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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01 Jan 2013
TL;DR: In this paper, a Mx/G/1 retrial queue with unreliable server and general retrial times is investigated, where the server is subject to breakdowns and takes some setup time before starting the repair.
Abstract: The present investigation deals with Mx/G/1 retrial queue with unreliable server and general retrial times. The server is subject to breakdowns and takes some setup time before starting the repair. The server renders first essential phase of service (FES) to all the arriving customers whereas second optional phase services (SOS) are provided after FES to only those customers who opt for it. The impatient customers are allowed to balk depending upon server’s status; they may also renege after waiting sometime in the queue. By incorporating the supplementary variables corresponding to service time, repair time, retrial time and setup time and then using generating function method, the queueing analysis has been done to obtain the queue size and orbit size distributions, and some other queueing as well as reliability measures. The effects of several parameters on the system performance are examined numerically by taking an illustration.
2 citations
TL;DR: This article analyzes an unreliable retrial queue with persistent and impatient customers having different general service distributions and obtains the joint probability distribution of the server state and the number of customers in orbit in terms of Laplace and z-transforms.
Abstract: SYNOPTIC ABSTRACTIn this article, we analyze an unreliable retrial queue with persistent and impatient customers having different general service distributions. The server is subject to active and ...
2 citations
TL;DR: This work proposes another approach based on the relative state values that appear in the Howard equations that outperforms the previous approaches in terms of both accuracy and computation cost for the most common performance parameters used in retrial systems.
2 citations
23 Aug 2011
TL;DR: The negative arrival plays an important role in this paper and it controls the congestion in the orbit by removing one customer from the orbit only if server is busy and further the access from orbit to the service facility is governed by the classical retrial policy.
Abstract: Consider a single server retrial queueing system with negative arrival under Coxian phase type service in which customers arrive in a Poisson process with arrival rate λ. The negative arrival rate follows a Poisson distribution with parameter v. Let k be the number of phases in the service station. The service time follows an exponential distribution with parameter μj for jth phase where j = 1, 2, 3,. . ., k. The services in all phases are independent and only one customer at a time is in the service mechanism. Let qj be the probability that the customer moves from jth phase to (j + 1)th phase and (1 − qj) be probability to leave the system for j = 1, 2, 3,. . ., k −1. 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. The sequence of phases could be arranged one after the other in a series formation, with the provision of termination after the completion of any phase that is the customer may itself terminate at any stage and leaves the system. If the server is busy, then the arriving customer goes to orbit and becomes a source of repeated calls. The negative arrival plays an important role in this paper and it controls the congestion in the orbit by removing one customer from the orbit and further we assume that it removes the customer from the orbit only if server is busy. Otherwise, the system state does not change. We assume that the access from orbit to the service facility is governed by the classical retrial policy. This model is solved by using Direct Truncation Method. Numerical studies have been done for analysis of mean number of customers in the orbit (MNCO), Truncation level (OCUT), Probabilities of server free, busy for various values of λ, q1, q2, q3,. . ., qk-1, μ1, μ2,. . ., μk, v, k and σ in elaborate manner and also various particular cases of this model have been discussed.
2 citations
TL;DR: In this article, the M/G/1 retrial queue with two-way communication and n type of outgoing calls is analyzed from a stochastic comparison viewpoint, and the performance measures of the system considered can be estimated by those of the same M/M/1 system with two way communication when the service time distribution is NBUE (respectively, NWUE).
Abstract: In this article we analyze the M/G/1 retrial queue with two way communication and n type of outgoing calls from a stochastic comparison viewpoint. The main idea is that given a complex Markov chain which cannot be analyzed numerically, we propose to bound it by a new Markov chain which is easier to solve by using a stochastic comparison approach. Particularly, we analyze the notion of monotonicity of the transition operator of the embedded Markov chain relative to the stochastic and convex orderings. Bounds are also obtained for the stationary distribution of the embedded Markov chain at departures epochs. Additionally, the performance measures of the system considered can be estimated by those of the M/M/1 retrial queue with two way communication when the service time distribution is NBUE (respectively, NWUE). Finally, we test numerically the accuracy of the proposed bounds.
2 citations