Higher-order approximations for general open queueing networks

Many sophisticated modern systems such as automated manufacturing systems, computer and communication systems are often modeled as queueing networks. Two of the most important issues in the design, control and operation of these systems are accurate modeling and performance evaluation. The stochastic nature of queueing networks makes them difficult to be analyzed in closed form, except for some special cases. On the other hand, computer simulation is expensive and time consuming. Hence, researchers and practitioners have sought approximation techniques to model and analyze queueing networks.;This thesis contributes to enhanced and more accurate approximation methods through higher order approximations. The results form frameworks for studying the effects of higher moments and correlations on the accuracy of queueing performance measures. This thesis starts with the single server queue with general independent and Markov-modulated interarrival and service time distributions. A higher order approximation is developed based on the MacLaurin series of the moments of the performance measures. A novel interpolation approximation is proposed which combines the heavy traffic limits and any number of the light traffic derivatives using the theory of multipoint Pade approximation. Numerical results show that this approximation produces improved estimates of the waiting and interdeparture time moments over the second order approximations when compared with computer simulation. Two procedures for approximately modeling correlated arrivals in communication networks are also derived by matching moments as well as autocorrelations.;The above analysis is then extended to tandem and general queueing networks. Higher order approximations based on parametric decomposition and moment matching are developed. Essential features of general queueing networks such as splitting, merging and feedback are studied. Numerical examples are presented to illustrate the accuracy of these approximations. It is observed that the higher order approximations improve the estimation of the moments of the waiting time.;Finally, an application to manufacturing is reported as a case study. The principles and methods drawn from queueing networks and optimization theory are used to enhance the performance of a semiconductor wafer fabrication line whose average throughput increased by 40%.