On the optimality of field-line routing in massively dense wireless multi-hop networks

Abstract

A B S T R A C TWe consider the load balancing problem in large wireless multi-hop networks by applying the continuum approximation. The task is to find routes, geometric curves, such that the maximal traffic load in the network is minimized. In finite fixed networks, multi-path routes generally yield a lower congestion and thus allow higher throughput. In contrast, we show that in dense wireless multi-hop networks, the optimal load balancing can be achieved by a destination based single-path routing referred to as field-line routing. This is because any routing can be transformed to the corresponding field-line routing with the same or better performance, by using as paths, the field lines of the so-called destination flow associated with the original routing. The concepts are illustrated with two examples. In the case of a unit disk with unit traffic, the maximal load of 0.389 of a multi-path routing system is reduced to 0.343 by using the field-line routing. Similar improvements are also demonstrated for the unit square.

Continuum equilibria and global optimization for routing in dense static ad hoc networks

“…The forwarding load appears to correspond to the scalar sum of traffic flows of different classes. This means that the optimal solution (with respect to this objective) can be achieved by single path routes, a result obtained also in [15]. Similar problems have been also studied in [8], as well as in works doing load balancing by analogies to Electrostatics (see e.g.…”

Gauss-seidel correction algorithm

“…They further showed that, in the limit of massively-dense networks, multiple-path routing for optimal load balancing can be achieved by using single-path routing [Hyytiä and Virtamo 2007a]. In addition, such a single-path routing depends on destination but not source and thus may be represented as a routing field [Hyytiä and Virtamo 2009]. Altman et al [2008] examined the routing problem of massively-dense networks in the context of road traffic engineering.…”

When does content float? Characterizing availability of anchored information in opportunistic content sharing

“…In order to analyze the floating content concept, it is important to characterize the movement, e.g., how often a node crosses a given line segment. To this end, let ϕ(r, φ) denote the so-called angular node flux at r in direction φ, which is defined as the rate of nodes moving in direction (φ, φ+dφ) across a small perpendicular line segment of ds divided by ds · dφ at the limit ds, dφ → 0 [13], [15], as illustrated in Fig. 2.…”

“…We develop models for analyzing the feasibility of the floating content concept by using spatial modeling techniques adopted from physics [13], similarly as have been used for modeling the capacity of so-called dense wireless multihop networks, see, e.g., [14], [15]. The fundamental objective is to establish the criticality condition for the system, i.e., an explicit relation which determines when the information remains available within the anchor zone infinitely long at the fluid limit (large population).…”