Recursive computation for a multi-rate model with elastic traffic and minimum rate guarantees

The main objective of the present paper is to develop an effective algorithm to calculate the performance measures for best-effort traffic transmitting over a multi-service network. We define the single link as a multi-rate loss model with elastic traffic. Elastic flows are assumed to share link capacity in an egalitarian processor sharing (EPS) manner. To ensure flows´ minimum transmission rate minimum rate guarantees are introduced. We apply state space partitioning for the number of ongoing elastic flows and maximum of their rate guarantees to obtain a recursive formula, which is the analogue of the well-known Kaufman-Roberts formula for a multi-rate system with streaming unicast traffic. In the paper, we define properties of the state space subsets and corresponding unnormalized probabilities, which are used for the recursive formula derivation. We propose a method to calculate the main model performance measures, i. e. blocking probabilities and mean transfer time.