Modeling and analysis of threshold queues with hysteresis using stochastic Petri nets: the monoclass case

We consider a monoclass threshold queue with hysteresis. Many applications of such a system can be found in the transport protocols of communication networks. Thresholds help to smooth the variations of delay and throughput, and hysteresis limits the number of (expensive) switches of the control mechanism. The queues are modeled and analysed by means of Stochastic Petri Nets (SPNs), a powerful paradigm to represent complex systems. The representation is shown to be very simple and can aid in the study and configuration of the queue to conform to design specifications. Moreover, Fluid Stochastic Petri Nets (FSPNs) are used as an approximation which might be helpful to analyse high speed networks. Numerical illustrations are given in order to validate the choice of threshold queues with hysteresis and their representation by SPNs and FSPNs.