Retrial queue

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

Analysis of M/G/1 Priority Retrial G-Queue with Bernoulli Working Vacations

Abstract: In this investigation, a priority retrial queue with working vacations and negative customers is addressed. The priority clients don’t shape any line and have an elite preemptive priority to get their services over normal customers. When the orbit is noticeably empty at the season of service consummation, the server takes for a working vacation. In working vacation period, the server works at a lower rate of service. Utilizing the supplementary variable technique (SVT), the probability generating function (PGF) of the system capacity is found. Some important special cases are discussed.

A study of discrete - time multi server retrial queue with finite population and fuzzy parameters

Abstract: Our aim in this work is to deal with the discrete-time multi server retrial queue with finite population and fuzzy parameters. First, we describe this system and mentioned its effective characteristics in a crisp case. Then, we apply the concepts of cuts and extension principle to construct membership functions of the system characteristics using paired NLP models in the fuzzy case. Key words: Retrial queue, fuzzy, discrete-time.

Analysis of MAP/PH/1 Retrial Queue With Constant Retrial Rate, Bernoulli Schedule Vacation, Bernoulli Feedback, Breakdown and Repair

Abstract: A retrial queueing model in which the inter arrival times follow Markovian Arrival Process(MAP) and the service times follow phase type distribution is studied. At the end of receiving the service, the customer has two options namely, either he may go to orbit with probability q1 to get the service again, if he is not satisfied or with probability p1, he may depart the system. Similarly, at the end of providing service, the server can either opt to take vacation with probability p2 or be idle with probability q2. During the busy period, the server may experience breakdown. Both the breakdown times and repair times of the server follow exponential distribution with parameter σ and δ respectively. The resulting QBD process is analysed in the steady state by employing matrix analytic method. The busy period analysis of our model has also been done. Finally, the numerical and graphical illustration of our model has been given.

Analysis of non-pre-emptive priority retrial queueing system with two-way communication, Bernoulli vacation, collisions, working breakdown, immediate feedback and reneging

Abstract: In this study, we investigate a single server priority retrial queueing system including two-way communication, collision, working breakdown, repair, immediate feedback, Bernoulli vacation and reneging. Incoming requests (calls) appear at the service station according to a compound Poisson process. During the idle time, the server can make an outgoing call with an exponentially distributed time. The incoming call that identifies the server occupied will join an orbit or collide with the call currently in service. The server renders the service following a non-pre-emptive priority service rule. The server takes a Bernoulli vacation. The server may become inactive due to normal breakdown and the call currently in service will get the remaining service at a moderate service rate. The repair process starts instantly. After the completion of service, vacation and repair the server is in an idle state. We allow reneging to happen at the orbit. Using the supplementary variable technique, the stability condition is derived.

An M X /G/1 unreliable retrial queue with two phase service and persistence behaviour of customers in service

Abstract: This paper describes an unreliable server batch arrival retrial queue with two types of repair and second optional service. The server provides preliminary first essential service (FES) to the primary arriving customers or customers from retrial group. On successful completion of FES, the customer may opt for second optional service (SOS) with probability α . The server is subject to active break downs. The customer under FES (or SOS) during the failure decides, with probability q , to join the orbit( impatientcustomer ) and, with complementary probability p , to remain in the server for repair in order to conclude his remaining service ( patientcustomer ). Both service and repair times are assumed to have general distribution. It is considered that the repair time of server during the presence of patient customer and the repair time of the server while the customer ( impatientcustomer ) joining the orbit due to failure, are different. For this queueing system, the orbit and system size distributions are obtained. Reliability of the proposed model is analysed. Some particular cases are also discussed. Other performance measures are also obtained. The effects of several parameters on the system are analysed numerically.