Canonical approximation in the performance analysis of distributed systems

Abstract

The problem of analyzing distributed systems arises in many areas of computer science, such as communication networks, distributed databases, packet radio networks, VLSI communications and switching mechanisms. Analysis of distributed systems is difficult since one must deal with many tightly-interacting components. The number of possible state configurations typically grows exponentially with the system size, making the exact analysis intractable even for relatively small systems. For the stochastic models of these systems, whose steady-state probability is of the product form, many global performance measures of interest can be computed once one knows the normalization constant of the steady-state probability distribution. This constant, called the system partition function, is typically difficult to derive in closed form. The key difficulty in performance analysis of such models can be viewed as trying to derive a good approximation to the partition function or calculate it numerically. In this Ph.D. work we introduce a new approximation technique to analyze a variety of such models of distributed systems. This technique, which we call the method of Canonical Approximation, is similar to that developed in statistical physics to compute the partition function. The new method gives a closed-form approximation of the partition function and of the global performance measures. It is computationally simple with complexity independent of the system size, gives an excellent degree of precision for large systems, and is applicable to a wide variety of problems. The method is applied to the analysis of multihop packet radio networks, locking schemes in database systems, closed queueing networks, and interconnection networks