On Product Form Approximations for Communication Networks with Losses: Error Bounds

This paper studies communication networks with packet or message losses due to collisions, transmission errors and finite buffer constraints. A priori and easily computable error bounds are established for simple product form approximations. These approximations are based on ignoring and/or bounding loss probabilities. Two extreme situations are considered: (i) Networks with infinite capacities but s tate dependent loss probabilities. (ii) Networks with finite capacities (buffers) and losses due to sa turated buffers. The error bounds are of order |3, thought of as small, when: (i) The loss probabilities are uniformly bounded by |3, or (ii) The steady state probability of capacity excess is of order 0. The results provide formal justification for practical engineering and seem of interest for further extension to more complex communication networks. Key-words Packet switching « circuit switching • communication networks « loss probabilities * product form approximations • er ror bounds. Acknowledgement The research of this paper has been supported by a grant from the "Centre National de la Recherche Scientifique". The f i rs t author also wishes to thank the Network Department of the "Ecole Nationale Supérieure des Télécommunications" in Paris for i ts hospitality and the organization of the visits during which this paper was written.