Abstract
This paper deals with the time-dependent behaviour of two queueing systems in series, with a Posson arrival stream and exponential service times. The Laplace transform of the probability p0(t) that the tandem system is empty at time t given that it was empty at time 0 is obtained by reducing the functional equation for the generating function of the joint queue length distribution to a Riemann-Hilbert boundary value problem. From this Laplace transform the relaxation time of p 0(t) is determined for all parameter values, and the first term of the asymptotic expansion of p 0(t)-p 0(∞) as t →∞ is found in the ergodic and in the null recurrent cases.
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