Wireless Netw (2006) 12:481–494

DOI 10.1007/s11276-006-6547-9

Energy-aware on-demand routing protocols for wirelessad hoc networksBaoxian Zhang · Hussein T. Mouftah

Published online: 8 May 2006C© Springer Science + Business Media, LLC 2006

Abstract Energy use is a crucial design concern in wire-

less ad hoc networks since wireless terminals are typically

battery-operated. The design objectives of energy-aware

routing are two folds: Selecting energy-efficient paths and

minimizing the protocol overhead incurred for acquiring such

paths. To achieve these goals simultaneously, we present the

design of several on-demand energy-aware routing proto-

cols. The key idea behind our design is to adaptively select

the subset of nodes that are required to involve in a route-

searching process in order to acquire a high residual-energy

path and/or the degree to which nodes are required to par-

ticipate in the process of searching for a low-power path

in networks wherein nodes have transmission power adjust-

ing capability. Analytical and simulation results are given to

demonstrate the high performance of the designed protocols

in energy-efficient utilization as well as in reducing the pro-

tocol overhead incurred in acquiring energy-efficient routes.

Keywords Wireless ad hoc networks · Energy use · Routing

1. Introduction

Energy use is crucial in designing wireless ad hoc net-

works since wireless terminals are typically battery-operated.

Recently, designing energy-aware routing protocols has at-

tracted a lot of attention for prolonged network operational

B. Zhang (�)College of Software Engineering, Graduate University of theChinese Academy of Science, Beijing 10049, P.R. Chinae-mail: bxzhang@gucas.ac.cn

H. T. MouftahSchool of Information Technology and Engineering,University of Ottawa, Ottawa, Ontario, Canadae-mail: mouftah@site.uottawa.ca

time and much work has been carried out. The design ob-

jectives of energy-aware routing are in general two folds:

selecting energy-efficient routes and simultaneously mini-

mizing the overhead incurred for acquiring such routes. Fur-

ther, scalability is also a big concern for a routing proto-

col to be employed in dynamic wireless ad hoc networks

wherein nodes can move freely and energy availability at

nodes changes over time.

Source routing algorithms (e.g., [1, 2]) can in general

achieve global energy-use optimization at the expense of

prohibitive overhead for gathering, exchanging, and storing

global state information, and also high computational over-

head. Such algorithms thus do not scale well. On demand

energy-aware routing protocols are attractive due to their on-

demand nature. One approach for this purpose is to execute a

traditional on-demand protocol (e.g., AODV [3] or DSR [4])

in networks wherein a localized topology controlling algo-

rithm (e.g., [5, 6]) or a distributed energy-aware dominating

set generating algorithm (e.g., [7]) is running at nodes. As

a result, for delivering data packets, only those low-power

links are selected as relaying links for the former case or

only those energy-rich nodes are chosen as relaying nodes

for the latter case. Such protocol design can also reduce the

communication overhead consumed for route discovery. This

is because the degree to which nodes are required to for-

ward route request messages is reduced significantly for the

former case; or the number of nodes being required to for-

ward such control messages is reduced greatly for the latter

case. However, their respective implementations require the

availability of one- or two-hop neighborhood knowledge at

nodes. This requirement can consume bandwidth and burn

energy for gathering such information at nodes constantly in

dynamic networks. To avoid such proactive overhead, some

other on-demand protocols (e.g., [8, 9, 10]) work without

assuming any topological knowledge at nodes and they are

Springer

482 Wireless Netw (2006) 12:481–494

desirable in particular in networks wherein the request rate

is not very high. Existing protocols falling into this aspect

can lead to energy-efficient paths. However, they have not

considered the minimization of the overhead consumed in

acquiring such routes.

The protocols that we design aim at acquiring energy-

efficient paths at low overhead. The designed protocols be-

long to the category of on-demand protocols and they work

with no any topological information assumed at nodes. More-

over, since Global Positioning System (GPS) receivers are

still considered expensive and energy-consuming at least in

a short term, we assume that no GPS receivers are equipped

at nodes in the implementation of our designed protocols.

Our protocol design comes from the following observa-

tions. A high-residual-energy path can be acquired if only

those nodes with high residual energy are considered as re-

laying node candidates, or a low-power path can be resulted

with high probability if only those low-power links are con-

sidered as its constituent link candidates. This is because low-

power paths prefer paths with more short-range hops other

than those with fewer long-range hops in networks wherein

nodes can adjust their transmission power levels. In this way,

a restriction posed on the quality of candidate relaying nodes

or links can lead to high-quality paths as a result. Accord-

ingly, in the design of a restricted flooding process of a route

request (RREQ) for route discovery, specific criterion is en-

forced to adaptively select the subset of nodes (measured in

terms of nodal remaining energy levels) that are required to

retransmit the RREQ and thus to potentially serve as relaying

nodes for data transmissions later; or to regulate the degree

(measured in terms of transmission power) to which nodes

are required to involve in such a routing process to minimize

the maximum link power of resulted paths. As long as a

connected network component that contains both the source

and the intended destination is created, a high-quality path is

identified. The communication overhead per request can be

reduced largely due to the above design. Moreover, this over-

head is charged to those energy-rich nodes for the former case

or being equally minimized at each RREQ re-transmitting

node for the latter case. We accordingly present the design

of protocols for selecting routes, which maximize the min-

imum nodal remaining energy and minimize the maximum

link power, respectively. We also present hybrid protocols

that work by integrated considering nodal residual energy

and link transmission power in route selection for further

improved performance.

Existing energy-aware on-demand protocols work either

to discover energy-aware paths via flooding (or its variations)

without considering the minimization of the resulted commu-

nication overhead or to build an efficient delivering structure

for reduced redundancy in a flooding operation without con-

sidering the quality of resulted paths. To our knowledge, this

is the first work that designs on-demand routing protocols

for discovering energy-efficient routes while minimizing the

resulted communication overhead in discovering such routes

without any topological information assumed at nodes. A

simplified partial version of this paper was presented in [11].

The rest of this paper is organized as follows. Section 2

formulates the network under study and the routing problems

to be addressed. Section 3 provides a brief review of related

work for energy-efficient routing in wireless ad hoc networks.

Section 4 gives design details of a protocol for acquiring the

path maximizing the minimum nodal residual energy and its

related analytical results. Section 5 presents the design of a

protocol for acquiring the path minimizing the maximum link

power and its related analytical results. Section 6 presents hy-

brid protocols by considering both max-min nodal remaining

energy and min-max link power in route selection for further

improved performance. Section 7 provides simulation results

for performance evaluation. Section 8 concludes this paper.

