9404947 Kobayashi Network technologies have been progressing rapidly toward faster and larger networks which are capable of providing integrated services. These technical developments in turn require advances in analytic methodologies that can be effectively used in the design and control of future networks such as ATM-based B-ISDN, all-optical networks and wireless communication networks. Emerging high-speed integrated communication services require us to analyze network systems, in which information loss probabilities range from 10**-2 (e.g., call connection loss) to as small as 10**-10 (e.g., ATM cell loss). In this proposed study we will develop a theoretical foundtion for evaluation and control of connection-oriented services, which in particular will enable us to handle this wide range of loss probabilities. We begin by generalizing the product form solutions obtained for loss networks with fixed routing. Our formulation encompasses a broad range of state-dependent call generation patterns, different types of network services, and the whole range of traffic levels. Using our experience in computational algorithms for closed queueing network models, we will develop new practical methods for estimating loss probabilities in connection-oriented services. In order to insure the accuracy of approximate formulas, we will develop appropriate error bounds. A refinement and a rigorous validation of the reduced load approximation method, also referred to as the Erlang's fixed point method in the case of Poisson arrivals, will be attempted for networks with state dependent arrivals. In parallel with the above algorithmic and asymptotic methods, we will explore a model of connection-oriented network services based on a multi-dimensional Ornstein-Uhlenbeck diffusion process. The diffusion process approach will allow us not only to evaluate more general types of networks (i.e., loss/queueing networks not amenable to product form solutions) but also to obtain time-dependent, i.e., transient, solutions for network behavior. Finally, we will formulate and solve network control policy problems such as call admission control and routing decisions. ***
