Asymptotic analysis of multiclass closed queueing networks: Common bottleneck

Asymptotic expressions for the values of throughputs, utilizations, mean cycle times, and mean queue lengths are derived for certain types of multiclass queueing networks with load independent stations. The relation between these results and their counterparts for single class queueing networks are analysed. The behaviours of the performance figures derived for each individual class are discussed with an emphasis on the presence of correction factors in the limit expressions for the response times. Extrapolations of the limit results to finite population values are proposed as approximations of the actual behaviour of the network for intermediate load conditions. Numerical values are presented to substantiate the practical relevance of these results.