Mathematical Study of Queueing Theory

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In this project we gave a theoretical analysis on efficiencies of queueing networks.(1) A model to represent a queueing network for aomplicated arrivals of customers was given and its mathematical representation was shown based on random measures. (2) Generalized semi-Markov Processes was extended mathematically and applied to the queueing networks in case that group service and service time for customer on each node are depended each other. (3) A new model of a queueing network was presented for the case that the stop of the service for customers and choice of path depended on the network was investigated and the analytical class of network models was characterized mathematically. (4) The analytical network models was given by the change of the conditions of the original model which is not so easy to find the stationary distribution in the network and its relation was investigated. (5) The analytic method for a queueing network which happens some change at the same time was developed.