servers and service rate simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimization approach as well as the effect of various parameters on system performance measures.