An M/M/2 Queueing System with Heterogeneous Servers Including One with Working Vacation

Achyutha Krishnamoorthy · C. Sreenivasan

27 citations0/0 files storedInternational Journal of Stochastic Analysis

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

This paper analyzes an M/M/2 queueing system with two heterogeneous servers, one of which is always available but the other goes on vacation in the absence of customers waiting for service. The vacationing server, however, returns to serve at a low rate as an arrival finds the other server busy. The system is analyzed in the steady state using matrix geometric method. Busy period of the system is analyzed and mean waiting time in the stationary regime computed. Conditional stochastic decomposition of stationary queue length is obtained. An illustrative example is also provided.

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References

1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1984Matrix-Geometric Solutions to Stochastic Models 1986Queueing systems with vacations ? A survey 2002M/M/1 queues with working vacations (M/M/1/WV)2005M/G/1 queue with multiple working vacations 2004Analysis of a GI/M/1 queue with multiple working vacations 1976An M/M/s Queue With Servers’ Vacations 1979A Markovian Queue with N Servers Subject to Breakdowns and Repairs

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2014M/M/1 Multiple Vacation Queueing Systems With Differentiated Vacations and Vacation Interruptions 2017Heterogeneous two-server queueing system with reverse balking and reneging 2015Balking and Reneging Multiple Working Vacations Queue with Heterogeneous Servers 2019Modelling and optimisation of a two-server queue with multiple vacations and working breakdowns

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