| 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. |
