Transient Behavior of Retrial Queueing Model with Non Persistent Customers, Random Break Down, Bernoulli Vacation and Orbital Search

G.Ayyappan; S. Shyamala

doi:https://doi.org/10.14445/22315373/IJMTT-V7P517

International Journal of Mathematics Trends and Technology

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Volume 7 | Number 2 | Year 2014 | Article Id. IJMTT-V7P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V7P517

Transient Behavior of Retrial Queueing Model with Non Persistent Customers, Random Break Down, Bernoulli Vacation and Orbital Search

G.Ayyappan , S. Shyamala

Abstract

We investigate a single server batch arrival retrial queueing system with Bernoulli vacation and orbital search. Batches are arriving in accordance with Poisson process with arrival rate  and are served one by one with first come first served basis. At the arrival epoch, if the customer finds the server busy, breakdown or vacation can either join the orbit with probability p or he/she can leave the system with probability 1-p, such customers are called non-persistent. As the server is considered as unreliable one, it may encounter break down at any time. For to resume its service it has to go for a immediate repair process. At the completion epoch of a service, the server may go for a vacation with probability  or stay back in the system to serve a next customer with probability 1 , if any. We obtain the transient solution and steady solution of the model by using supplementary variable technique. Also we derive the system performance measures and reliability indices.

Keywords

Batch size, Bernoulli, Orbit Search, Reliability Indices, Steady Solution, Transient Solution.

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Citation :

G.Ayyappan , S. Shyamala, "Transient Behavior of Retrial Queueing Model with Non Persistent Customers, Random Break Down, Bernoulli Vacation and Orbital Search," International Journal of Mathematics Trends and Technology (IJMTT), vol. 7, no. 2, pp. 126-135, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V7P517