Quantitative system performance: computer system analysis using queueing network models
Quantitative system performance: computer system analysis using queueing network models
RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks
Journal of the ACM (JACM)
IEEE Transactions on Computers
IEEE Transactions on Computers
Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets
Performance Evaluation
Mean value analysis of stochastic Petri nets
Performance Evaluation
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Product Form and Local Balance in Queueing Networks
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Generalized Stochastic Petri Nets: A Definition at the Net Level and its Implications
IEEE Transactions on Software Engineering
Product Form Solution for Generalized Stochastic Petri Nets
IEEE Transactions on Software Engineering
Performance engineering with product-form models: efficient solutions and applications
Proceedings of the 2nd ACM/SPEC International Conference on Performance engineering
Hi-index | 0.01 |
In this paper we study the relations between multi-class BCMP-like service stations with Coxian service time and generalized stochastic Petri nets (GSPN). We consider multi-class product-form service center types of QN and their representation with GSPN, in order to investigate the relation between the product-form solutions of the two models. Representing queueing discipline with GSPN models is not easy. We focus on representing multi-class queueing systems with LCFSPR scheduling discipline and Coxian distributed service time. Note that the queueing discipline in general affects performance measures in multi-class systems. For example, BCMP-like service centers with First Come First Served (FCFS) and with Last Come First Served with Preemptive Resume (LCFSPR) have a (different) product-form solution under different hypotheses. We define a structurally finite GSPN model with product- form that does not belong to the class of known product-form GSPN. Then we show that this model is equivalent to the multi-class M/COX/k/LCFSPR queueing system, in terms of steady state probability and average performance measures. The main idea is to define a finite GSPN model that simulates the behavior of the given queue discipline by defining some appropriate random choices. Moreover, we prove that the combination of the introduced equivalent GSPN model has a closed-form steady state probability by the M ⇒ M property.