2. Routing problems

In this paper, we study multi-hop wireless networks wherein

all nodes cooperate in order to fulfill a given communica-

tion task. Such a network can be modeled as follows. An

ad hoc network can be represented by a graph G = (V , E),

where V (G) is the set of nodes and E(G) is the set of links

connecting nodes in V (G). We assume that the maximum

transmission range R associated with each node is the same.

A link (i , j) belongs to E(G) if node i and node j is within

each other’s transmission range. Hereafter, we will use the

terms “node”, “terminal”, and “host” interchangeably unless

otherwise stated.

2.1. Routing problems

Before formulating the problems to be addressed, we first

define some terms to be used later. The remaining energy

of a path is decided by the node with the minimal residual

energy along the path. Specifically, for a source s ∈ V (G)

and a destination t ∈ V (G)-{s}, the remaining energy as-

sociated with a path P that connects the s-t pair is de-

fined as E(P) = min {Ex |x ∈ V (P) ∧ x �= t}, where Ex rep-

resents the amount of remaining energy available at node

x . The maximal link power associated with path P , called

the MLP value of path P for convenience, is defined as

MLP(P) = max{e(i, j)|(i, j) ∈ E(P)}, where e(i, j) rep-

resents the link power value of link (i, j) for a success-

ful transmission from i to j . In this paper, we address the

following two routing problems for energy-efficient unicast

communications.

The Max-Min Remaining Energy Routing problem:Find a simple path P ′ connecting a given source s and a

given destination t such that E(P ′) is the maximum among

all those paths connecting the s-t pair.

Springer

Wireless Netw (2006) 12:481–494 483

The Min-Max Link Power Routing problem: Find a sim-

ple path P ′ connecting a given s-t pair such that MLP(P ′) is

minimized among all those paths connecting the s-t pair.

Both of the above problems are polynomial and can be

solved by using a source-based routing algorithm such as a

simple modification of Dijkstra’s algorithm [12, 13] with

accurate global state information, which is also referred

to as the widest routing or shortest-widest routing in the

context of QoS routing, or alternatively by using a wide-

area distance-vector routing algorithm such as modified dis-

tributed Bellman-Ford algorithm [12, 13]. However, the scal-

ability issue associated with either algorithm above makes

their practical use quite limited in dynamic wireless ad hoc

networks wherein network topology and the amount of resid-

ual energy at nodes can change with time.

2.2. Radio propagation models

Here, we discuss how to determine the transmission power

for successful transmissions between neighboring nodes. We

present here two commonly used propagation models: the

free-space propagation model and the two-ray ground re-

flection model, and accordingly show how to calculate the

transmission power in either model. In the free-space model,

the relation between the transmitted signal power (Pt ) and

the received signal power (Pr ) is as follows.

Pr = Pt Gt Gr

(λ

4πd

)2

, (1)

where Gt and Gr are the antenna gain of the transmitter and

the receiver, respectively, λ is the wavelength, and d is the

distance between the sender and the receiver. In the two-ray

model, the relationship between Pt and Pr is as follows.

Pr = Pt Gt Gr (ht hr )2

d4, (2)

where ht and hr is the antenna height of the sender and the

receiver, respectively.

As a generic form, the relation between Pt and Pr can

be rewritten as Pt = l × Pr , where l is a function of Gt ,

Gr , ht , hr , λ, d, and l is time-invariant if all the parameters

are time-invariant. To determine the mini-power required for

transmissions, each node x ∈V (G) specifies the power Pt

that it uses to transmit a packet (e.g., a RREQ). A receiv-

ing node y can then determine the value of l using the re-

ceived signal power Pr such that l = Pr /Pt . Accordingly,

the transmission power for node x to successfully send a

message to its neighbor y is l × γ , where γ is the minimal

reception power level for y to successfully decode a received

message.

3. Related work

Recently, much work has been carried out to support energy-

aware routing in wireless ad hoc networks. Here, we will first

briefly discuss related work for energy-aware routing and

then present a brief discussion of previous work for efficient

broadcast in wireless ad hoc networks, which is an essential

operation in route discovery in on-demand routing protocols.

3.1. Energy-aware routing

In [1, 2], the authors proposed algorithms to maximize the

network operational time by balancing the energy draining

rates among nodes using precise global state information. In

[14], Rodoplu and Meng applied the distributed Bellman-

Ford algorithm to a reduced network topology to establish

the minimum-power paths from every node to a master site.

In [15], Narayanaswamy et al. designed an approach named

COMPOW, which works to find the minimal common value

of node transmission range to maintain the network connec-

tivity. For this purpose, multiple proactive wide-area routing

daemons are required to run in the network, one for each

power level. In [16], the COMPOW approach has been en-

hanced to further reduce the energy consumed in packet for-

warding in heterogeneous networks, which is closely related

to a protocol designed in this paper. To reduce the power con-

sumed for packet forwarding, each intermediate node for-

wards a packet further at the lowest power level at which

the intended destination is reachable, as indicated in its lo-

cal forwarding table. However, running multiple wide-area

distance-vector routing daemons in networks can introduce

excessive overhead and has the scalability issue.

Several on-demand energy-aware routing protocols have

been designed. In [17, 18], localized rerouting techniques

were presented to perform per-link localized optimizations

to improve the power efficiency of a power-unaware path

by iteratively reroute each of the high-power links via a lo-

cal low-power alternate path, if possible. In [19], Xue et al.

designed geographical forwarding discipline such that each

node with a packet to forward performs per-hop power-aware

forwarding with the assistance of position information of the

destination, neighboring nodes and the node itself. The above

designs can achieve good energy use efficiency. However,

their respective implementations require the availability of

neighborhood knowledge at nodes. Updating and collecting

such information in dynamic networks can consume consid-

erable resources.

