On product form approximations for communication networks with losses
Nico M. Van DIJK, H. Körezlioğlu · Digital Academic REpository of VU University Amsterdam (Vrije Universiteit Amsterdam) · 1991
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:Networks with infinite capacities but state dependent loss probabilities.(ii) Networks with finite capacities (buffers) and losses due to saturated 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.