Pointwise stationary fluid models for design and control of stochastic processing systems.

摘要

This thesis consists of three articles addressing design and control of stochastic processing systems. The first two parts are concerned with the special structure of telephone call centers, or customer contact centers, whereas the third part considers a more general kind of stochastic processing network.; In the first part, we analyze a call center model with m customer classes and r agent pools. The model is one with doubly stochastic arrivals, which means that the m-vector lambda of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of call center management are considered: staffing the r pools of agents and dynamically routing calls to agents. The system manager's objective is to minimize the sum of personnel costs and abandonment penalties. We consider a limiting parameter regime that is natural for call centers. For that parameter regime we prove an asymptotic lower bound on the expected total cost, which uses a strikingly simple distillation of the original system data. We then propose a method for staffing and routing based on linear programming (LP), and show that it achieves the asymptotic lower bound on the expected total cost; in that sense the proposed method is asymptotically optimal.; The second part considers the same model as before. However, the system manager does not know the distribution of the arrival rates. Instead, he has access to a historical database of call arrivals. We propose a simple and computationally tractable method for sizing the server pools that requires no information about arrival processes other than the historical data. Further, we derive asymptotic bounds on the performance of this data-driven staffing solution.; In the final part, we generalize the analysis of staffing and routing in telephone call centers to include the following: a processing network with multiple server pools, jobs that may require several processing operations, doubly stochastic input flows, differentiated processing modes, and other features as well. We address the two-level problem of capacity choice and dynamic system control. A tractable modeling framework is proposed, generalizing the analytical method developed earlier for call centers. In this approach a pointwise stationary fluid model (PSFM) is used to approximate the system's dynamics.