On Mx/( G1 G2 )/1/G(BS)/Vs vacation queue with two types of general heterogeneous service

Kailash C. Madan · Z. R. Al-Rawi · Amjad D. Al‐Nasser

21 citations0/0 files storedJournal of Applied Mathematics and Decision Sciences

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Advanced Queuing Theory Analysis Optimization and Search Problems Age of Information Optimization

Abstract

We analyze a batch arrival queue with a single server providing two kinds of general heterogeneous service. Just before his service starts, a customer may choose one of the services and as soon as a service (of any kind) gets completed, the server may take a vacation or may continue staying in the system. The vacation times are assumed to be general and the server vacations are based on Bernoulli schedules under a single vacation policy. We obtain explicit queue size distribution at a random epoch as well as at a departure epoch and also the mean busy period of the server under the steady state. In addition, some important performance measures such as the expected queue size and the expected waiting time of a customer are obtained. Further, some interesting particular cases are also discussed.

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References

1982Poisson Arrivals See Time Averages 1986Queueing systems with vacations ? A survey 1995Queueing analysis: A foundation of performance evaluation 1986Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules 2000An M/G/1 queue with second optional service 1995Batch arrival queue with N-policy and single vacation 1994Analysis of the Mx/G/1 queue by N-policy and multiple vacations 1986On the Mx/G/1 queue with vacation time

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2017An M/G/1 queue with two types of general heterogeneous service and optional repeated service subject to server’s breakdown and delayed repair 2014Mathematical Analysis of Queue with Phase Service: An Overview 2011An M[X]/G/1 Queue with Bernoulli Schedule General Vacation Times, General Extended Vacations, Random Breakdowns, General Delay Times for Repairs to Start and General Repair Times

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