Transmission Times in Buffed Full-Crossbar Communication Networks with Cyclic Arbitration

In this paper we consider the distribution of message transmission times in buffered full cross bar interconnection networks with cyclic arbitration in which the input buffers are serviced in a ´round robin´ fashion. The system is modelled as an open queue ing network in which the queues appear at the net work outputs and with the cyclic arbiter being mod elled by queue jumping. We obtain the Laplace Trans form of the transmission time by deriving a condi tional Laplace Transform and solving by the use of a generating function. The density function is then enumerated by numerical inversion and compared with similar results from a simulation model. The analysis is then extended to general service times by modelling each output as a LCFS queue with a suitably modified arrival rate. In the special case of exponential service times, this model is less versatile than the previous one since it only works in the case where the jump probability is fixed. In this case, however, it is shown to produce the same result as the original.