Overload Analysis of the PH/PH/1/K Queue and the Queue of M/G/1/K
Type with Very Large K
We consider the PH/PH/1/K queue and the queue of M/G/1 type
with very large buffer size $K$ and operating
in overload condition. By rotating the resulting transition matrix through
180 degrees we turn it into a queue with underload condition. By
approximating the latter queue
by an infinite buffer system we are able to study it using the
matrix-geometric method.
A procedure for estimating the blocking
probabilities is presented.
We apply the procedure to
a telephone system with both patient and impatient customers.
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