ANALYTIC SOLUTION OF STOCHASTIC ACTIVITY NETWORKS WITH EXPONENTIAL AND DETERMINISTIC ACTIVITIES by Bhavan

Stochastic activity networks, which contain only exponentially distributed timed activities, behave as a Markov process, and can hence be solved using known techniques. When deterministically distributed activities are considered together with exponentially distributed activities, solution becomes di cult due to the non-memoryless property of deterministically distributed activity time. Such systems can be solved for their steady state behavior by employing a transient analysis during the activity time of deterministic activities and applying a correction based upon the fraction of time spent in di erent states during the activity times of deterministic activities. In this thesis, a method to solve stochastic activity networks with deterministic activities concurrently and/or competitively enabled with exponential activities is implemented as a part of a larger software package known as UltraSAN. In addition, a switch, called the \Low Loss Or Low Delay Switch," for an ATM based network is modeled and cell loss probabilities and average cell delays in the switch are obtained for di erent types of bursty tra c.