Analyzing GI/Er/1 queues
In this paper we study a single-server system with Erlang-r distributed
service times and arbitrarily distributed interarrival times.
It is shown that the waiting-time distribution
can be expressed as a finite sum of exponentials,
the exponents of which are the roots of an equation.
Under certain conditions
for the interarrival-time distribution, this equation
can be transformed to r contraction equations, the roots of
which can be easily found by successive substitutions. The conditions are
satisfied for several practically relevant arrival processes.
The resulting numerical procedures are easy to implement and efficient and
appear to be remarkably stable,
even for extremely high values of r and for values of the traffic load
close to 1. Numerical results are presented.
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