Localized Max-Min Remaining Energy Routing for ... - Semantic Scholar

Localized Max-Min Remaining Energy Routing for WSN using Delay Control Abdelmalik Bachir and Dominique Barthel France Telecom R&D 28 chemin du Vieux Chˆene, BP 98 38243 Meylan, FRANCE Email: {abdelmalik.bachir, dominique.barthel}@francetelecom.com Abstract— We present the use of an appropriate metricmapping function to turn a pre-existing min-delay routing algorithm into max-min routing. Some candidates for such a mapping function are presented, and their performances are discussed. We then apply this idea to make Directed Diffusion sensitive to the level of energy remaining in the forwarding nodes. The resulting algorithm, Localized Max-Min remaining Energy Routing (LMMER), is then implemented in a network simulation, and we show that it significantly prolongs the life of energycritical nodes.

I. I NTRODUCTION Sensor networks are wireless multihop networks in which nodes cooperate to perform routing and environmental phenomena sensing. These easily deployable, self-organized, and relatively low-cost networks are expected to be massively deployed in many applications such as habitat monitoring [1], disaster relief [2], surveillance [3], etc. The success of these applications is related to the network lifetime which depends on the life span of nodes. Hence, energy saving is a crucial factor to design long-living sensor networks particularly because nodes are often powered by batteries which may be costly, difficult or even impossible to replace or recharge. Designing a universal scheme for energy optimization is challenging due to the variety of applications of sensor networks. However, for most of these applications, measurements [4], [5] show that radio communication is a major energy drain. Therefore, at each protocol stack layer, algorithms are proposed to minimize the energy used by communications. For example, at the MAC layer, many power-saving protocols attempt at turning off the radio receiver as much as possible, thereby minimizing idle-listening. Such MAC algorithms include 802.11-inspired SMAC [6] and TMAC [7], TDMAbased TRAMA [8] and preamble-sampling-based WiseMAC [9] and BMAC [10]. Other savings come from minimizing the amount of control traffic. At the application layer, in-network processing such as local data aggregation or collaborative signal processing drastically reduces the amount of data moved across the entire network, which also achieves significant energy savings. At the network layer, routing algorithms aim at selecting routes that consume minimal global energy, where the global energy is computed by adding up the energies consumed by each hop comprising the route. An example of such minenergy algorithm is found in [11].

However, no matter how well energy usage is minimized at all protocol layers, some nodes eventually deplete their energy reserves. When these nodes are mission-critical (e.g., they carry a sensor type not found elsewhere in their vicinity), it is desirable that they be gradually exempted from generic chores, such as data forwarding, so that they live longer. More generally, when networks have an ’N out of N’ life model (such networks are considered dead as soon as their first node dies), some way of preserving energy-critical nodes is required to maximize lifetime. Such preservation can be found in [12]. Most of the known solutions to this problem are heavyweight in that they either radically modify the existing routing algorithm, or they introduce new overheads like the transfer of metadata between neighbors. In this paper, we propose a lightweight algorithm that does neither. We achieve this by coding the metadata into transmission delay, so that we don’t have to send the metadata itself. Furthermore, our algorithm can be easily plugged into existing min-delay routing protocols, such as Directed Diffusion [13], that we introduce hereafter. Directed Diffusion is a destination-initiated routing that implements a min-delay algorithm : data collectors (also called sinks) periodically interrogate potential data publishers (also called sources), asking for specific types of data. This phase, similar to a Route Request in on-demand routing protocols, is called interest propagation. It installs local data-forwarding pointers (called gradients) at intermediate nodes. The sources then generate the requested data streams, which flow along the local gradients back to the sinks. Directed Diffusion comes in several flavors, the one called ”one phase pull” being the best fit when few sinks collect the data published be many sources [14]. Since this is a common case in sensor networks, we thereafter only address ”one phase pull” Directed Diffusion. Our motivations to use Directed Diffusion are the following: • There is no exchange of overhead information like hello or route metrics messages, which saves energy. • The routing computation complexity is small. • Routing tables only require one entry per active interest, consisting of a pointer toward the next node downstream. • Each node only needs to broadcast one interest message during the interest propagation, and only needs to receive one interest message to setup its routing table (it can ignore the subsequent interest messages related to that same interest).

