Computation of the residual packet loss probability in a binary multicast tree

In order to achieve a better quality of service (QoS), the use of reliable multicasting has become increasingly important especially with the emergence of Internet-based applications such IP telephony, audio/video conferencing. In this paper, the residual packet loss probability in a complete binary multicast tree which consists of N routers with a given probability of successful delivery to the next router is evaluated, when automatic repeat request (ARQ) multicast repairs is employed. In this paper, we also derive and compare two other mathematical expressions, which can be used to calculate the final packet loss probability in a binary tree where reliable ARQ multicasting is used. These expressions can be used in the case of IP or MPLS multicasting. The first expression, which is called the average packet loss probability for ARQ deals only with the number of routers that should have correct transmissions (no loss and no errors) during the repair trial of one previous loss depending on the location of this previous loss. The second one, which is called the accurate expression, takes into account the number of trials, the number of errors and the position of each error (at which level the error occurred).