Analysis of an $$M/M/1+G$$M/M/1+G queue operated under the FCFS policy with exact admission control

Authors:
Sudipta Das;Lawrence Jenkins;Debasis Sengupta
Affiliations:
Department of Electrical Engineering, Indian Institute of Science, Bangalore, India 560012;Department of Electrical Engineering, Indian Institute of Science, Bangalore, India 560012;Applied Statistical Unit, Indian Statistical Institute, Kolkata, India 7000108
Venue:
Queueing Systems: Theory and Applications
Year:
2013

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Abstract

In this article, we present an exact theoretical analysis of an $$M/M/1$$M/M/1 system, with arbitrary distribution of relative deadline for the end of service, operated under the first come first served scheduling policy with exact admission control. We provide an explicit solution to the functional equation that must be satisfied by the workload distribution, when the system reaches steady state. We use this solution to derive explicit expressions for the loss ratio and the sojourn time distribution. Finally, we compare this loss ratio with that of a similar system operating without admission control, in the cases of some common distributions of the relative deadline.