Data Centers (DCs) are required to be scalable to large data sets so as to accommodate ever increasing demands of resource-limited embedded and mobile devices. Thanks to the availability of recent high data rate millimeter-wave frequency spectrum such as 60GHz and due to the favorable attributes of this technology, wireless DC (WDC) exhibits the potentials of being a promising solution especially for small to medium scale DCs. This paper investigates the problem of throughput scalability of WDCs using the established theory of the asymptotic throughput of wireless multi-hop networks that are primarily proposed for homogeneous traffic conditions. The rate-heterogeneous traffic distribution of a data center however, requires the asymptotic heterogeneous throughput knowledge of a wireless network in order to study the performance and feasibility of WDCs for practical purposes. To answer these questions this paper presents a lower bound for the throughput scalability of a multi-hop rate-heterogeneous network when traffic generation rates of all nodes are similar, except one node. We demonstrate that the throughput scalability of conventional multi-hopping and the spatial reuse of the above bi-rate network is inefficient and henceforth develop a speculative 2-partitioning scheme that improves the network throughput scaling potentials. A better lower bound of the throughput is then obtained. Finally, we obtain the throughput scaling of an i.i.d. rate-heterogeneous network and obtain its lower bound. Again we propose a speculative 2-partitioning scheme to achieve a network with higher throughput in terms of improved lower bound. All of the obtained results have been verified using simulation experiments.
in @cite_11 , removed the gap between the throughput of randomly located and arbitrarily located nodes, and showed the total throughput scales by @math .
@cite_11
2116844604 2108190032 2507181206 2115678412
In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling characterization of throughput scaling for random extended wireless networks (i.e., n nodes are placed uniformly at random in a square region of area n). They showed that for small path-loss exponents alpha isin (2,3], cooperative communication is order optimal, and for large path-loss exponents alpha > 3, multihop communication is order optimal. However, their results (both the communication scheme and the proof technique) are strongly dependent on the regularity induced with high probability by the random node placement. In this paper, we consider the problem of characterizing the throughput scaling in extended wireless networks with arbitrary node placement. As a main result, we propose a more general novel cooperative communication scheme that works for arbitrarily placed nodes. For small path-loss exponents alpha isin (2,3], we show that our scheme is order optimal for all node placements, and achieves exactly the same throughput scaling as in Ozgur. This shows that the regularity of the node placement does not affect the scaling of the achievable rates for alpha isin (2,3]. The situation is, however, markedly different for large path-loss exponents alpha > 3. We show that in this regime the scaling of the achievable per-node rates depends crucially on the regularity of the node placement. We then present a family of schemes that smoothly ldquointerpolaterdquo between multihop and cooperative communication, depending upon the level of regularity in the node placement. We establish order optimality of these schemes under adversarial node placement for alpha > 3. We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider n identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other nodes. Throughput is measured in bit-meters per second. We provide a very elementary deterministic approach that gives achievability results in terms of three key properties of the node locations. As a special case, we obtain spl Omega ( spl radic n) throughput for a general class of network configurations in a fixed area. Results for random node locations in a fixed area can also be derived as special cases of the general result by verifying the growth rate of three parameters. For example, as a simple corollary of our result we obtain a stronger (almost sure) version of the spl radic n spl radic (logn) throughput for random node locations in a fixed area obtained by Gupta and Kumar. Results for some other interesting non-independent and identically distributed (i.i.d.) node distributions are also provided. Given any r and n, we present an explicit construction of high-rate maximum distance separable (MDS) array codes that can optimally repair any d failed nodes from any h helper nodes for all h, 1 ≤ h ≤ r and d, k ≤ d ≤ n − h simultaneously. These codes can be constructed over any base field F as long as |F| ≥ sn; where s = lcm(1, 2, …, r). The encoding, decoding, repair of failed nodes, and update procedures of these codes all have low complexity. Our results present a significant improvement over earlier results which can only construct explicit codes for the case of at most 3 parity nodes, and these existing constructions can only optimally repair a single node failure by accessing all the surviving nodes. In the second part of the paper we give an explicit construction of Reed-Solomon codes with asymptotically optimal repair bandwidth. Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per source-destination pair is Theta(1 radic(nlogn)). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant throughput scaling per source-destination pair. In most applications, delay is also a key metric of network performance. It is expected that high throughput is achieved at the cost of high delay and that one can be improved at the cost of the other. The focus of this paper is on studying this tradeoff for wireless networks in a general framework. Optimal throughput-delay scaling laws for static and mobile wireless networks are established. For static networks, it is shown that the optimal throughput-delay tradeoff is given by D(n)=Theta(nT(n)), where T(n) and D(n) are the throughput and delay scaling, respectively. For mobile networks, a simple proof of the throughput scaling of Theta(1) for the Grossglauser-Tse scheme is given and the associated delay scaling is shown to be Theta(nlogn). The optimal throughput-delay tradeoff for mobile networks is also established. To capture physical movement in the real world, a random-walk (RW) model for node mobility is assumed. It is shown that for throughput of Oscr(1 radic(nlogn)), which can also be achieved in static networks, the throughput-delay tradeoff is the same as in static networks, i.e., D(n)=Theta(nT(n)). Surprisingly, for almost any throughput of a higher order, the delay is shown to be Theta(nlogn), which is the delay for throughput of Theta(1). Our result, thus, suggests that the use of mobility to increase throughput, even slightly, in real-world networks would necessitate an abrupt and very large increase in delay.