Uniform approximation of the distribution for the number of retransmissions of bounded documents

Retransmission-based failure recovery represents a primary approach in existing communication networks, on all protocol layers, that guarantees data delivery in the presence of channel failures. Contrary to the traditional belief that the number of retransmissions is geometrically distributed, a new phenomenon was discovered recently, which shows that retransmissions can cause long (-tailed) delays and instabilities even if all traffic and network characteristics are light-tailed, e.g., exponential or Gaussian. Since the preceding finding holds under the assumption that data sizes have infinite support, in this paper we investigate the practically important case of bounded data units 0≤ Lb≤ b. To this end, we provide an explicit and uniform characterization of the entire body of the retransmission distribution Pr[Nb > n] in both n and b. This rigorous approximation clearly demonstrates the previously observed transition from power law distributions in the main body to exponential tails. The accuracy of our approximation is validated with a number of simulation experiments. Furthermore, the results highlight the importance of wisely determining the size of data units in order to accommodate the performance needs in retransmission-based systems. From a broader perspective, this study applies to any other system, e.g., computing, where restart mechanisms are employed after a job processing failure.