Colored stochastic Petri nets for modelling and analysis of multiclass retrial systems.

*(English)*Zbl 1165.90361Summary: Most retrial models assume that customers and servers are homogeneous. However, multiclass (or heterogeneous) retrial systems arise in various practical areas such as telecommunications and cellular mobile networks. Multiclass models are far more difficult for mathematical analysis than single class ones. So, explicit results are available only in few special cases. Actually, so far multiclass retrial systems have been analyzed only by means of queueing theory and almost all studies consider models with several customer’s classes and a service station consisting in one single server or multiple homogeneous (identic) servers and an infinite population size. In this paper, we propose an approach for modelling and analyzing finite-source retrial systems with several customer’s classes and server’s classes using the Colored Generalized Stochastic Petri Nets (CGSPNs). This high-level mathematical model is appropriate for describing and analyzing the performance of systems exhibiting concurrency and synchronization, possibly with heterogeneous components. Using a high-level formalism makes the description of the system easier, while preserving the possibility of obtaining exact performance results. We show how the main steady-state performance indices can be derived and we analyze the behaviour of heterogeneous retrial systems under two service disciplines. The numerical results are graphically displayed to illustrate the effect of system parameters and service discipline on the mean response time.

##### MSC:

90B15 | Stochastic network models in operations research |

68Q85 | Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) |

##### Keywords:

finite source multiclass retrial systems; heterogeneous customers; heterogeneous servers; colored generalized stochastic Petri nets; modelling; performance measures
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\textit{N. Gharbi} et al., Math. Comput. Modelling 49, No. 7--8, 1436--1448 (2009; Zbl 1165.90361)

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