On loss probabilities in presence of redundant packets with random drop

The purpose of this paper is to study the loss probabilities of messages in an M/M/1/K queueing system where in addition to losses due to buffer overflow there are also random losses in the incoming and outgoing links. We focus on the influence of adding redundant packets to the messages (as in error correction coding, e.g. Reed–Solomon code, etc.). In the first part we use multi-dimensional probability generating functions for solving the recursions which generalize those introduced by Cidon et al. [IEEE Trans. Inform. Theory 39 (1) (1993) 98] for computing the loss probabilities and derive analytical formulae for a special case. In the second part of the paper we use combinatorial arguments and Ballot theorem results to alternatively obtain the loss probabilities. The analytical results allow us to investigate when does adding redundancy decrease the loss probabilities.