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II. R ELATED W ORK

III. M AX -M IN TO M IN MAPPING FUNCTION

In [15], Shah et al. consider the negative impact of pure minimum-energy routing on the survivability of the network. To reduce the load on minimum energy routes, they propose a probabilistic scheme which works as follows : to each route to a given destination, they assign a probability of being selected such that the minimum energy route has the highest probability, and other routes have lower probabilities. When forwarding packets to that destination, they pick a route at random according to the set of probabilities. Routes with unreasonably high energy consumption are assigned a zero probability and will never be selected. This algorithm requires to explicitly transmit link cost information and to receive packets from all routes in order to compute the corresponding selection probabilities. In [16], Li et al. describe max-min zPmin , an on-line routing algorithm addressing the network lifetime maximization problem. Their algorithm first computes Pmin , the minimum energy needed to transmit a packet from a source node to a destination node across all possible routes. It then uses a maximum-minimum remaining energy metric to pick a route (see Section III.A for details on this metric), thereby balancing the load among the different nodes, unless the cost is higher than zPmin , (z ≥ 1), in which case it picks the min energy route, avoiding excessive energy consumption. The authors propose a centralized algorithm based on the gradient descent technique to determine the optimal value of z. In [17], the same authors describe a distributed version of the algorithm, but it requires to establish synchronized mini slots at the MAC layer. The above papers [15], [17] emphasize the idea of combining minimum energy and max-min remaining energy metrics to optimize the lifetime of sensor networks. However, these distributed algorithms requires explicit transmission of energy information which goes counter the objective of energy optimization. Taking this overhead into account and inspired from [18] and [19], Guo [20] proposes a lightweight broadcast scheme for network lifetime maximization. His algorithm encourages nodes with high remaining battery to retransmit the broadcast message and works as follows. When a node receives a broadcast message, it defers the retransmission of this message to see if there is another neighboring node with higher remaining energy that would retransmit it first. The applied delay is inversely proportional to the remaining energy of the node. Guo’s algorithm cuts down on the number of nodes forwarding a broadcast message without the overhead of explicitly exchanging remaining energy information, but it misses out some nodes in a sparse network. Besides, it implements neither a minimum energy nor a max-min remaining energy algorithm. In this paper we propose LMMER, a distributed max-min remaining energy routing algorithm with no explicit energy information exchange, no stringent synchronization requirement and no complex routing tables computation.

This section describes how the use of an appropriate metricmapping function can turn min routing into max-min routing. In our description, we use remaining energy as the target metric since it is used for network lifetime maximization, but the same principle would apply to other metrics as well. For example, we could map available bandwidth so that an existing min-routing algorithm would select routes with maximum available bandwidth. Likewise, we use delay as the pre-existing metric since min-delay is commonly found in existing routing algorithms, such as Directed Diffusion. We’ll first arrive at approximate solutions for the desired mapping function, then analyze how well they perform. A. Problem definition Let’s consider a source node S and a destination node D and let’s assume, without loss of generality, that there are N disjoint routes from S to D (see Figure 1). Each route Ri , i = 1..N contains Mi intermediate nodes nij , j = 1..Mi , and can be written using the notation Ri = S − ni1 − ni2 − .. − nij − .. − D. Let’s call ξij , with 0 ≤ ξij ≤ 1, the relative residual energy of node nij . The available energy Ei on route Ri is the lowest energy level of all nodes forming this route, i.e. Ei = minj {ξij }. Maximum minimum available-energy routing selects the route with maximum Ei , i.e. route Rk whose k satisfies: 
k = argmax (1) min {ξij } 1≤i≤N

1≤j≤Mi

Let’s now examine min-delay routing. We call δij the delay introduced by each node nij . Route Ri experiences a total Mi delay of di = j=1 δij . Min-delay routing therefore selects the route with minimum di , i.e. Rk whose k satisfies:   Mi   k = argmin δij (2)  1≤i≤N  j=1

Our goal is to solve (1) by solving (2) on a suitable set of δij = f (ξij )

(3)

where function f maps the residual energy of nodes into an intentional transmission delay.