In [9], Doshi et al. extended the DSR protocol to sup-

port power-aware routing and this extended protocol works

as follows. A working path is first identified through a

power-unaware route-discovering circle. Each node that is

not on the identified working path sends a reply message to

the source node if it would be power-efficient by inserting

Springer

484 Wireless Netw (2006) 12:481–494

itself onto the route. The source can then draw a partial view

of network state by using information extracted from the re-

ceived reply messages, with which it can locally calculate

a (sub) lowest power route. In [9], simulation results indi-

cate that this protocol can suffer from information inaccuracy

caused by node mobility. In [8], Li et al. designed a defer-

ring approach called the Positional Attribute-based Nexthop

Determination Approach—Transmission Power (PANDA-

TP), to be employed at intermediate nodes for them to de-

fer their retransmissions of non-duplicate RREQs that they

receive. Such deferring is to encourage those RREQs tak-

ing higher-quality routes to propagate faster. Power-efficient

paths can be acquired as a result of such collective be-

havior at intermediate nodes. In [10], Domingo et al. de-

signed a simple energy-aware DSR protocol (SEADSR) by

considering the remaining energy levels at nodes in route

discovery. It works to discover energy-aware routes in a

way such that an intermediate node x , ∀x ∈V (G)-{s,t}, de-

fers its retransmissions of a non-duplicate RREQ that it

receives proportional to E max−ExEmax

· τmax, where Emax repre-

sents the battery capacity and τmax is a design parameter

that represents the maximum delay introduced. As a result

of such collective deferring at nodes, SEADSR is expected

to choose the route P that minimizes∑

x∈V (P)−{s,t}1

Ex. A

salient feature of the protocols in [8, 9, 10],is that their im-

plementation does not assume any topological information at

nodes.

3.2. Efficient broadcast

Network-wide broadcast is an essential operation in the de-

sign of wireless ad hoc networks and also in route discovery

since RREQs are flooded network-wide for routes to intended

destinations.

In [20], Ni et al. proposed distance-, count-, and

probability-based schemes to reduce broadcast redundancy.

In [21], Haas et al. designed gossip-based protocol to support

probabilistic broadcast to reduce the communication over-

head in route discovery. With this protocol, every node for-

wards a RREQ with a uniform probability p. An advantage

of the above protocols is that their implementations do not

assume any topological knowledge. However, they work to

reduce the broadcast redundancy without consideration on

the energy properties of resulted paths.

To support efficient broadcast, some approaches (see [22]

and references therein) work with one- or two-hop neigh-

borhood stored at each node for it to independently make a

decision on whether or not it needs to re-transmit a received

packet further on behalf of its own neighbors that are believed

to be uncovered yet in the flooding operation. In this way,

unnecessary retransmissions can be suppressed to a large ex-

tent. Building and maintaining a small connected dominant

set (see [7, 23] and references therein), which is known to

be NP-hard, is another strategy for reduced broadcast redun-

dancy. A set of the nodes of a network is a dominating set if

every network node not in the set is adjacent to at least one

node in the set. For a connected dominating set, there is at

least one path connecting every pair of nodes in the set via

a path not passing through any node outside the set. As a

result, only nodes in this set are required to relay packets to

perform network-wide broadcasting. However, the necessity

of dynamically gathering neighborhood knowledge at nodes

as required in their implementations can be communication

costly and negatively affect the operational lifetime of the

network.

To address the issue of minimum-energy broadcasting in

ad hoc networks wherein nodes has transmission power ad-

justing capabilities, centralized heuristics for example [24]

and hop-by-hop routing heuristics for example [25] have

been proposed for constructing power-efficient trees. These

heuristics require either the global state information or certain

localized topology controlling algorithms, which proactively

run with one- or two-hop neighborhood information assumed

at nodes.

It is worthy pointing out that the above protocols were

mainly designed for reducing the broadcast redundancy or

the total power to perform network-wide flooding on a pre-

built delivery structure. Directly employing one of them for

route selection may lead to the selection of inefficient route

for unicast communications thus reduce the likelihood of

prolonging the network lifetime since the operations in these

protocols have not considered the quality of resulted paths

for unicast communications.

4. Max-min remaining energy routingprotocol (MREP)

The MREP protocol is designed to address the max-

min remaining energy routing problem as defined in Sec-

tion 2. This protocol can work in environments wherein

nodes operate at a uniform transmission power for all

transmissions. Recall again that protocols that we de-

sign work without any topological information assumed at

nodes.

MREP follows the basic philosophy behind on-demand

routing protocols and it works to find energy-aware routes

upon request. Specifically, it aims at searching for the path

maximizing the path remaining energy at a low communi-

cation overhead. To achieve this goal, we design MREP to

adaptively select the subset of nodes that are required to for-

ward RREQs and thus to involve in the route-searching pro-

cess. Nodes in the forwarding subset are those with residual

energy equal to or above a specific threshold. MREP works

Springer

Wireless Netw (2006) 12:481–494 485

to gradually relax value of the threshold until a path is found

or no path can be found even when the threshold value drops

to zero or min{Ex |x ∈V (G)}, if applicable.

4.1. Protocol design

MREP consists of two major components: route discovery,

which searches for an energy-aware route connecting a given

pair of nodes with a desire for communications; route recov-

ery, which searches for a new route when the working route

breaks.

4.1.1. Route discovery

Upon receiving a request for a route to an intended destina-

tion t ∈V (G) − {s} but no route is known, the source s ini-

tiates a route-searching process, denoted by MREP (1), for

an energy-efficient route to t . Source s first decides the value

of its initial energy threshold, denoted by L1 or Ls1 without

causing confusion, a key parameter in MREP (1), and then

floods the network with a RREQ carrying L1. Upon receiving

a non-duplicate RREQ, an intermediate node u∈V (G)-{s, t}forwards the RREQ further provided that its remaining en-

ergy level Eu is equal to or greater than the energy threshold

that the RREQ carries, after locally recording the last hop as

the node from which the RREQ was received for backward

learning. Upon receiving a non-duplicate RREQ, destination

t sends a route reply (RREP) packet back to the source salong the reverse path to notify the successful discovery of

such a path.

If timed out without receiving a RREP, the source broad-

casts the RREQ again with a threshold L2, which is less

than L1 by a certain amount. This relaxation is to include

some more nodes with lower energy to enroll into the route-

searching process in a controllable manner since the pre-

ceding route-searching operation fails. This relaxing process

continues until a path is found or no path can be found even

after the source sets the energy threshold L M (M ≥1) down

to zero or min{Ex |x ∈V (G)} (if applicable), in which case

all nodes are obligated to participate in the route-searching

effort.

Obviously, for a path p connecting the s-t pair, acquired

in MREP(k), 1≤ k ≤ M , it is guaranteed that Ex ≥ Lk,∀x ∈V (p) − {s,t}, k. Thus the path remaining energy of the dis-

covered path is ≥ Lk , irrespective of the order in which

intermediate nodes forward RREQs. The MREP implemen-

tation can filter out as much energy-starving nodes as pos-

sible from participating in either the route-searching at-

tempts or the subsequent data transmissions, it thus can max-

imally prolong the operational time of those energy-starving

nodes.

