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Distribution of the Number of Retransmissions of Bounded Documents
| Content Provider | Scilit |
|---|---|
| Author | Jelenković, Predrag R. Skiani, Evangelia D. |
| Copyright Year | 2015 |
| Description | 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 ℙ[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. |
| Related Links | http://www.ee.columbia.edu/~predrag/mypub/Truncated_Oct31_arxiv.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/545BA3F587F8E1E610A9605B9F61FF96/S0001867800007928a.pdf/div-class-title-distribution-of-the-number-of-retransmissions-of-bounded-documents-div.pdf |
| Ending Page | 449 |
| Page Count | 25 |
| Starting Page | 425 |
| ISSN | 00018678 |
| e-ISSN | 14756064 |
| DOI | 10.1017/s0001867800007928 |
| Journal | Advances in Applied Probability |
| Issue Number | 02 |
| Volume Number | 47 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2015-06-01 |
| Access Restriction | Open |
| Subject Keyword | Advances in Applied Probability Telecommunications Channel with Failure Truncated Distribution Gamma Distribution tailed Distribution |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability |