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Fig. 1.

Example Network

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Fig. 2.

Mapping functions

Fig. 3.

By choosing f to be a strictly decreasing function, we can rewrite (1) as : 
 k = argmin f (4) min {ξij } 1≤j≤Mi

Obviously, a function f such that, for all i in 1..N ,  Mi  f (ξij ) = f min {ξij } 1≤j≤Mi

j=1

(5)

would meet our goal. An approximate solution is obtained with f a convex function [0, 1] → [0, 1]. Indeed, if f is convex and decreasing, the minimal ξij along route Ri makes a dominant contribution to the sum to the left of (5), i.e. for m = argmin {ξij }

(6)

1≤j≤Mi

we have f (ξim ) >>

Mi 

f (ξij )

(7)

min {ξij }

(8)

j=1,j=m

and therefore Mi 

f (ξij ) ≈ f (ξim ) = f

j=1



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B. Approximate Solution

1≤i≤N

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In a practical implementation, f would likely be discrete and tabulated but, to get some practice, we explored a family of decreasing convex functions, based on (1/x)η . We shifted and shrunk them so that they map [0, 1] → [0, 1]. The resulting set of functions, labeled Fη, is plotted in Figure 2, where η takes integer values from 1 to 4. C. Route Selection Efficiency In this subsection, we look at how efficiently these functions select the max-min route. We ran a series of C++ simulations on a network similar to the one shown on Figure 1, with 10 disjoint routes. Simulations were run for maximum hop counts ranging from 2 to 20, showing as the x-coordinate in Figure 3.

Selection success ratios in isolation

For each maximum hop count value, 104 simulations were run, with each of the 10 routes being assigned a random number of hops uniformly distributed from 2 to that maximum, and each node on these routes being assigned a random relative residual energy picked in a gaussian distribution centered at 0.25 and of standard deviation 0.2 (therefore simulating an aging network). We define the route selection success as the ratio Ek /Ek where Ek represents the available energy on the route selected by our algorithm and Ek is the real maximum available energy. These success ratios are arithmetically averaged over the 104 simulations. 1) Convexity: We first ran a simulation with only the energy-related delays, i.e. measuring the mapping function performance in total isolation from any practical system. The average success ratios are plotted in Figure 3. For high values of the maximum number of hops along the routes, the success ratio of the mapping functions increases as η increases. We explain this by the impact of η on the convexity of the function F η. The following example shows a situation where F 1 does not select the route with the maximum available energy. Consider two routes R1 = 0.2 − 0.2 and R2 = 0.4 − 0.4 − 0.4 − 0.4 − 0.4 − 0.4 where 0.2 and 0.4 represent the residual energies of nodes on these routes. Applying F 1 results in cumulative delays of ∆1 = 2 · F 1(0.2) = 0.40 along R1 and ∆2 = 6 · F 1(0.4) = 0.54 along R2 . In this case, ∆1 is smaller than ∆2 so R1 is wrongly selected as the route with maximum available energy. By contrast, applying F 2 results in ∆1 = 2·F 2(0.2) = 0.08 and ∆2 = 6·F 2(0.4) = 0.042, which correctly selects R2 as the route with maximum available energy. The more convex the mapping function is, the better it meets Equation 7. 2) Sensitivity Threshold: We then simulated more realistic conditions, with other delays introduced in the network : as listed in Table I, we added to each node a packet transmission time, a system processing time, and a random back-off delay mimicking that introduced by a contention-based MAC for collision mitigation. The energy-related delay is the output of the mapping function F η, scaled to 500 times the packet transmission time, i.e. it is upper-bounded by about 20 s.