4.1.2. Route maintenance

When a route break occurs, appropriate operations must be

taken to discover a new path. A node is assumed to be able to

detect a link break by for example receiving a link layer feed-

back signal from the MAC protocol,1 or not receiving passive

acknowledge. When a route is disconnected, the immediate

upstream node of the broken link sends a Route Error (RERR)

packet to the source node of the session to notify the route

invalidation. Nodes along the reverse path relay this message

to the source node. When a node receives a RERR packet, it

also removes the entry associated with the particular desti-

nation from its routing table. If the source does not have any

alternate route to reach the destination, it enforces a route

re-discovery process immediately to search for a new route

to the destination if it still has data to send to the destination.

4.2. Analytical results

Next, we present analytical results and bounds related to

the MREP implementation concerning the quality of its re-

sulted paths, communication overhead, and route acquisi-

tion latency, respectively. In our analysis, we assume that the

medium access protocol is ideal, which can guarantee packet

delivery without loss.

We first deduce the worst-case inaccuracy of a path

by MREP away from the optimal solution in terms of

the path remaining energy value. We study here a generic

case of concern such that the set of energy thresholds en-

forced (as necessary) by source s is limited and with dis-

crete values. Without loss of generality, we assume this

set as {L1, L2, . . . , L M |L1 ≤ Emax ∧ L M ≤ min∀x∈V (G)

Ex ∧M ≥ 1}, which is sorted in monotonically decreasing or-

der. For a path p by MREP (k), its path remaining en-

ergy level E(p) can be deduced as follows. If k = 1, then

we have E(p) ∈ [L1, Emax] with a worst-case inaccuracy of

Emax − L1, else E(p) ∈ [Lk, Lk−1) with a worst-case inac-

curacy Lk−1 − Lk . A special case is when the source is the

bottleneck node on the optimal path. In this case, a single in-

vocation of MREP(1) can lead to the optimal path by setting

L1 to Es . As a result, we can see that the implementation of

MREP can reduce the communication overhead with a con-

trollable penalty in path quality and route acquisition latency.

The precondition under which an end-to-end path can be ac-

quired by MREP(k), 1≤ k ≤ M , is that nodes with remaining

energy ≥ Lk form a connected subnetwork containing both sand t .

The total amount of energy (normalized over the uniform

maximum transmission power) consumed for acquiring a

1 MAC protocols such as MACAW [26] and IEEE 802.11 [27] have thiscapability.

Springer

486 Wireless Netw (2006) 12:481–494

path until MREP(K ) is enforced, K ≥ 1, is∑K

k=1

∑|V |x=1 δk

x

and this value represents also the total number of retransmis-

sions of RREQs. δkx is a binary indicator and it takes value

one if node x ∈V (G) forwards the RREQ in the process of

executing MREP(k), or zero otherwise, K is the total number

of rounds that an MREP route-searching process experiences

before it returns a path. It is worthy noting that the communi-

cation overhead is mainly charged to those nodes with high

residual energy, which has a minimal negative influence on

the lifetime of the network.

The route acquisition latency can be calculated as TK +∑K−1i=1 T , where T is the length of the timer scheduled at

the source for it to collect RREPs in the case of that timers

scheduled for different rounds of MREP processes are with

the same length, TK is the latency experienced in implement-

ing MREP(K ) from the instant that s issues a RREQ to the

instant that it receives a corresponding RREP and the second

item stands for the total time experienced due to the pre-

ceding K -1 unsuccessful processes MREP(k) from k = 1 to

K − 1, if K > 1. The analysis here focuses on the cases such

that the network is strongly connected and at least one path

connecting the s-t pair exists.

4.3. Determining initial energy thresholds at nodes

One question still remains open concerning how a node

u∈V (G) determines its initial energy threshold for it to initi-

ate an MREP(1) process as well as the values of subsequent

thresholds (if needed), in a decentralized manner. For this

purpose, we design here a simple but efficient method for

disseminating the residual energy status at nodes with light

communication overhead. Firstly note that it is in general nei-

ther necessary nor overhead-efficient for each node to keep

track of an image of the exact amount of residual energy at

other nodes. In MREP, the main effort focuses on discourag-

ing those energy-starving nodes from energy draining. Ac-

cordingly, updating the energy status of those energy-starving

nodes is of great concern.

For our scheme to work, the full range of energy capacity

Emax is divided into M intervals indexed from 0 to M − 1.

Here, we assume these intervals are equally spaced although

other dividing strategies can be used as well. The energy

index associated with a node u∈V (G) is denoted by Iu .

For a node u∈V (G) associated with an index k, where kis an integer and 0 ≤ k ≤ M − 1, we have Eu ∈ [k · Emax

M ,

(k + 1) · Emax

M ). As a result, a node v can deduce the range of

Euby knowing the energy index of u, ∀u∈V (G) − {v}. The

higher the index is, the higher remaining energy the corre-

sponding node has. A simple strategy for disseminating nodal

indexes is that each node floods its index whenever its index

changes (decreases). This strategy causes an overall amount

of O(M |V |) retransmissions for sending control packets car-

rying such index information at each network node.

Our scheme aims at reducing this overhead without caus-

ing penalty in the performance of MREP. Initially, each

node floods its index number when the network is first de-

ployed. This causes a number of |V | retransmissions at each

node. Accordingly, each node x ∈V (G) can have the range

of residual energy of other nodes by using their energy in-

dexes that x received. Given a percentage number perc (0

≤ perc < 1), there exists a corresponding integer X , 0 ≤X ≤ M − 1, such that |{n|In ≤ X, n ∈ V (G)}| ≥perc·|V |.For a node x with Ix > X , it floods its (changed) index if

and only if Ix decreases down to X − 1. Nodes with indexes

≤ X are said to be in energy-critical region. If Ix ≤ X , xfloods its index across the network whenever its index value

changes (decreases). In this way, changes of energy avail-

ability at nodes with indexes >X are ignored provided that

such changes do not lead to a change of the energy-critical

region.

The overhead associated with the above scheme can

be deduced as follows. Without loss of generality, we as-

sume initially X = X0 (0 ≤ X0 ≤ M − 1) when the net-

work is first deployed. Whenever there are a total number

of perc·|V | network-wide disseminations carrying a par-

ticular index x as initiated by different nodes such that

x < X (initially X = X0), X will automatically drop to x .

