DocumentCode :
3624974
Title :
Can Retransmissions of Superexponential Documents Cause Subexponential Delays?
Author :
P. R. Jelenkovic;J. Tan
Author_Institution :
Columbia Univ., New York
fYear :
2007
fDate :
5/1/2007 12:00:00 AM
Firstpage :
892
Lastpage :
900
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 {(Ai, E/j)}iles1 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 les Ai, the transmission was considered successful; otherwise, we wait for the next period Ai+i 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 it was proved that the waiting time T follows a power law when the distributions of L and A1 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 alpha as long as logP[L > x] apalphalogP[A1 > 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 A1 may be. In particular, both L and A1 can decay faster than any exponential, which we term superexponential. For example, if L and A1 are Gaussian with variances sigma2 L and sigma2 A, respectively, then N and T have power law distributions with exponent alpha = sigma2 A/sigma2 L; note that, if sigma2 A<sigma2 L, the transmission time has an infinite mean and, thus, the system is unstable. The preceding model, as recognized in (Fiorini et al., 2005), 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.
Keywords :
"Delay","Wireless sensor networks","Power system modeling","Automatic repeat request","Communications Society","Channel capacity","Power engineering and energy","Sensor phenomena and characterization","Web pages","Internet"
Publisher :
ieee
Conference_Titel :
INFOCOM 2007. 26th IEEE International Conference on Computer Communications. IEEE
ISSN :
0743-166X
Print_ISBN :
1-4244-1047-9
Type :
conf
DOI :
10.1109/INFCOM.2007.109
Filename :
4215691
Link To Document :
بازگشت