Performance measures of erlangian queueing systems : a regression approach

Abstract

One of the fundamental problems for system design engineers is to estimate the performance measures of a given system prior to its implementation. At present, there does not exist an easy to use approximate methodology for dealing with multi-channel, finite capacity queueing systems with Erlang distributed arrival and service processes. Furthermore, a review of the literature has indicated that research from a queuing theoretic viewpoint has been directed to and for the academic community. In this area, there are no research methodologies that may be readily utilized by the engineering practitioner. Therefore, the purpose of this research is to provide an approximation technique for predicting the performance measure of multichannel, finite capacity queueing systems with Erlang arrival and service processes. The intended user of this technique is the system designer whose responsibility is the design and upgrading of production systems. The research used the methodologies of digital simulation and statistical regression analysis to provide a set of statistically significant predictive equations for estimating the primary system performance measures of the aforementioned systems. The response variable included the mean time in queue, mean time in system, mean server utilization, probability of waiting, probability of balking, mean inter-departure interval, variance of inter-departure intervals, and the actual mean arrival rate (into the system). The independent variable consisted of the nominal mean arrival rate, Erlang shape parameter for inter-arrival intervals, the number of service channels, maximum system capacity, traffic intensity, and the Erlang shape parameter for service times. Initially, a model was constructed to simulate the behavior of a multi-channel, finite capacity queueing system with Erlang inter-arrival intervals and service times. A wide range of systems were simulated under a full factorial experimental design. Regression analysis was then performed in an attempt to relate the performance measure to the values of the system descriptor (independent) variables. The problem of heteroscedasticity that was encountered necessitated segregating the data set into three separate subsets, according to the value of the traffic intensity...