Modeling and Analysis of Multi-class Threshold-Based Queues with Hysteresis Using Stochastic Petri Nets

This paper deals with multi-class queueing systems where thresholds are included in order to smooth the variations of throughput and delay by modifying the queue behaviour. Hysteresis is also inserted, so that the control mechanism will not switch too much. One motivation for using multiple classes of customers is its capability to model heterogeneous traffics like data, voice and video. Moreover, threshold queues have many applications in the transport protocols of communication networks. The analysis is done using Stochastic Petri Nets and Fluid Stochastic Petri Nets. This powerful paradigm helps to obtain a very simple representation of the systems and the analysis is transparent using an available Petri net package. Numerous numerical illustrations are given in order to validate the use of threshold queues with hysteresis as well as their representation by SPNs and FSPNs and performances of various scheduling schemes are compared in order to minimize a cost function.

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