The queueing theory of the Erlang distributed interarrival and service time

This dissertation details the study on non-Markovian queueing systems contributed mainly to Erlang distributed interarrival and service time that expands beyond the knowledge outlined in Poisson arrival and departure rate.;The Erlang distribution can be used to model interarrival and service time with a low coefficient of variation (less than one). This author introduced a new method of Possible Probability Stages Searching Algorithm (PSA) and applied stochastic algebra, calculus and the theory of Martingales to derive the System Measures that had never been obtained. He also utilized the simulation method to further estimate the point beyond today's computational ability.;Queueing theory can be applied in a wide variety of fields - including the purview of Management Science. Despite the said fact, works to date have focused primarily on the estimation of the queueing statistics based upon the Poisson arrival and Poisson departure rate on Exponential distribution.;The principle objective of this dissertation is to develop tables of standardized queueing statistics determined by coefficient of variation deriving from Erlang distribution to facilitate the arbitrary interarrival and arbitrary service time in order to yield more precise queueing statistics given by any statistic distribution that differs from the Exponential to be applied and referred to by workers/researchers. In the process of developing these tables, all the queueing statistics calculated by the Erlang distribution form a predictable pattern. The interpretation will allow estimating the statistic measures for any Cov from 0.0 to 1.0.