Integration of multi-class queueing networks in generalized stochastic Petri Nets

In this paper, we extend Petri Nets including Queueing Networks (PNiQs) with several job classes and define Multi Class-PNiQs (MC-PNiQ). A MC-PNiQ is a Generalized Stochastic Petri Net (GSPN) which contains multiclass queueing networks (MC-QNs). This approach allows to combine the advantages of both concepts on the modelling level as well as on the analysis level. The use of MC-QNs permits concise modelling of waiting room, server and queueing and offers many fast analysis algorithms for large multiclass systems. Additionally, GSPN provide the expressiveness and flexibility for modelling of more complicated structures like fork/join, etc. The definition of MC-PNiQs is especially designed to allow a qualitative analysis based on a reduced state space, as well as automated approximate analysis by aggregation of the multi-class queueing nets and replacing them with GSPN elements. The resulting GSPN can then be analyzed with state-of-the-art methods and tools.