M/G/1 Retrial Queueing System with Bernoulli
Feedback and Modified Vacation

Pankaj Sharma

doi:https://doi.org/10.14445/22315373/IJMTT-V61P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 61 | Number 1 | Year 2018 | Article Id. IJMTT-V61P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V61P502

M/G/1 Retrial Queueing System with Bernoulli Feedback and Modified Vacation

Pankaj Sharma

Citation :

Pankaj Sharma, "M/G/1 Retrial Queueing System with Bernoulli Feedback and Modified Vacation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 61, no. 1, pp. 10-21, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V61P502

Abstract

This paper is concerned with the M/G/1 retrial queueing system with Bernoulli feedback, discouragement, modified vacation and server breakdowns. The arrival stream occurs according to Poisson process with state dependent rates. On finding the server busy, under setup, under repair or on vacation, the customers either join to the orbit or balk from the system. From the orbit, the customers retry after a random interval of time. The customer whose service has just been completed immediately joins the head of the queue again with probability ‘1-q’ and requests for more service, or departs forever with probability ‘q’(0 < 𝑞 ≤ 1). The server is subject to random breakdowns at any time. The repairman, who restores the server, requires some time to start repair; this time is called as setup time. The service time, setup time and repair time are independent and general distributed. On finding the orbit empty, the server goes on at most J vacations repeatedly until at least one customer is recorded in the orbit.

Keywords

- M/G/1 retrial queue, Discouragement, Bernoulli feedback, Modified vacations, unreliable server

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