Server Breakdown and Delayed Repair in Three Phases of Service for an M/G/1 Retrial Queueing System


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Authors

  • Rohit Singh Tomar Department of Mathematics, Shrimant Madhavrao Scindia Government Model Science College, Gwalior, Madhya Pradesh, India
  • R. K. Shrivastav Department of Mathematics, Shrimant Madhavrao Scindia Government Model Science College, Gwalior, Madhya Pradesh, India

Keywords:

First phase of service, second phase of service, third phase of service, random breakdowns, delayed repair, M/G/1 queue, stationary queue size distribution, reliability index

Abstract

This paper deals with an unreliable server having three phases of heterogeneous service on the basis of M/G/1 queueing system. We suppose that customers arrive and join the system according to a Poisson's process with arrival rate $\lambda$. When the server is working with any phase of service, it may breakdown at any instant. After breakdown, when the server is sent for repair then server stops its service and arrival customers are waiting for repair, which we may called as waiting period of the server. This waiting time stands for delay time/delay repair. In this model, first we derive the joint probability distribution for the server. Secondly, we derive the probability generating function of the stationary queue size distribution at a departure epoch as a classical generalisation of Pollaczek - Khinchin formula. Third, we derive Laplace Stieltjes transform of busy period distribution and waiting time distribution. Finally, we obtain some important performance measures and reliability analysis of this model. By using a supplementary variable method, we obtain the transient and the steady state solutions for both queueing and reliability measures.

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Published

15-06-2020

How to Cite

Rohit Singh Tomar, & R. K. Shrivastav. (2020). Server Breakdown and Delayed Repair in Three Phases of Service for an M/G/1 Retrial Queueing System. International Journal of Mathematics And Its Applications, 8(2), 35–47. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/155

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Section

Research Article