This work deals with the problem of estimating performance measures for spatially distributed networks serviced by mobile servers. The demands are generated stochastically at the nodes and the service units, stationed in service centers when available, travel to the calls and service them according to a pre-selected policy. These types of networks are frequently encountered in the manufacturing industry, for example robotic repair systems found in textile plants and flexible auto manufacturing plants, as well as in public sector service industries like emergency services (police, ambulance and fire service). Another important manifestation is in the design of field support for products. In this work, we concentrate on developing models for obtaining the performance measures of interest, namely the fraction of time the machine are up and running in the case of manufacturing facilities, and the average response time to a random call for an emergency service facility or a product support facility. Whenever a call is placed, a service unit will travel (immediately, if available) to the call's location and will provide the service required. Otherwise, the call will enter a queue at that node that may have finite or infinite capacity. The service units travel from node to node serving the calls and return to the service center only when there are no more calls waiting. Thus, travel times play a major role in designing the system. The system can be modeled by using a semi-Markov chain but the technique is manageable only under certain special conditions, for example in the case of small or symmetric networks with only one server. For most practical cases, however, the exact models are too complicated to solve because they require considering exponentially large number of states of the system. Approximate methods seem to be the only promising way of modeling these complicated systems to obtain the desired performance measures which can then be used to make strategic (e.g. location) or operational (e.g. dispatching) decisions. This thesis presents several such methods based on relatively simple approximations which are tested using simulation and found to give good results.

We propose four models for evaluating and benchmarking performance in Emergency Medical Service (EMS) systems. We begin by studying tiered EMS systems, whose fleets are comprised of ambulances providing either Advanced Life Support (ALS) or Basic Life Support (BLS), with the goal of studying the effects of vehicle mix (that is, the combination of ALS and BLS ambulances deployed) on system performance. The ideal choice of vehicle mix has been the subject of some debate in the medical literature, and we contribute to this debate by developing a framework with which quantitative comparisons between vehicle mixes can be made. Noting that vehicle mix affects how resources are allocated to emergency calls, we build two stylized, but complementary models to study decisionmaking in tiered EMS systems. First, to examine how ambulances would be dispatched to incoming calls of varying severity, we consider the problem of routing and admission control in a loss system featuring two classes of servers and arriving jobs. We formulate this problem as a Markov decision process, and study its theoretical properties. Second, to study how ambulances would be deployed to base locations to maximize coverage, we formulate an integer program. By combining insights from our models, we conclude there are rapidlydiminishing marginal returns associated with biasing towards all-ALS fleets. Next, we consider systems practicing ambulance redeployment, the strategic relocation of idle ambulances in real time to improve responsiveness to future calls. Finding an optimal redeployment policy is computationally intractable, and a number of heuristic policies have been proposed. We complement this stream of literature by proposing two upper bounds on the performance of optimal redeployment policies (which, in turn, serve as benchmarks for existing heuristic policies). First, we adapt an existing upper bound so that it is provably valid for EMS providers who operate loss systems. Second, we develop a new upper bound based upon a perfect information relaxation of the EMS provider's problem (in which the decisions-maker is clairvoyant), which we tighten by penalizing policies that use future information to make decisions. We evaluate our bounds through extensive computational experiments, and find that they are reasonably tight in small-scale systems.

The Rapid Visual Screening (RVS) handbook can be used by trained personnel to identify, inventory, and screen buildings that are potentially seismically vulnerable. The RVS procedure comprises a method and several forms that help users to quickly identify, inventory, and score buildings according to their risk of collapse if hit by major earthquakes. The RVS handbook describes how to identify the structural type and key weakness characteristics, how to complete the screening forms, and how to manage a successful RVS program.