A non-exponential communication network statistical study

Abstract

In large data communication network applications, message switching concentration technique is known to be the most advantageous among various line-sharing schemes. Existing network model for analysis and synthesis of such a communication network is too simple to be usefully applicable in many realistic situations. To remedy that shortcoming is the main purpose of this work. Two models are proposed. Model 1 assumes messages of exponentially distributed length arrive in group as a Poisson process to the channel. The group size is geometrically distributed. Model 2 represents each communication node in the network by a selective multiservers queue, to which messages of exponentially distributed lengths arrive as a Poisson process and can only be transmitted over specified output channels. The distribution of waiting messages before a number of channels while leaving remaining channels idle obeys the Bose-Einstein statistics. Both models are analysed in detail. Message delay suffered in the transmission over the entire network is proved to be obtainable on a node-by-node basis. Optimum channel capacity assignment problems are worked out. The analytical results obtained are plotted and may be used as guide in network design. For model I/ the effects of bulk arrivals on message delay and waiting time suffered at a single link is analysed, as well as those encountered in priority queues with and without preemption, and at a node in a K-connected data communication network. The originality of this work is the assumptions that (1) messages are allowed to enter the network in groups of geometrically distributed sizes, and (2) the selectivity in channel service, which are introduced in models 1 and 2, respectively.