In this paper, formulas are derived for queueing systems where the delayed customers are controlled by a stochastic time out, i.e., the delays are limited by a timeTthat is drawn from a general probability distribution. Formulas are also worked out for the case of a limitation of the time spent in the total system (queue + servers). In order to simplify numerical calculations, an approximate method is worked out and numerical examples are shown.

This paper discusses two classical methods of calculating grade of service parameters for link systems, i.e., the methods of Jacobaeus and Lotze. The possibility of extending these theories to cover delay systems and in particular to calculate the waiting time distribution is looked into. Numerical results from the theories are compared with simulations results. Throughout this paper, pure Poisson arrivals and negative exponentially distributed service times are considered.