APPROXIMATING NONSTATIONARY MULTIVARIATE QUEUEING MODELS
Abstract
Phase distributions take a variety of shapes from deterministic to exponential to approximately normal, and thus are useful in constructing realistic models. Inter-arrival and service processes in real queueing systems are more typically nonstationary than stationary. This research develops a method to accurately approximate the behavior of finite capacity queueing systems that have nonstationary phase processes for inter-arrival and service processes. The algorithms avoid the usual evaluation of large sets of Kolmogorov forward equations by making use of a moment matching surrogate distribution approximation (SDA) approach. SDA methods are also used to approximate overflow models and models where either the arrival mechanism or the servers can fall randomly for a random amount of time. Performance measures produced by the SDA algorithms are nonstationary queue size probabilities and moments as well as nonstationary virtual wait-time distributions and moments. Numerical results show that SDA methods are efficient, accurate and robust to the particular types of time-dependent phase distributions being analyzed.
Degree
Ph.D.
Subject Area
Industrial engineering
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.