A batch arrival unreliable server delaying repair queue with two phases of service and Bernoulli vacation under multiple vacation policy

Gautam Choudhury · Mitali Deka

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Advanced Queuing Theory Analysis Reliability and Maintenance Optimization Age of Information Optimization

Abstract

This paper deals with an MX/G/1 unreliable queue with two phases of service and Bernoulli vacation schedule under multiple vacation policy, where after each vacation completion or service completion, the server takes sequence of vacations until a batch of new customer arrive. Further concept of the delay time is also introduced. We assume that customers arrive to the system according to a Poisson process with rate . While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. After completion of both phases of service, the server either goes for a vacation with probability p(0 ≤ p ≤ 1) or may continue to serve the next unit, if any, with probability q(= 1 – p). Otherwise; it remains in the system until a customer arrives. For this model, we derive queue size distributions at various epochs, busy period distribution, waiting time distribution under the steady-state condition. Next, we derive reliability function and related reliability indices of this model. Finally, some numerical examples are presented for illustrative purpose.

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References

1982Poisson Arrivals See Time Averages 1986Queueing systems with vacations ? A survey 1985Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations 1983A First Course in Bulk Queues 1962A Waiting Line with Interrupted Service, Including Priorities 1975Utilization of Idle Time in an M / G /1 Queueing System 1958Queuing with Preemptive Priorities or with Breakdown 1986Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules

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