Mixtures of exponential distributions in the gi/g/1 queue (with and without warming up)

摘要

We consider the GI/G/1 queue and its generalization with warming up in the stationary state. There are shown so called conservation theorems for mixtures of ex-ponential distributionswhere also negative weights Fk are allowed. By means of studying the corresponding characteristic functions at its poles and zeros we obtain the following results: If the service time distribution function (d. f.) is such a mixture and its characteristic function satisfies a certain condition then both the waiting time d.f. and the sojourn time d.f. are such mixtures in the GI/G/1