Name
Abstract | ||
|---|---|---|
Consider a generic data unit of random size L that needs to be transmitted over a channel of unit capacity. The channel dynamics is modeled as an on-off process {(A(i), U-i)}(i >= 1) with alternating independent periods when channel is available Ai and unavailable Ui, respectively. During each period of time that the channel becomes available, say Ai, we attempt to transmit the data unit. If L < Ai, the transmission was considered successful; otherwise, we wait for the next period A(i+1) when the channel is available and attempt to retransmit the data from the beginning. We study the asymptotic properties of the total transmission time T and number of retransmissions N until the data is successfully transmitted.In recent studies [1], [2], it was proved that the waiting time T follows a power law when the distributions of L and A, are of an exponential type, e.g., Gamma distribution. In this paper, we show that the distributions of N and T follow power laws with exponent a as long as log P[L > x] approximate to alpha log P[A(1) > x] for large x. Hence, it may appear surprising that we obtain power law distributions irrespective of how heavy or light the distributions of L and A(1) may be. In particular, both L and A(1) can decay faster than any exponential, which we term superexponential. For example, if L and A(1) are Gaussian with variances sigma(2)(L) and sigma(2)(A), respectively, then N and T have power law distributions with exponent alpha = sigma(2)(A)/sigma(2)(L); note that, if sigma(2)(A) < sigma(2)(L), the transmission time has an infinite mean and, thus, the system is unstable.The preceding model, as recognized in [1], describes a variety of situations where failures require jobs to restart from the beginning. Here, we identify that this model also provides a new mechanism for explaining the frequently observed power law phenomenon in data networks. Specifically, we argue that it may imply the power laws on both the application as well as the data link layer, where variable-sized documents and (IP) packets are transmitted, respectively. We discuss the engineering ramifications of our observations, especially in the context of wireless ad hoc and sensor networks where channel failures are frequent. Furthermore, our results provide an easily computable benchmark for measuring the matching between the data and channel characteristics that permits/prevents satisfactory transmission. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1109/INFCOM.2007.109 | INFOCOM 2007, VOLS 1-5 |
Keywords | Field | DocType |
ad hoc networks,automatic repeat request,gamma distribution,sensor network,power law,web pages,internet,channel capacity,link layer,wireless sensor networks,power law distribution | Discrete mathematics,Exponential function,Exponent,Computer science,Computer network,Communication channel,Gaussian,Transmission time,Gamma distribution,Exponential type,Power law | Conference |
ISSN | Citations | PageRank |
0743-166X | 25 | 1.80 |
References | Authors | |
4 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Predrag R. Jelenkovic | 1 | 219 | 29.99 |
| Jian Tan | 2 | 25 | 1.80 |