This paper examines numerical issues in computing solutions to networks of stochastic automata. It is well-known that when the matrices that represent the automata contain only constant values, the cost of performing the operation basic to all iterative solution methods, that of matrix-vector multiply, is given by ρ N = Π N i-1 n i × Σ N i=1 n i , where n i is the number of states in the i th automaton and N is the number of automata in the network. We introduce the concept of a generalized tensor product and prove a number of lemmas concerning this product. The result of these lemmas allows us to show that this relatively small number of operations is sufficient in many practical cases of interest in which the automata contain functional and not simply constant transitions. Furthermore, we show how the automata should be ordered to achieve this.

A methodology for modeling a system composed of parallel activities with synchronization points is proposed. Specifically, an approach based on a modular state-transition representation of a parallel system called the stochastic automata network (SAN) is developed. The state-space explosion is handled by a decomposition technique. The dynamic behavior of the algorithm is analyzed under Markovian assumptions. The transition matrix of the chain is automatically derived using tensor algebra operators, under a format which involves a very limited storage cost.>

The resequencing or serialization problem is of basic interest in distributed systems and computer communication systems.This is because a flow of packets, messages, or updates entering a communication system in chronological order from the same port or from different ports may be disordered.The receiving port must then ensure that these objects are resequenced in the appropriate order before they are fed to the output of the system.In this paper we analyze the end-to-end delay recurred by objects traversing such a system, including the d~sordering delay, the delay introduced by the resequencing algorithm, and the delay due to the output server at the receiving port.The analysis is carded out via factorization methods.

In this paper an M/G/∞queue is considered that receives a stream of numbered tasks. Results are derived concerning the probabilistic properties of the reordering done by the queue.

We consider the effect on system performance of the distribution of a data base in the form of multiple copies at distinct sites. The purpose of our analysis is to determine the gain in READ throughput that can be obtained in the presence of consistency preserving algorithms that have to be implemented when UPDATE operations are carried out on each copy. We show that READ throughput diminishes if the number of copies exceeds an optimal value. The theoretical model we develop is applied to a system in which consistency is preserved through the use of Ellis' ring algorithm.