PNiQ: Integration of queuing networks in generalised stochastic Petri nets

Abstract

Generalised stochastic Petri nets (GSPN) and queuing networks are combined at the modelling level by defining Petri Nets including Queuing Networks (PNiQ). The definition is especially designed to allow approximate analysis by aggregation of the queuing nets and replacing them with GSPN elements. Usually the aggregation of combined GSPN and queuing network models is carried out manually which limits the use of this technique to experts and furthermore may easily lead to modelling errors and larger approximation errors than inherent in the method. These are avoided by the definition of PNiQ which shows how to incorporate queuing networks into GSPN and provides interfaces between them. This makes combined modelling easier and less error-prone. Steady state analysis of the model can be carried out automatically: queuing network parts are analysed with efficient queuing network algorithms for large nets and replaced by GSPN subnets that model the delay of tokens in the queuing network. The resulting GSPN can then be handled with state-of-the-art tools.