Abstract
We consider the transient analysis of the M/G/1/0 queue, for which Pn(t)
denotes the probability that there are no customers in the system at time t, given
that there are n(n=0,1) customers in the system at time 0. The analysis,
which is based upon coupling theory, leads to simple bounds on Pn(t) for the
M/G/1/0 and M/PH/1/0 queues and improved bounds for the special case
M/Er/1/0. Numerical results are presented for various values of the mean arrival rate λ to demonstrate the increasing accuracy of approximations based upon
the above bounds in light traffic, i.e., as λ→0. An important area of application
for the M/G/1/0 queue is as a reliability model for a single repairable component. Since most practical reliability problems have λ values that are small relative to the mean service rate, the approximations are potentially useful in that
context. A duality relation between the M/G/1/0 and GI/M/1/0 queues is also
described.