That is, the number of nodes with indexes ≤ x is now

≥perc·|V |. This process continues until a first node runs

out of its energy, if the network lifetime is measured this

way. Since X0 ≤ M − 1, the total number of retransmis-

sions for disseminating indexes information at each node,

in the worst case, is O(perc·X0|V |) + |V | = O(perc·M |V |).In case network lifetime is measured until a given percent-

age PREC of nodes run out of their energy, we typically

choose perc ≥ PERC. In this case, the total number of re-

transmissions of index information at each node, in the

worst case, will be O((perc + PREC)M |V |), or O(M |V |) if

perc + PREC ≥ 1.

For a node u∈V (G) to initiate a MREP(1) process, it sets

Lu1 to the energy level, which its selected initial percentage

perc1 (0 ≤ perc1 < 1) corresponds to, such that it is expected

that a number of (1 − perc1) · |V | nodes are with energies

≥ Lu1 and these nodes are required to involve in MREP(1).

In case MREP (2) is needed, Lu2 is set to an energy level

that another percentage perc2 corresponds to, which is less

than perc1 by a certain amount. This process continues until

a path is found or percM (M ≥1) drops to zero such that

all nodes are obligatory to enroll into the routing process.

The smaller perc1 is, the higher the probability at which a

route is acquired in MREP(1). Further, for networks wherein

nodes are distributed uniformly, it is expected when perc1 is

low enough to a certain level, the (1 − perc1)∗100 percent

of nodes being requested to involve in MREP(1), is likely to

create a connected dominating set of the network with a very

high probability.

Springer

Wireless Netw (2006) 12:481–494 487

5. Min-max link power routing protocol (MLRP)

The MLRP protocol is designed to address the min-max link

power routing problem as defined in Section 2 and it aims at

acquiring low-power routes in networks wherein nodes can

adaptively adjust their transmission powers depending on the

transmission ranges. The design goal is to minimize the en-

ergy depleting rate at individual nodes by selecting paths con-

stituent of links with power as low as possible. MLRP follows

the basic idea in MREP for route discovery but it converges

with respect to a different metric and accordingly employs

different procedures. MLRP works by gradually relaxing the

common transmission power, which is decided by the rout-

ing initiator and used for intermediate nodes to forward non-

duplicate RREQs that they receive, if earlier route-searching

attempts fail. In this way, the routing process attempts to

minimize the power consumed at each individual node for

participating in such a path-searching process and also to

improve the power quality of the resulted path as a whole.

5.1. Protocol design

The design details of MLRP are as follows. The source node

of a communication request first initiates an MLRP(1) pro-

cess by flooding a RREQ across the network, which car-

ries the value of a common transmission power P1(0 < P1 ≤PTXmax

, where PTXmaxrepresents the full transmission power

of nodes), which the source locally decides. A RREQ carries

the end-to-end power (initially zero) on the subpath that it

takes and also a sequence number uniquely assigned by the

source. If timed out without receiving a corresponding RREP,

the source invokes an MLRP(2) process by re-broadcasting

the RREQ carrying another power value P2, which is greater

than P1 by a certain amount. This process continues until a

path is found or no path can be found even after increasing

the common transmission power PM (M ≥ 1) up to PTXmax.

Upon receiving a non-duplicate RREQ belonging to

MLRP(k), 1≤ k ≤ M , an intermediate node u∈V (G) −{s, t} forwards it further by using the transmission power

value Pk that the RREQ carries after updating the power

value on the subpath from the source to the current node

and recording the last hop as the node from which node ureceived the RREQ. Upon receiving a non-duplicate RREQ,

destination t sends a RREP back to the source s to inform the

successful discovery of such a path p. Upon receiving such a

RREP, the source s then can start to send data packets along

the path. Note that the actual transmission power at which

data packets are forwarded to traverse a link (i , j) ∈ E(p)

is the minimal link power value required for a successful

transmission from node i to its adjacent node j , instead of

using the common transmit power at which node i honestly

forwarded RREQ(s) earlier as the source suggested for route

discovery blindly.

5.2. Analytical results

We study the case wherein the set of power thresholds in-

spected is small and with discrete values. Without loss of

generality, this set is assumed as {P1, P2, . . . , PM |PTXmax ≥P1 > 0 ∧ PM = PTX max ∧ M ≥ 1} sorted in monotonically

increasing order. Suppose that a path is resulted by imple-

menting MLRP(k), the asymptotical worst-case inaccuracy

away from the optimal solution in terms of the maximum

link power of constituent links is limε→0+ (P1 − ε) = P1 if

k = 1, or Pk − Pk−1 otherwise. For networks wherein nodes

operate at a limited number of X (X ≥1) discrete power lev-

els, by setting the set of thresholds to be inspected the same

as the set of discrete power levels, an optimal path can be ac-

quired with a number of up to X times of invoking MLRP(k)

from k = 1 up to X , and accordingly increasing the uniform

power value from P1 = PTX min to PX = PTX max, if a path

connecting the s-t pair exists.

We further present the following results concerning the

performance of MLRP.

Result 1: For a path p returned by MLRP(k), we have

e(u, v) ≤ Pk , ∀(u, v) ∈ E(p).

Result 2: For a path p returned by MLRP(k), we have

∃(u,v) ∈ E(p) such that e(u,v) ∈ (Pk−1, Pk].

This is easy to understand since otherwise a path should

have been identified in the preceding process MLRP(k−1),

which leads to a path with a smaller maximum link power.

Result 3: The energy consumed in acquiring a path by

MLRP is∑K

k=1

∑|V |x=1 δk

x · Pk such that the MLRP(K ) suc-

cesses in acquiring a path while all its preceding K − 1 at-

tempts fail in doing so.

Result 4: Energy-stretch ratio of MLRP is |V | − 1.

Energy-stretch ratio is defined to be the ratio of the power

value associated with a path acquired by using MLRP, in the

worst case, over that associated with the global mini-power

path. This property can be established through the following

example. Consider a ring network consisting of a number of

|V | nodes and also a number of |V | links such that one link,

say (u,v), is associated with a power of 1 + ε. ε is a very

small positive real number and the rest links are associated

with a unit power. In this case, the path connecting u and

v by using MLRP contains |V | − 1 hops and accordingly

associated with a power of |V | − 1 if P1 is set to one in

implementing MLRP(1) while the optimal path is the direct

link (u,v) with a power of 1 + ε . This worst-case stretch is the

same as that of constrained relative neighborhood graph [5].

