CONTRIBUTIONS TO THE THEORY OF SPATIALLY DISTRIBUTED FACILITY UTILIZATION IN A STOCHASTIC SERVICE SYSTEM

Effective regional planning and management of service facilities operating in a stochastic environment require a solid understanding of the demand processes of the customers being served. This thesis is concerned with the analysis of descriptive and normative models for the distribution of facility utilization. Descriptive models involve modeling the individual customer\u27s facility choice in terms of probabilities which are functions of facility attributes. The theoretical foundation of the resulting disaggregate stochastic choice model and its equilibrium properties are examined. Results include proof of existence, uniqueness and global stability of an equilibrium for facility utilization for the general case where demand may be affected by congestion levels at the facilities. The disaggregate choice model is then applied to the particular case of the spatial distribution of hospital utilization within a region. Specifically, a multinomial logit model of hospital utilization is developed, estimated and evaluated, using data from a statewide hospital system. The results indicate that the disaggregate choice model gives a very good fit to the data. The role of physicians in the patient\u27s hospitalization decisions leads to the development of a normative facility utilization model. This model assumes that customers have to interact with agents who direct them to the service facilities. This model, formulated as a multiple-facility and multiple-channel queueing system with parallel input streams from multiple-agents, is analyzed in three ways. First, the problem of optimal customer allocation by an agent is considered, using performance measures such as the agent\u27s workload and customer\u27s average waiting time. A marginal allocation algorithm is developed. Second, we consider a game-theoretic formulation for the problem in which agents simultaneously optimize their customer allocation decisions. Equilibrium analysis of such a game include existence, uniqueness, stability and system efficiency of the equilibrium point. Third, the normative model is used to evaluate the possibility of collaboration, which involves exchanges in the rates of customer allocation, among agents. It is shown that, depending upon the performance measures used, agents may or may not have incentives to participate in such collaboration