Finite-Source Queueing Systems and their Applications
Finite-Source Queueing Systems and their Applications
Finite-Source Queueing Systems and their Applications
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János Sztrik 2001/08/05<br />
In the above mentioned case since mµ is the overall service rate:<br />
ρ = λ<br />
mµ<br />
, (4)<br />
<strong>and</strong> ρ can be used to formulate the condition for stationary behavior<br />
mentioned previously. The condition for stability is:<br />
ρ < 1 , (5)<br />
i.e., on average the number of jobs that arrive in a unit of time must be<br />
less than the number of jobs that can be processed.<br />
Throughput γ: The throughput of an elementary queueing system is defined<br />
as the mean number of jobs whose processing is completed in a single unit<br />
of time, i.e., the departure rate. Since the departure rate is equal to the<br />
arrival rate λ for a queueing system in statistical equilibrium, the throughput<br />
is given by:<br />
γ = m · ρ · µ (6)<br />
<strong>Finite</strong>-<strong>Source</strong> <strong>Queueing</strong> <strong>Systems</strong> <strong>and</strong> <strong>their</strong> <strong>Applications</strong>
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