5.3. Determining initial power thresholds at nodes

The initial power threshold values (denoted by Pu1 , ∀u∈

V (G)) can be greatly affected by network topology as well

Springer

488 Wireless Netw (2006) 12:481–494

as node distribution, which changes in dynamic networks as

nodes move. Here, we provide procedures for nodes ∈ V (G)

to adaptively adjust their threshold values. Intuitively, for

fast route acquisition, Pu1 (∀u) is to be set to a level large

enough such that (a) the network is likely to be connected

by using those links with power ≤ Pu1 or (b) the intended

destination t ∈ V (G) − {u} is likely to be reachable through

a connected subgraph judged by using the information that

u gathers recently, if possible. In either case, a sub-optimal

route can be acquired with high probability through invoking

MLRP(u, t , 1).

We now proceed to discuss how to adaptively adjust

the initial power thresholds at different nodes for a good

tradeoff between route-acquisition latency, communication

overhead and path quality. In general, for an arbitrary node

u∈V (G), if it overhears a successful route discovery carried

out at an power threshold <Pu1 , it can reduce Pu

1 by a

certain amount; On the other hand, if it overhears a route

acquired only after the threshold value increase to a level

>Pu1 , node u should increase Pu

1 by a certain amount to

keep track of the topology changes. We further present

the following results to ease the understanding of MLRP

implementation.

Result 5: For a node u∈V (G) − {s}, if it receives a RREQ

∈ MLRP(s, t , k), k > 1, without receiving any RREQ be-

longing to the preceding MLRP(s, t, k − 1) process, then

we have that, at this moment, the source s is only reachable

from node u itself via a path p such that the MLP value

associated with p is > Psk−1.

Result 6: For a node u∈V (G) − {s,t}, if it receives a

RREQ ∈ MLRP(s, t, k), k > 1, then t is unreachable at this

moment from either s or u at a common link power value

≤ Psk−1; Further, for an MLRP process that successfully

terminates at a K th round (K > 1), upon receiving a RREQ

∈ MLRP(s, t, K ), u can learn that at this moment t can

only be reachable from itself via a path with an MLP value

> PsK−1.

The detailed procedures for a node u∈V (G) to adap-

tively adjust its initial energy threshold are as follows. Upon

overhearing the success of an MLRP (s, . . . , K ) process,

which is determined by without overhearing any RREQ ∈MLRP(s, . . . , K + 1), if Pu

1 > PsK , u can then decrease Pu

1

by an amount of �P; else if Pu1 < Ps

K and K > 1, u then

increases Pu1 by an amount of �P ′. The values of �P and

�P ′ can be affected by other system parameters and are to

be tuned in the network design.

6. Hybrid adaptive energy-aware routingprotocol (HEAP)

The MLRP protocol presented in the preceding section aims

at reducing the power of resulted paths by including links

with power as low as possible. Thus we can see that MLRP

has not taken the remaining energy at nodes into consider-

ation. A nature extension is to combine the idea of maxi-

mizing the minimum nodal residual energy in MREP and

that of minimizing the maximum link power in MLRP for

a hybrid protocol. The hybrid design is expected to bal-

ance the energy depletion among nodes and also to min-

imize the energy consumed per routing task. Albeit sim-

ple at the first glance, the respective design objectives in

MREP and MLRP are independent since a path maximiz-

ing the minimal nodal remaining energy is not necessar-

ily the path minimizing the maximum link power, or vice

versa. Thus tradeoff is needed for a good compromise be-

tween the two measures. We start with a straightforward

protocol design from the intuitive observations, referred to

as HEAP-0, and then derive two variations, referred to as

HEAP-1 and HEAP-2, respectively, to ease the protocol

implementation.

6.1. HEAP-0

HEAP-0 is straightforward and it works in the following

way for route discovery. Source s first initiates a HEAP-

0(1) process for a path to an intended destination t by flood-

ing a RREQ carrying initial threshold tuple < L1, P1 >. If

timed out without receiving a corresponding RREP, s in-

vokes a HEAP-0(2) process by re-broadcasting the RREQ

that carries another threshold tuple < L2, P2 >, such that L2

is smaller than L1 by a certain amount and P2 is greater than

P1 by a certain amount. This process continues until a path

is found or no path can be found even after increasing PM

(M ≥ 1) up to PTXmaxand also decreasing L M down to zero or

min{Ex |x ∈V (G)}, if applicable. For an intermediate node

u∈V (G) − {s,t}, upon receiving a non-duplicate RREQ be-

longing to HEAP-0(k), it forwards the RREQ further at the

transmission power Pk recommended by s after updating the

subpath information, iff Eu ≥ Lk . Destination t can choose

the path minimizing PkLk

if it receives multiple RREQs, each

taking a distinct path. t can then send a RREP back to source

s along the reverse path to notify the successful discovery of

such a path.

The difficulty in implementing HEAP-0 lies in how to

adaptively adjust the threshold values. It is difficult to quickly

acquire a path that minimizes the maximum link power value

and simultaneously maximizes the minimum remaining en-

ergy without global network state due to the independency

of the two metrics. Also, it is difficult to adjust the respec-

tive threshold values at nodes using the information that

they gather. Details are as follows. For a source s∈V (G),

an unsuccessful HEAP-0(s,t ,k) process indicates only there

exists no route from s to t , which meets Lk and of Pk si-

multaneously. s is unable to judge which one or neither of

the two threshold values meets their respective bottom line

Springer

Wireless Netw (2006) 12:481–494 489

requirements. On one hand, respectively inspecting all possi-

ble combinations of Li and Pj , ∀i , j , for route acquisition us-

ing flooding is time consuming and associated with excessive

communication overhead. It is therefore not feasible. On the

other hand, simultaneously relaxing the two thresholds could

be too conservative and low-quality path can be acquired as

a result. Similar situations exist for nodes ∈ V (G) − {s, t}as listeners to adjust their own initial threshold values based

on the results of HEAP-0(s,t ,k), ∀s,t ,k. This is because the

properties given in result 5 and result 6 for MLRP do not

hold for HEAP-0.

Next, following the strategy of divide and conquer, we

present the design of HEAP-1 and HEAP-2, respectively,

by establishing different viewpoints to ease the protocol

implementation. HEAP-1 and HEAP-2 differ away from

the above HEAP-0 design only in how nodes adjust their

threshold values.

