Flow level performance analysis of a multi-service system supporting elastic and adaptive services

We consider a multi-rate loss system where two types of non-peak allocated traffic flows receive service. Both elastic and adaptive flows are associated with a peak- and a minimum bandwidth requirement and they tolerate bandwidth compression while in service. The holding time of elastic flows depends on their received throughput, while the holding time of the adaptive flows is insensitive to that. Unfortunately, while this system is Markovian under quite non-restrictive assumptions (that are often used in the literature), it is not reversible. We propose a method whereby the approximation of this system by a reversible system is possible. We derive recursive formulas for determining the occupancy distribution and the mean number of flows in the system. By using a continuous approximation of the discrete state space, we also derive an explicit formula for the average throughputs that is independent of the size of the state space. The recursive formulas and the continuous approximation together provide a powerful tool for the performance analysis of this quite general system in the sense that they allow the calculation of the blocking probabilities and the mean throughputs in medium and large systems as well.