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4 F1 F2 F3 F4

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The selection success ratios are plotted in Figure 4 which shows that, under the conditions listed, function F 1 is best when the maximum number of hops is less than 6. In this interval, the smaller the value of η, the better the success. Indeed, as can be seen in Figure 2, for η > 2, the energyrelated node delay is extremely small for all values of residual energy larger than 0.25, which we call the sensitivity threshold. This makes functions F η with high η’s insensitive to these energy values: if two parallel routes have one node each, n1 and n2 respectively, with two different residual energies ξ1 and ξ2 such that ξ1 and ξ2 > 0.25, the delays at n1 and n2 will be dominated by the random MAC back-off values, and the route will be selected randomly. A smaller η increases the sensitivity threshold. But η also affects the convexity as discussed in the previous subsection. In addition, η affects the average route delay, as shown on Figure 5. Higher values of η reduce the average delay, with F 3 and F 4 keeping the average delay below 1s for routes up to 20 hops, under the energy distribution described above. Scaling down the energyrelated delay (e.g. down to 100 transmission times) would also reduce the average route delay, but at the expense of route selection success, since the MAC random delay would get a larger relative influence. Note that the route delay only applies to ”Route Request” packets, not to data being forwarded along those routes. Therefore, the response time of the network to an external event is not impacted, but its re-programming or reaction to topology changes gets slower.

Fig. 5.

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routing protocol. As described above, Diffusion selects routes based on min-delay, so we simply added the mapping function described in the previous section on top of Directed Diffusion in an NS2 simulation environment. The MAC layer we used is contention-based, with a random back-off for collision avoidance. In addition to the parameters already listed in Table I, we set the transmit and receive power consumptions to 3 and 2 mW respectively. Other MAC protocols could be used, as long as nodes have the same sense of elapsed time (this includes fixed duty-cycled radios or TDMA protocols). This restriction applies the same way to any min-delay routing algorithms including Directed Diffusion. Series of simulations were run on regular and random topologies to compare pure Directed Diffusion with LMMER. In each case, we consider one sink and several source nodes. The sink refreshes the network about its interest at regular intervals, and the sources keep sending data in reaction to the interest. We measure how many data messages we eventually receive at the sink from the various sources. The data streams dry up at the sink at some point in time because of energy

IV. L OCALIZED M AX -M IN REMAINING E NERGY ROUTING We took Directed Diffusion [13] as a starting point to build LMMER, our lightweight localized max-min remaining energy TABLE I D ELAY SUMMARY Transmission time

16

Maximum number of Hops

41.6 ms (52 bytes at 10kbps)

System time

15 to 45 ms, uniform

MAC random back-off

0 to 10 * transmission time, uniform

Energy-related delay

0 to 500 * transmission time

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Fig. 6.

Regular Network

V. C ONCLUSION In this paper, we showed how to use a mapping function on top of a min routing algorithm to turn it into a max-min algorithm. We exhibited some such functions that implement various trade-offs between delay and route selection success. We then applied this idea to design LMMER, a purely local add-on to Directed Diffusion that encodes energy in time to make Diffusion sensitive to available energy. We measured a significant increase in the total amount of data collected from critical sources over the life of the network, while keeping the additional delays compatible with the mission of a sensor network. R EFERENCES

Fig. 7.

Random Network

exhaustion, either at the source or, more likely, at intermediate nodes. Figure 6 show one of the regular topologies we simulated to check our implementation. Node 0 (center) is the sink and nodes 1 through 8 are sources. As expected, the simulation shows that sources 1 and 3 lower the energy level of intermediate nodes 9 and 11, and LMMER correctly adapts to the situation by routing data from source 2 through node 10 only. In this configuration, LMMER with function F 1 achieves a consistent 26% improvement in the amount of data transfered from sources 2, 4, 5 and 7 to the sink over the life of the network. Figure 7 shows one interesting random network topology that was produced by our simulation set-up. Node 0 (near the center) is the sink and nodes 1 through 5 are the sources. In this topology, it is clear that no matter how well LMMER performs, there is no improvement possible in the amount of data received from sources 3 and 4 (on the left side) over Directed Diffusion. This is because node 27, adjacent to the sink, belongs to all possible routes between these sources and the sink, so it will fail first and stop the data forwarding. The situation on the right, by contrast, is similar to the regular topology example discussed above. As Table II shows, on a range of simulations using F 1, we measured significant improvements on the amount of data from sources 1 and 5, and no change for sources 3 and 4.

TABLE II R ANDOM N ETWORK S IMULATION R ESULTS Source node

Improvement in amount of data

1

+53 to +80%

2

-5 to +10%

3

-5 to +5%

4

-5 to +5%

5

+12 to +20%

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