6.2. HEAP-1

HEAP-1 aims at discovering the path with the max-min

remaining energy on a connected subgraph G ′, which

is decided by a transmission power value e such that

V (G ′) = V (G), E(G ′) ={(u,v) ∈ E(G)|e(u, v) ≤ e ∧ 0 <

e ≤ PTXmax} and the value of e is minimized. e is reflected

by the initial power thresholds at each node u such that

Pu1 ≥ e, ∀u. In this way, HEAP-1 tries to avoid using unnec-

essary extra-long links for unicast communications. When

e = PTXmax, HEAP-1 degenerates to MREP.

In HEAP-1, procedures for a node u to adjust its initial

power threshold Pu1 are as follows. Upon receiving a RREQ ∈

HEAP-1(s, . . . , k), s �= u, if Pu1 < Ps

k , then Pu1 = Ps

k ; else

if Pu1 > Ps

k and u does not receive a subsequent RREQ ∈HEAP-1(s, . . . , k + 1), then Pu

1 = Pu1 − �PHEAP−1, where

�PHEAP−1 is a very small positive number. The greedy man-

ner in which u (∀u) increases Pu1 is to quickly reach the

expected value of e or slightly larger at different nodes such

that the network is connected using those links with power

≤ e. In contrast, the slow decreasing in Pu1 (∀u) is solely

to deal with potential network dynamics so as to avoid e to

stay on a very large value unnecessarily long. In HEAP-1,

procedures for each node x ∈V (G) to adjust its initial energy

threshold are the same as that in MREP.

For a node u∈V (G) to initiate a HEAP-1(1) process, it

will use the values of Pu1 and Lu

1 obtained using the above

procedures for route discovery. If timed out without receiving

a corresponding RREP, u will initiate a HEAP-1(2) process

by reducing the energy threshold by a certain amount as does

in MREP. If no path can be found when the energy threshold

LuM drops to zero or min{Ex |x ∈V (G)} (if applicable) such

that all nodes are obligatory to involve in the route-searching

task, then u starts to increase the power threshold until reach-

ing PTX max or a path is found. As we can see, HEAP-1 relaxes

only one of the two thresholds each time in route discovery,

which eases the protocol implementation.

6.3. HEAP-2

HEAP-2 aims at discovering the path with the min-max link

power on a connected dominating set of the network such that

only nodes with residual energy ≥ L are included in the set

and L is maximized. Accordingly, we can see that HEAP-2

tries to avoid using those nodes with extra-low remaining en-

ergy as relaying nodes for multi-hop communications. When

L = 0, HEAP-2 degenerates to MLRP.

In HEAP-2, procedures for each network node to deter-

mine its initial energy threshold and initial power threshold

are the same as in MREP and MLRP, respectively. To discover

a route using HEAP-2, a source adjusts the values of the two

thresholds in a way similar to that in HEAP-1 but with the

transmit power threshold value relaxed (increased) first until

reaching PTX max and the energy threshold value relaxed (re-

duced) second until reaching zero or min{Ex |x ∈V (G)}, as

necessary. To ensure a connected dominating set to be formed

as the backbone structure with high probability, the initial

energy thresholds at nodes should be chosen low enough. In

our protocol implementation, it means that the percentage

of nodes whose energies are above the chosen initial energy

threshold should be high enough.

7. Simulation results

In this section, we conduct simulations to evaluate the per-

formance of the designed protocols by designing a discrete-

event simulator. The parameter settings are as follows. The

number of nodes is 100. The maximum transmission range Ris set to 250 meters. Nodes are initially uniformly distributed

in a square area whose size is calculated to obtain a desirable

node density of ten with an actual average degree of 9.1 due

to border effect. The mobility model used is similar to that

in [4]. Each node stays at its current location for a period of

time, which is called the stationary time, and then it moves

to another randomly chosen location. Each node repeats this

behavior, alternatively staying and moving to another loca-

tion. The velocity of node movement is randomly selected

between 1 and 20 meters per second. The time a node takes to

reach a new location is called the moving time. The mobility

ratio of a node is defined as follows.

mobility ratio = total moving time

total moving time + total stationary time.

(3)

By adjusting the stationary time, we can change the mobility

ratio.

Springer

490 Wireless Netw (2006) 12:481–494

Each link has a power value normalized over the maximum

transmission power. Each node is assigned a random initial

energy ∈[Emin, Emax] = [5000, 10000]. Simulations were

repeated using different randomly generated initial networks.

In each network, there were totally ten connections routed

at any time. Each connection was associated with a ran-

domly selected source-destination pair. The duration of each

request lasted for a period of [5, 15] seconds and the packet-

generating rate per connection was four packets per second.

In our experiment, each data packet and control packet was

associated with a (normalized) length of five and one, re-

spectively. Each packet transmission will charge an equiv-

alent amount of energy to the corresponding sending node.

The receipt power at receiving nodes is assumed to be small

and accordingly ignored. In the simulations, we assume that

the MAC layer is ideal, which can guarantee packet delivery

without loss; Packet propagation speed is significantly higher

than node movement speed, so that routes do not change

while packet forwarding is in progress.

We compare the average lifetime of a network implement-

ing the following protocols: MREP, MLRP, HEAP-1, HEAP-

2, SEADSR [10], and PANDA-TP [8]. All these protocols

discover paths on demand without assuming topological in-

formation at nodes. The lifetime of a network is measured as

the duration until a first node in the network runs out of its

energy. In the implementations of all the protocols, caches

replies are set off to avoid using outdated information as does

in [8, 10].

The following implementation decisions were made in

implementing MREP and MLRP. In MREP, the full energy

capacity Emax was divided into 16 equally spaced intervals;

perc1, perc2, and perc3 for determining the values of se-

quentially enforced energy thresholds were set to 20, 10,

and 0 percent, respectively. That is, 80, 90, and 100 percent

of the network nodes are expected to involve in MREP(1),

MREP(2), and MREP(3), respectively, in the process of route

discovery. In MLRP, (normalized) power decrement �P was

set to PTX max

/16 = 1

16, and power increment �P ′ was set to

2 × �P = 18. The latter setting is for accelerated route acqui-

sition when consecutive MLRP processes are to be enforced

to search for a path.

In implementing HEAP-1, perc1 , perc2 , and perc3 were

set the same as in MREP for adjusting energy thresholds;

transmit power decrement �PHEAP−1 was set to �P8

= 164

.

