Diffusion Models for Computer-Communication Networks

The diffusion theory is used to model a computer-communication network in which messages flow from one computer center to another. The idea is to approximate the various queueing processes that occur in the system of discrete nature themselves as continuous-state processes. The messages waiting at the queues to be transmitted are considered of small duration so that in the limit the flow of messages is continuous. With these ideas a general model for routing of messages in a computer network is established and expressions for the diffusion parameters drift and covariance per unit time are derived in terms of the network traffic. The mean length of the queues can thus be calculated and procedures to minimize the system overall queue size may be applied. Examples for simple networks are shown. One of them corresponds to a load-sharing computer system and it is indicated how the general diffusion methods derived earlier for message routing, can be used. Finally, a comparison is made between the expressions obtained by diffusion techniques and those corresponding to the classical exponential MMl queue.