| Many real-world systems can be modeled as queueing networks, including manufacturing and transportation systems, call centers, emergency rooms, and internet traffic. However, queueing models designed to analyze the behavior of these systems typically utilize assumptions that may be inappropriate, such as independent arrivals or interarrival and service time distributions with time-stationary parameters, to provide long-run performance measures such as the limiting queue-length and wait-time distributions (and their respective moments, such as mean and variance). In nonstationary queueing models, such long-run performance measures are not applicable instead, transient results should be provided in the form of time-dependent performance measures. Even when long-run measures for stationary queueing networks are of interest, they can be difficult to obtain if the stochastic inputs are not exponential.In this dissertation we contribute to three areas in the stochastic modeling and simulation of nonstationary queueing networks. First, we provide a comprehensive survey of techniques for approximating a general point process by a Markovian point process, with an emphasis on those techniques that utilize a nonrenewal Markovian Arrival Process in capturing some measure of the original process' dependence structure. We also develop techniques for simulating arrival processes with non-constant arrival rates that may be more or less variable than Poisson, and extend these techniques to simulating nonrenewal arrival processes. Finally, we propose techniques for modeling the departure flow from an upstream node in a nonstationary tandem queueing network as the arrival process input to its immediate downstream node. |
