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Three Power-aware Routing Algorithms

for Sensor Networks

Javed Aslam, Qun Li, Daniela Rus

Department of Computer Science

Dartmouth College

Hanover, NH 03755

{jaa, liqun, rus}@cs.dartmouth.edu

July 16, 2002

Abstract

This paper discusses online power-aware routing in large wireless ad-hoc networks (es- pecially sensor networks) for applications where the message sequence is not known. We seek to optimize the lifetime of the network. We show that online power-aware routing does not have a constant competitive ratio to the off-line optimal algorithm. We develop an approximation algorithm called max-min zPmin that has a good empirical competitive ratio. To ensure scalability, we introduce a second online algorithm for power-aware rout- ing. This hierarchical algorithm is called zone-based routing. Our experiments show that its performance is quite good. Finally, we describe a distributed version of this algorithm that does not depend on any centralization.

1 Introduction

The proliferation of low-power analog and digital electronics has created huge opportunities for the field of wireless computing. It is now possible to deploy hundreds of devices of low computation, communication and battery power. They can create ad-hoc networks and be used as distributed sensors to monitor large geographical areas, as communication enablers for field operations, or as grids of computation. These applications require great care in the utilization of power. The power level is provided by batteries and thus it is finite. Every message sent and every computation performed drains the battery.

In this paper we examine a class of algorithms for routing messages in wireless networks subject to power constraints and optimization. We envision a large ad-hoc network consisting of thousands of computers such as a sensor network distributed over a large geographical area. Clearly this type of network has a high degree of redundancy. We would like to develop a power-aware approach to routing messages in such a system that is fast, scalable, and is online in that it does not know ahead of time the sequence of messages that has to be routed over the network.

The power consumption of each node in an ad-hoc wireless system can be divided according to functionality into: (1) the power utilized for the transmission of a message; (2) the power uti- lized for the reception of a message; and (3) the power utilized while the system is idle. Table 1 lists power consumption numbers for several wireless cards. This suggests two complementary

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levels at which power consumption can be optimized: (1) minimizing power consumption dur- ing the idle time and (2) minimizing power consumption during communication. In this paper we focus only on issues related to minimizing power consumption during communication - that is, while the system is transmitting and receiving messages. We believe that efficient message routing algorithms, coupled with good solutions for optimizing power consumption during the idle time will lead to effective power management in wireless ad-hoc networks, especially for a sparsely deployed network.

Card Tr Rv Idle Slp Power

mA mA mA mA Sup. V

RangeLAN2-7410 265 130 n/a 2 5

WaveLAN(11Mbps) 284 190 156 10 4.74

Smart Spread 150 80 n/a 5 5

Table 1: Power Consumption Comparison among Different Wireless LAN Cards ([2, 12, 1]). For RangeLAN2, the power consumption for doze mode (which is claimed to be network aware) is 5mA. The last one is Smart Spread Spectrum of Adcon Telemetry.

Several metrics can be used to optimize power-routing for a sequence of messages. Mini- mizing the energy consumed for each message is an obvious solution that optimizes locally the power consumption. Other useful metrics include minimizing the variance in each computer power level, minimizing the ratio of cost/packet, and minimizing the maximum node cost. A drawback of these metrics is that they focus on individual nodes in the system instead of the system as a whole. Therefore, routing messages according to them might quickly lead to a system in which nodes have high residual power but the system is not connected because some critical nodes have been depleted of power. We choose to focus on a global metric by maxi- mizing the lifetime of the network. We model this as the time to the earliest time a message cannot be sent. This metric is very useful for ad-hoc networks where each message is important and the networks are sparsely deployed.

In this paper we build on our previous work [22] and show that the online power-aware message routing problem is very hard (Section 3). This problem does not have a constant competitive ratio to the off-line optimal algorithm that knows the message sequence. Guided by this theoretical result, we propose an online approximation algorithm for power-aware message routing that optimizes the lifetime of the network and examine its bounds (Section 4). Our algorithm, called the max-min zPmin algorithm, combines the benefits of selecting the path with the minimum power consumption and the path that maximizes the minimal residual power in the nodes of the network. Despite the discouraging theoretical result concerning the competitive ratio for online routing, we show that the max-min zPmin algorithm has a good competitive ratio in practice, approaching the performance of the optimal off-line routing algorithm under realistic conditions.

Our proposed max-min zPmin algorithm requires information about the power level of each computer in the network. Knowing this information accurately is not a problem in small networks. However, for large networks it is difficult to aggregate and maintain this information. This makes it hard to implement the max-min zPmin algorithm for large networks. Instead,

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we propose another online algorithm called zone-based routing that relies on max-min zPmin and is scalable (Section 5). Our experiments show that the performance of zone-base routing is very close to the performance of max-min zPmin with respect to optimizing the lifetime of the network.

Zone-base routing is a hierarchical approach where the area covered by the (sensor) network is divided into a small number of zones. Each zone has many nodes and thus a lot of redundancy in routing a message through it. To send a message across the entire area we find a “global” path from zone to zone and give each zone control over how to route the message within itself. Thus, zone-based power-aware routing consists of (1) an algorithm for estimating the power level of each zone; (2) an algorithm computing a path for each message across zones; and (3) an algorithm for computing the best path for the message within each zone (with respect to the power lifetime of the zone.)

The algorithm max-min zPmin has the great advantage of not relying on the message sequence but the disadvantage of being centralized and requiring knowledge of the power level of each node in the system. These are unrealistic assumptions for field applications, for example involving sensor networks, where the computation is distributed and information localized. The third type of routing we describe is a distributed version of our centralized algorithms. distributed version of the max-min zPmin algorithm has the flavor of the distributed Bellman- Ford algorithm. This distributed algorithm requires n message broadcasts for each node if there is no clock synchronization, and only one message broadcast if the host clocks are synchronized.

2 Related Work

We are inspired by exciting recent results in ad-hoc networks and in sensor networks. Most previous research on ad-hoc network routing [19, 15, 24, 25, 27, 31, 20] focused on the protocol design and performance evaluation in terms of the message overhead and loss rate. To improve the scalability of routing algorithms for large networks, many hierarchical routing methods have been proposed in [21, 10, 23, 4, 13, 29, 36]. In [26, 18], zones, which are the route maintenance units, are used to find the routes. This previous work focused on how to find the correct route efficiently, but did not consider optimizing power while sending messages.

Singh et al. [32] proposed power-aware routing and discussed different metrics in power- aware routing. Some of the ideas in this paper are extensions of what that paper proposed. Minimal energy consumption was used in [30]. Stojmenovic and Lin proposed the first localized power-aware algorithm in their paper series [33]. Their algorithm is novel in combining the power and cost into one metric and running only based on the local information. Chang and Tassiulas [5] also used the combined metric to direct the routing. Their algorithm is proposed to maximize the lifetime of a network when the message rate is known. Their main idea, namely to avoid using low power nodes and choose the short path at the beginning, has inspired the approach described in this paper. We also use the same formula to describe the residual power fraction. The work presented in this paper is different from these previous results in that we develop online, hierarchical, and scalable algorithms that do not rely on knowing the message rate and optimize the lifetime of the network. In [14], Gupta and Kumar discussed the critical power at which a node needs to transmit in order to ensure the network is connected. Energy efficient MAC layer protocols can be found in [9, 8, 39]. Wu et al.[35] proposed the power-aware approach in dominating set based routing. Their idea is to use rules based on energy level to prolong the lifetime of a node in the refining process of reducing the the number of nodes in

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the dominating set. An