07-06-2010, 06:11 PM
Presented By:
G. Caroglio* , C.-F. Chiasserini* , M. Garetto , E. Leonardi*
Introduction
Mobile wireless networks are receiving an increasing interest due to the possibility of ubiquitous communications they offer. In particular, mobile ad hoc networks (MANETs) enable users to maintain connectivity to the xed network or exchange information when no infrastructure, such as a base station or an access point, is available. This is achieved through multihop communications, which allow a node to reach far away destinations by using intermediate nodes as relays. The selection and maintenance of a multihop path, however, is a fundamental problem in MANETs. Node mobility, signal interference and power outages make the network topology frequently change; 1 as a consequence, the links along a path may fail and an alternate path must be found. To avoid the degradation of the system performance, several solutions have been proposed in the literature, taking into account various metrics of interest. A method that has been advocated to improve rout- ing efciency is to select the most stable path [1“3, 29] so as to avoid packet losses and limit the latency and overhead due to path reconstruction. In this work, we focus on the stability of a routing path, which is subject to page link failures caused by node mobility. We dene the path duration as the time interval from when the route is established until one of the links along the route becomes unavailable, while we say that a path is available at a given time instant t when all links along the path are active at time t. Then, our objective is to derive the probability of path duration till time t and the probability of path availability at time t. Clearly, the probabilities of path duration and path availability strongly depend on the mobility pattern of the network nodes. Indeed, the path duration (availability) is determined by the duration (availability) of its links, which on its turn depends on the movement of a node with respect to the other. To characterize the nodes position with respect to each other, we need the spatial distribution of a single node over time. One would like to be able to evaluate these quantities in presence of various mobility models, however the analysis is extremely difcult even under simple mobility patterns [4]. (Please see Section 2.2 for a detailed discussion on related work and previous results.) Here we focus on bidimensional random mobility [5], and we consider nodes moving according to the Random Direction (RD) mobility model, which was rst introduced in [6, 7]. According to such model, each node alternates periods of movement (move phase) to periods during which it pauses (pause phase); at the beginning of each move phase, a node independently selects its new direction and speed of movement [6]. Speed and direction are kept constant for the whole duration of the node move phase. The main contributions of our work are as follows. ¢ We derive for the rst time an expression for the transform of the distribution of a node mov- ing according to the RD model. This expression can be numerically inverted to obtain the 2 temporal evolution of the probability density function of the node position, given an assigned initial condition. Closed-form expressions for the temporal evolution of the distribution mo- ments can also be derived directly from the transform (Section 4). ¢ We propose a simple, approximate expression for the probability of page link availability under the RD model, which leverages the derivation of the second moment of the node spatial distribution (Section 4.2). Our ndings suggest that, as time proceeds, the probability of page link availability under a generic mobility model can be obtained through a similar approximation. The same approach can be applied to the computation of the probability of path duration (Section 4.3). ¢ Based on our results on the probabilities of page link availability and page link duration, we study the same metrics for multihop paths, again in the case of RD mobility. We discuss the validity of the page link independence assumption, which is widely used, and compare it against a rened assumption that accounts for page link correlation (Section 5). We observe that the page link independence assumption provides sufciently accurate results. ¢ We show how our analysis can be exploited to improve the efciency of trafc routing in MANETs. In particular, we show how to select the optimal route in terms of path availability and how to determine the optimal number of hops between source and destination, taking into account the initial distance between the nodes (Section 7). We then propose an approach to nd and select routes, which accounts for the expected data transfer time over the path and allows to reduce the overhead of reactive routing protocols.
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http://tlc-networks.polito.it/leonardi/p...-MANET.pdf
