Distribution of the Number of Retransmissions of Bounded Documents

TL;DR

This paper analyzes the distribution of retransmissions for bounded data units in communication networks, revealing a combined power law and Gamma distribution model that aids in system design and performance prediction.

Contribution

It provides a novel explicit characterization of retransmission distributions for bounded data, showing their structure as a product of power law and Gamma distributions.

Findings

Retransmission distribution can be modeled as a product of power law and Gamma distribution.

The model accurately predicts tail behavior and is validated by simulations.

Results assist in designing systems with specific retransmission performance requirements.

Abstract

Retransmission-based failure recovery represents a primary approach in existing communication networks that guarantees data delivery in the presence of channel failures. Recent work has shown that, when data sizes have infinite support, retransmissions can cause long (-tailed) delays even if all traffic and network characteristics are light-tailed. In this paper we investigate the practically important case of bounded data units 0 <= L_b <= b under the condition that the hazard functions of the distributions of data sizes and channel statistics are proportional. To this end, we provide an explicit and uniform characterization of the entire body of the retransmission distribution Pr[N_b > n] in both n and b. Our main discovery is that this distribution can be represented as the product of a power law and Gamma distribution. This rigorous approximation clearly demonstrates the coupling of a power law distribution, dominating the main body, and the Gamma distribution, determining the exponential tail. Our results are validated via simulation experiments and can be useful for designing retransmission-based systems with the required performance characteristics. From a broader perspective, this study applies to any other system, e.g., computing, where restart mechanisms are employed after a job processing failure.