Speeding up computer system simulations using hierarchical modeling

Abstract

Hierarchical modeling has been applied with great success in analyzing queueing network models of computer systems, where a direct solution is not possible. A primary example is a memory-constrained timesharing (MCT) system. In a typical two-level model, the analysis of the higher level model is carried out using performance parameters, which are obtained by analyzing the lower-level model. The higher-level model can be usually represented by a multi-dimensional Markov Chain (MC), which is generally very expensive to solve due to the large number of its states. Also the transition probabilities among the states of the MC cannot be obtained or are difficult to obtain in most cases (e.g., models for concurrency control performance). Approximate (iterative) solution methods have been adopted to alleviate the cost of solving linear equations, but the accuracy of such solutions is less predictable than decomposition. In this paper, we discuss the use of simulation for solving the higher level model. This method termed hierarchical simulation is applied to the solution of MCT systems. The accuracy of this technique is checked against direct simulation results for a set of test cases reported in the literature. We then compare the cost of hierarchical simulation against that of direct simulation and comment on its applicability.