Retrial queue

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

Research on Geo/Geo/1 Retrial Queue with Working Vacation Interruption and Nonpersistent Customers

Abstract: Queueing phenomenon is prevalent in all areas of society and a reasonable queueing design can improve service efficiency and customer satisfaction. In order to adapt to the new requirements of web service system, this paper studies a Geo/Geo/1 retrial queue with working vacation interruption and nonpersistent customers. Firstly, a series of assumptions about the queueing system are put forward and the corresponding transition probability matrix is obtained. Then the stationary condition of the queueing system is derived. After that, the stationary distribution and the performance measures are obtained by using the matrix-analytic method. Finally, numerical analysis is conducted to discuss the effect of parameters on performance measures, furthermore, the performance of the queueing model is optimized to obtain the best parameters and the minimum cost.

MX/G/1 retrial G-queue with multistage and multi-optional services, feedback, randomized J vacation and orbital search

Abstract: A single server batch arrival retrial G-queue with orbital search is considered. Positive customers arrive in batches and the negative customers arrive in single. After repair, the server starts servicing the new customer. The server provides services in two phases. The first phase is essential to all the arriving customers, whereas the second phase is optional. There are L stages of sequential services in the second phase. In each stage, there are multi optional heterogeneous services. After the completion of essential service, the customer may depart the system with probability d0, feedback to the orbit with probability δ0 or choose any one of the optional service in 1st stage of phase2 with probability pk1 (k1 = 1,2,. …,j1). In general, after the completion of mth (m=1,2, ,L-1) stage in second phase, the customer may depart the system with probability dm, feedback to the orbit with probability δm or choose kthm+1(km+1 = 1,2, … ,jm+1) optional service in (m+1)th stage of phase 2. After the completion of Lth stage, the customer may depart the system with probability dM or feedback to the orbit with probability δL. Whenever the system becomes empty, the server goes for vacation and takes at most J vacations repeatedly until at least one customer is recorded in the orbit. At the end of Jth vacation, even if the orbit is empty, the server remains idle in the system. During the idle period in the non-empty system, the server may search for customers in the orbit or remain idle. The arrival of negative customer makes the server down and pushes out the customer being in service. The probability generating functions and the number of customers in the orbit and in the system are obtained by supplementary variable technique. Expected system size, expected orbit size, availability of the server and failure frequency are derived. Numerical results are also presented.

Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates

Abstract: A two-class single-server retrial system with Poisson inputs is considered. In this system, unlike conventional retrial systems, each new ith class customer joins the ‘end’ of a virtual ith class orbit, and the ‘oldest’ customer from each orbit is only allowed to make an attempt to occupy server after a class-dependent exponential retrial time. Moreover, the server is assumed to be not reliable, and a customer whose service is interrupted joins the ‘top’ of class-i orbit queue. Thus FIFO discipline is applied in both orbits. Using regenerative methodology and Markov Chain approach we derive stability conditions of this system relying on analysis for less-complicated model with reliable server. Obtained conditions are verified by simulation. Additionally, we analyze a controllable variant of the main model operating under a $$c\mu $$ -rule. For that case the system becomes less stable comparing to the non-controllable counterpart.

On the impact of retrials on traffic burstiness

Abstract: Peakedness of an arrival process has been used as a measure of the process burstiness and it provides an effective method in approximating an autocorrelated process with a renewal process leading to simple loss and delay approximations in both single and multiple queue (node) environments. In this paper, we focus on the peakedness of processes generated in retrial queueing systems. More specifically, we derive a numerically efficient algorithm for the computation of the peakedness of the departure process of a single-server M/M/1 retrial queue. It is shown that the peakedness functional is a decreasing function of the retrial rate and its maximum is equal to 1 as the Poisson process.