By Matthew Andrews (auth.), Prathima Agrawal, Philip J. Fleming, Lisa Zhang, Daniel Matthew Andrews, George Yin (eds.)
This quantity includes papers in line with invited talks given on the 2005 IMA summer season Workshop on instant Communications, held on the Institute for arithmetic and Its purposes, collage of Minnesota, June 22 - July 1, 2005. The workshop supplied an excellent chance to facilitate the communications among academia and the undefined, and to bridge the mathematical sciences, engineering, info concept, and verbal exchange groups. The emphases have been on layout and research of computationally effective algorithms to higher comprehend the habit and to manage the instant telecommunication networks. As an archive, this quantity provides many of the highlights of the workshop, and collects papers protecting a huge spectrum of significant and urgent concerns in instant communications. All papers were reviewed. one of many book's distinctive positive factors is extremely multi-disciplinary. This booklet turns out to be useful for researchers and complex graduate scholars operating in verbal exchange networks, details conception, sign processing, and utilized chance and stochastic methods, between others.
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Mean values. The mean throughput of TCP is given by TCP(C,p) = 1° xf(x)dx. 5), after some algebraic manipulation, we can show that In the following theorem we obtain a closed form equation for TCP(C,p), which leads to a simple approximation for TCP(C,p). 10) with u ~ 1. e. 1 00 r(u) = e-Xxu-1dx . Note that f(·) is the well known gamma function and satisfies the identity I'( u + 1) == uf( u). For alIi ~ 0, define l III (u) == II (1 - 2- u- 2 k) . 11) k=O The following is proved in Appendix C. 2 (Mean TCP Throughput).
The probability of a packet error is thus ~(N) j P = j~l . [Q (0WYW [1- Q (0WY)] N-J' . Define () == (t + 1) IN. 6) where q == Q( jiiVY) and h(x) == -x log2(x) - (1- x) log2(1-x) is the binary entropy function. Notice that this approximation uses the dominant term of Stirling's formula, and that better expansions could be used. In order to determine t, or equivalently (), we use the Gilbert-Varshamov bound ( p. 463, , §IILA), which implies that for a given coding rate p, there exists a block code with "error correction capability" (), where () satisfies p == 1 - h(2()) .
At the same time, similarly to what happened for wireline networks, the emergence of high capacity applications (multimedia, gaming) and inherent mechanisms (multi-access interference) of wireless networks have led to the growing evidence of long range dependence and heavy tail characteristics in data traffic. Extending heavy traffic methods under these assumptions presents significant challenges. We discuss an approach for extending the methods in  under a heavy tail assumption only. The corresponding heavy traffic model is based on (non-Gaussian) stable Levy motion, not Brownian motion which is associated with a light tail assumption.
Wireless Communications by Matthew Andrews (auth.), Prathima Agrawal, Philip J. Fleming, Lisa Zhang, Daniel Matthew Andrews, George Yin (eds.)