Retrial queue

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

MX/G/1 Retrial queue with second optionalservice, feedback, admission controland vacation

Abstract: Single server batch arrival retrial queue with two phases of heterogeneous service and controllable arrival is analysed. If the server is idle, one of the customers in the batch admitted to the system receives the service immediately and the rest join the orbit, otherwise all the admitted customers enter the orbit. All the customers demand the first essential service, whereas only some of them opt for second optional service. After completion of essential or optional service if the customer is dissatisfied with the service he may join the orbit as a feedback customer. After completion of the optional service the server may go for a single vacation or remain idle in the system. Steady state analysis is performed and stability conditions are established. Results for particular cases are deduced. The stochastic decomposition property is verified.

Stability analysis of single server retrial queueing system with Erlang service

Abstract: The objective of this paper is to study the stability analysis of single server retrial queueing system with Erlang-k service under various constraints over the behavior of server and customers, in which customers arrive in a Poisson process with arrival rate λ. These customers are identified as primary calls. Let k be the number of phases in the service station. Further assume that the service time has Erlang-k distribution with service rate kμ for each phase. The services in all phases are independent and identically exponentially distributed and only one customer at a time is in the service mechanism. If the server is free at the time of a primary call arrival, the arriving call begins to be served in phase 1 immediately by the server then progresses through the remaining phases and must complete the last phase and leave the system before the next customer enters the first phase. If the server is busy, then the arriving customer goes to orbit and becomes a source of repeated calls. This pool of source of repeated calls may be viewed as a sort of queue. Every such source produces a Poisson process of repeated calls with intensity σ. If an incoming repeated call finds the server free, it is served in the same manner and leaves the system after service completion, while the source which produced this repeated call disappears. Otherwise, the system state does not change. In this paper, we analyse the stability of this system by introducing various concepts namely vacation policies, unreliable server and negative arrival. We assume that the access from orbit to the service facility is governed by the classical retrial policy. Stability conditions are derived by using Matrix geometric method in detailed.

Discrete Gamma Approximation in Retrial Queue MMPP/M/1 Based on Moments Calculation

Abstract: In the paper, the retrial queueing system of MMPP/M/1 type is considered. The process of the number of calls in the system is analyzed. The method for the approximate calculation of the first and the second moments is suggested. We propose the method of the discrete gamma approximation based on obtained moments. The numerical analysis of the obtained results for different values of the system parameters is provided. Comparison of the distributions obtained by simulation and the approximate ones is presented.