This work is devoted to the study of a class of queueing networks with certain properties, namely those with discontinuous performance measures. An important subclass consists of networks with real-time constraints, where jobs must arrive at their destination within given deadlines, otherwise they are considered lost. Performance in such networks is measured by the probability a job is lost. For a network of K parallel links with a probabilistic routing scheme, consider the problem of optimal routing. Assuming the availability of a closed-form expression for the probability of loss across each link, the problem is solved under general conditions and properties of the optimal flow allocation are given. However, an analytical expression often cannot be derived, in which case other optimization approaches are necessary. One alternative is to use approximate analysis. Two suboptimal heuristic routing schemes are presented and compared. A second alternative involves implementing an on-line gradient-based stochastic optimization algorithm. Such algorithms require performance gradient estimates with respect to the control parameter. The methods of Perturbation Analysis (PA) and the Likelihood Ratio (LR) have been developed to supply the derivative estimates required. Smoothed Perturbation Analysis (SPA) is a specific PA approach suited to gradient estimation problems with discontinuous sample performance functions. SPA overcomes the normal difficulty of discontinuities by defining alternative sample performance functions that are conditioned forms of the original sample functions, such that the discontinuities are smoothed out. Here, a new SPA approach is developed that extends the applicability of SPA to cover additional performance measures including the probability of loss in real-time networks. New SPA gradient estimators are presented for this and other problematic performance measures such as the probability an arriving customer finds an idle server and the network occupancy as seen by an arrival to a tandem network. The convergence rate of SPA and LR gradient estimators are compared experimentally. Furthermore, the effectiveness of SPA gradient estimation in on-line stochastic optimization problems is demonstrated by coupling an SPA algorithm with a sampling-controlled stochastic version of Gallager's algorithm for the routing problem described above.

Queueing Theory has been successfully and extensively applied to the scheduling, control, and analysis of complex stochastic systems. In this dissertation, the problems of optimal scheduling, control and analysis of bulk service queueing systems are studied. A Dynamic Programming formulation is provided for the optimal service strategy of a two-server bulk queue. An extension of the general bulk service rule is shown to be optimal in the sense of minimizing either the finite discounted or average waiting cost. It is shown that the optimal dispatching rule is a multi-stage threshold type where servers are dispatched only when the number of waiting customers exceeds certain threshold values depending both on the number of waiting customers and the number of servers available at decision epochs. It is conjectured that the result is extendable to the case for more than two servers. Exact analysis of the state probability in equilibrium is carried out under the optimal policy obtained for a queue with two bulk servers. Comparison of the optimal threshold policy is carried out by evaluating a single stage vs. a two-stage threshold two-server system. By calculating the mean number of customers waiting in the queue of both systems, it is shown that a two-stage threshold policy yields optimal performance over the general bulk service rule under any operating condition. Examples for different parameter sets are provided. A network of two bulk service queues served by a common transport carrier with finite capacity is analyzed where the general bulk service rule is applied only at one queue. Decomposition is employed to provide an exact analysis of the steady-state probability distribution, mean waiting time distribution, and mean number of customers waiting at both queues in equilibrium. Networks of more than two bulk service queues can be analyzed by direct extension of the methodology. An optimization procedure for the optimal threshold value to minimize total mean waiting cost is also discussed.

Cold extrusion of components (also called cold forging and cold impact extrusion) requires a sequence of operations to transform an initial simply shaped billet into a desired complex part. To determine the most feasible extrusion sequence is an intensive knowledge-based process planning task currently done by experienced process designers. In this study, a prototype of a knowledge-based system is developed which can become a very useful aide to human process planners. In the system, parts are classified into groups and a features representation is used. A new classification of extrusion operations is also introduced. To generate process plans, the system selects operators corresponding to the reverse of actual extrusion operations. The feasibility of each selected operator is checked with empirical rules. The strategy of backward exhaustive search for operators is employed. The current system requires input of the geometry of a part to be produced along with certain material and process data. Then the formable part geometry and process plans are generated automatically. The system also rates the process plans from the perspective of achieving economical production. A cost estimating model is proposed so that users can obtain production cost for a selected process plan based on the data they provide.

Today's Continuous Flow Manufacturing (CFM) systems are the integration of several manufacturing components found in traditional manufacturing facilities. They contain groups of machines (facilities, work centers or cells) linked together by transport systems (material handlers, conveyors, etc.). Series of parts are transported from one facility to the next depending on operation sequences. Usually, a major problem encountered in the optimal design of a CFM system is the assignment of these manufacturing components onto appropriate locations in the layout to obtain efficient CFM configurations with preferable flow of products and resource utilization. In this research, optimal operation allocations to groups of machines in a facility is termed the Resource Assignment Subproblem or RAS. The task of locating facilities onto predefined locations in the layout, taking into consideration operation sequences, is termed the Location Assignment Subproblem or LAS. Both the RAS and LAS generally involve complicated discrete mathematical models, thus, many past researchers have chosen to investigate them separately. Recent research conducted by Ketcham (1992a) has led to a mathematical representation which integrates LAS and RAS into a single model, called the Configuration Problem (CP). The solution method, which is a heuristic called the Resource Assignment algorithm, is also found to provide acceptably good solutions for complex models using reasonable computational efforts. The current implementation of the Resource Assignment algorithm, however, becomes inadequate for today's large-scale CFM facilities, where many products are produced at different sites. Thus, enhanced methodologies are developed in this research so that systems of various complexity and characteristics can be optimized more efficiently. The study of algorithm performance and solution characteristics has led to several enhancement techniques. The collection of these techniques, called the Meta-algorithm is a set of decision rules that suggests an optimization strategy, for the Resource Assignment algorithm, based on the characteristics of a given CFM system. The robustness of the Meta-algorithm is tested against a wide range of trial cases representing large-scale CFM systems found in industrial practice. Overall improved performance has been achieved by the Meta-algorithm, which is found most effective for segmenting and solving large-scale problems infeasible for the existing Resource Assignment algorithm.

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