A recursive aggragation-disaggregation method to approximate large-scale closed queueing networks with multiple job types

This paper deals with a new approximation method for large scale queueing network models with multiple job types. In recent years mean value oriented approximation algorithms have received much attention. Most of the approximation methods are based on decomposition and aggregation arguments and use iteration to obtain a fixed point of an implicitly defined set of non-linear equations for the relevant performance measures, such as mean response times, throughputs and mean queue lengths. In th is paper a recursive aggregation-disaggregation method is introduced to bypass the computational problems involved in evaluating the standard multi-dimensional recursive schemes associated with exact mean value analysis in separable queueing networks with multiple job types. As a side result we study the influence of Pollaczek-Khintchine type approximations for the mean response times at first in first-out single server queues with non-exponential service demand distributions. The power of the method is tested with a closed central server model involving multiple central processors, disk units and job types.