Deriving Performance Distribution of Queueing System by Maximum Entropy Principle

Assumptions on the distributions of customer interarrival time and severing time are the basis of queueing system analyzing. This paper demonstrates that these assumptions are actually not necessary if there are some known macro-indexes such as the capacity of system, mean number of customers in system, mean utilization of server. We are not concerned with the arrival time and severing time distributions. We go directly to the performance distributions. A queueing system is looked as a black box without any assumptions on arrival time and serving time distributions, maximum entropy models are developed to derive the performance distribution of queuing system with some empirically easy-to-get indexes of queueing systems. We perform a comparative analysis between the exact results and the maximum entropy results by chi-square fit goodness test. We demonstrate that the maximum entropy principle approach is accurate enough for practical purposes.