Discrete-Time Queueing Systems and Their Networks

Queueing systems in descrete time that can model certain computer communication systems are considered. First, a single-resource model consisting of a geometric server with feedback facility, to which packets arrive in independent bulks, is analyzed. Then, it is shown that a network of such geometric resources with packets arriving in independent Bernoulli streams (which, in a sense, is a discrete analog of Jackson's network) does not possess the independence property. A byproduct of this result is the fact that output of a geometric resource fed by two or more independent Bernoulli streams is not an independent Bernoulli stream.