Uwe Jansen

Stochastic Processes and Properties of Invariance for Queueing Systems with Speeds and Temporary Interruptions

In queueing theory the question of invariance is well known: under what conditions the stationary probabilities of states of the queueing system are independent on the form of distribution functions of the elements (for example, of the service time) if there are given finite values of mathematical expectation? For the Erlang loss system with independent service times Sevastjanov [1] gave a complete answer; in the case of depending service times in the sense of stochastic point process see [2], [5], [6]. For other systems Kovalenko [3] proved a condition of invariance. A theory of invariance including algebraic criteria of invariance and connection with the so called set up of product of Sevastjanov [1] for a formalized class of queueing and reliability models is found in [4], [5], [6].

On the poisson output of queueing systems with dependent service times

In this paper a method is stated to conclude that the output of given queueing system is POISSON from the steady-state probabilities and from the behavior of the queueing system at jump epochs, i.e. at epochs when the system state can be changed. The corresponding statement for queueing systems described by Markov processes with denumber-able state space will be generalized to systems which can have arbitrary service time distributions if the steady-state probabilities are insensitive with respect to these distributions.