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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TL;DR: In this paper, the M/M/s/K retrial queues were considered, where a customer who is blocked to enter a service facility may leave the system with a probability that depends on the number of attempts of the customer to enter the service facility.
1 citations
TL;DR: In this article, the stability conditions and the system state probabilities are investigated both in a transient and in a steady state for a queueing system with Poisson arrivals and arbitrarily distributed service times, vacation times, and start-up and close-down times.
Abstract: We consider a queueing system with Poisson arrivals and arbitrarily distributed service times, vacation times, and start-up and close-down times. The model accepts two types of customers—the ordinary and the retrial customers—and the server takes a single vacation each time he becomes free. For such a model the stability conditions and the system state probabilities are investigated both in a transient and in the steady state. Numerical results are finally obtained and used to observe system performance for various values of the parameters.
1 citations
25 Mar 2022
TL;DR: In this article , a single server queueing system in retrial is investigated, as well as optional re-service,customer search and delayed repair, and the server is permitted to take a vacation under Modified Bernoulli vacation.
Abstract: Single server queueing system in retrial is investigated, as well as optional re-service,customer search and delayed repair. Furthermore, the server is permitted to take a vacation under Modified Bernoulli vacation. In this model, some of the customer’s seek voluntary reservice for the identical service taken, dissatisfied with the first attempt without entering the retrial group (probability r1) or leaving the service area (probability 1 – r1). The failing server's repair begins after an arbitrary length of time termed delay time has passed. The supplementary variable technique is used to calculate orbit size, server status, and performance metrics. We explore several special situations of our suggested model and compare the results to previous research.
1 citations
15 Oct 2019
TL;DR: An approximate analysis of a Markovian multiserver infinite source retrial queuing with impatience, in which all the servers are subject to breakdown and repairs, to approximate the steady-state joint distribution of the number of customers in orbit and the number in the service area using a phase-merging Algorithm.
Abstract: This paper concerns an approximate analysis of a Markovian multiserver infinite source retrial queuing with impatience, in which all the servers are subject to breakdown and repairs. Customer who find the total number of busy and failed servers equal to $s$,i.e, he is given to choice to enter a retrial orbit for an random amount of time before attempting to reccess an available server or enter the queue of size $q$. Customer waiting in the queue start being served as an idle or repaired server assigned to them, they can also leave the queue and enter orbit due to impatience. Customers whose service is interrupted by a failure may have the option of leaving the system entirely or returning to the orbit to repeat or resume service. We assume that each server has its own dedicated repair person, and repairs begin immediately following a failure and all process are assumed to be mutually independent. The simultaneous effect of customer balking, impatience and retrials is analyzed. We try to approximate the steady-state joint distribution of the number of customers in orbit and the number of customers in the service area using a phase-merging Algorithm.
1 citations
TL;DR: In this article, a single server batch arrival retrial queue with se rver vacation under Bernoulli schedule is considered, and the necessary and sufficient condition for the system to be stab le is derived.
Abstract: A single server batch arrival retrial queue with se rver vacation under Bernoulli schedule is considere d. Arrivals are controlled according to the state of the server. The necessary and sufficient condition for the system to be stab le is derived. Explicit formulae for the stationary distributions and performance measur es of the system in steady state are obtained. Nume rical examples are presented to illustrate the influence of the parameters on se veral performance characteristics.
1 citations