A Simulation Analysis of Sojourn Times in a Jackson Network.
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH
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This thesis analyzes the total sojourn time distribution of a three queue acyclic Jackson network with the following characteristics. The network consists of three single server queues, Q1,Q2, and Q3, each having exponential service times. There is a Poisson exogenous arrival process to Q1. Customers departing Q1 go immediately to Q2, w.p. p, or to Q3, w.p. 1-p. Customers departing Q2 go immediately to Q3 and those departing Q3 leave the network. For different parameter settings, the network is simulated and the sojourn times at each of the queues are recorded. Due to the structure of the network, a simple simulation which correctly models the network can be constructed. It is known from Simon and Foley 1979, that the sojourn times of a customer in Q1 and Q3 are dependent. It is shown, that, except for extremely large sample sizes, 5000, that the correlation between the sojourn times in Q1 and Q3 is not significant. However, in the case of 5000 observations, this correlation is shown to be significantly greater than zero for certain parameter settings. Finally, the sample total sojourn time distribution is compared to one assuming independence of the sojourn times at each of the queues. It is shown that the sample distribution and the total sojourn time distribution assuming independence are not significantly different, except for pO. Author
- Statistics and Probability
- Computer Programming and Software