In HEAP-2, perc1 and perc2 were set to 10 and 0 percent,

respectively; power decrement �P was set to 18

and power

increment �P ′ = 2 × �P = 14. These settings for adjusting

power threshold values are to accelerate routing convergence

with certain penalty in path quality since there are two thresh-

olds to be adjusted in potential in the implementation of the

hybrid protocol.

In implementing HEAP-1, a change was made as fol-

lows for determining the initial transmit power thresholds

P1 at nodes. Upon receiving a RREQ ∈ HEAP-1(s, . . . , k),

which carries a power threshold Psk , if Pu

1 < Psk , node

u ∈ V (G) − {s} then adjusts Pu1 in a way such that Pu

1 =(1 + γ )Ps

k , γ > 0, an operation suggested as Pu1 ← Ps

k in

our earlier description. With this change, the radii by a trans-

mission of RREQ (in a HEAP-1(1) process initiated by ulater for route discovery) will accordingly increase a factor

of√

1 + γ − 1 in the free-space model or 4√

1 + γ − 1 in

the two-ray model. Consider that nodes are uniformly dis-

tributed, the average node degree in the resulting graph due

to the above change will increase approximately a factor of γ

and√

1 + γ − 1 in the free-space model and in the two-ray

model, respectively. A conservative degree increase in this

way can largely reduce the probability that certain (energy-

critical) nodes have to serve as relaying nodes for more multi-

hop connections on the subgraph obtained by using HEAP-1

due to the reduced connectivity. This has been verified to be

useful especially when the mobility ratio is low. In our sim-

ulations, γ was set to 0.2 such that the expected percentage

increase in degree is 20 percent and approximately 10 per-

cent in the free-space and two-ray models, respectively, in

the resulted graph by HEAP-1(1).

In the implementation of MREP and SEADSR, power ad-

justing capabilities are enabled as well at nodes in forwarding

data packets to make a fair comparison. In the original design

of PANDA-TP [8], how to determine the values of certain pa-

rameters in their given deferring function was not clarified.

To be consistent with the function given in [8], in our simula-

tions, the deferring function for a node i ∈ V (G) to defer its

retransmission of a non-duplicate RREQ that it receives from

a neighbor j is 4 × � e( j,i)PTX max

� × T + uniform(0, T ), where Tis a system parameter and function uniform (0, T ) will return

a random value uniformly distributed between 0 and T .

Figure 1 compares the network lifetime by implementing

each of the simulated protocols. In Fig. 1, we can see that the

network lifetime performance due to each of the simulated

protocols increases with mobility ratio. This is because mo-

bility helps to balance the traffic distribution among nodes

and avoid certain nodes to be over drained by having to serve

as relaying nodes for many connections too long. For the free-

space model, Fig. 1 shows that HEAP-2 and HEAP-1 result

in the longest network operational time. Further, MREP out-

performs MLRP, SEADSR, and PANDA-TP. The last three

protocols perform approximately the same in terms of net-

work lifetime performance. The reason that MREP achieves

higher performance is due to its good capability of adap-

tively selecting routes with high remaining energy, which

helps to balance traffic among nodes and to prevent energy-

critical nodes from energy draining as much as possible. By

excluding those unnecessary extra-long links, HEAP-1 fur-

ther enhances MREP. Although MLRP does not perform very

well, its enhancement HEAP-2 performs well. The reason is

because by working with our suggested energy availability

Springer

Wireless Netw (2006) 12:481–494 491

Two-Ray model

500

1000

1500

2000

2500

0.1 0.2 0.3 0.4 0.5 0.6

Mobility ratio

Net

wor

kL

ife

tim

e(s

e con

d)

HEAP-2HEAP-1MLRPMREPPANDA-TPSEADSR

Free-space model

400

800

1200

0.1 0.2 0.3 0.4 0.5 0.6

Mobility ratio

Net

wor

kL

ife

tim

e(s

econ

d)HEAP-2HEAP-1MREPSEADSRPANDA-TPMLRP

Fig. 1 Network lifetime by using different protocols versus mobility ratio in different propagation models

disseminating scheme, the HEAP-2 implementation can ef-

fectively filter out those energy-critical nodes from partici-

pating in multi-hop data communications.

For the two-ray model, Fig. 1 shows that the simulated pro-

tocols, sorted from the best to the worst in terms of network

lifetime, are HEAP-2, HEAP-1, MLRP, MREP, PANDA-TP,

SEADSR. Here, we first explain the reason why MLRP per-

forms much better in the two-ray model than in the free-space

model. The energy draining rate at nodes depends mainly on

the following two factors: The amount of energy charged

per packet transmission, and the total amount of load that a

node carries due to the diversity performance in route selec-

tions. The former is affected by the (average) length of links

used, while the latter depends on the route-searching strategy

employed. For the free-space model, the use of certain long

links for packet transmissions can help balancing the traf-

fic distribution without causing too much penalty in energy

consumption, which is the opposite when the decay factor

in path loss is large as in the two-ray model. By excluding

those nodes that are energy-critical from serving as relaying

nodes for multi-hop communications, HEAP-2 further en-

hances MLRP in prolonging network lifetime. HEAP-1 (or

MREP) is inferior to HEAP-2 (or MLRP) due to the less or

no considerations on quality of links that are used for packet

transmissions in their respective implementations.

Figure 2 compares the network lifetime due to MREP and

SEADSR in networks wherein no transmit power adjusting

capabilities are assumed at nodes. In this case, all transmis-

sions are carried out at full transmission power. Figure 2

shows that MREP outperforms SEADSR again in such net-

work environment.

Figure 3 compares the average amount of control power

consumed for acquiring a path (i.e., the amount of energy

consumed for sending control packets per route acquisition)

by different protocols. In Fig. 3, we can see that our designed

protocols can greatly reduce the communication overhead

incurred per route acquisition without using any topological

information at nodes. Protocols sorted from the smallest to

the largest in terms of control power overhead are MLRP,

HEAP-2 and HEAP-1, MREP, PANDA-TP and SEADSR

for both propagation models tested.

Figure 4 shows the average route acquisition latency due

to our designed protocols. In the simulations, instead of pro-

viding the actual average latency experienced in acquiring a

route using each of the designed protocols, more concern is

on the average number of searching rounds experienced in

acquiring a path by using these protocols. This measurement

can provide us an approximate estimation on the amount of

latency introduced in route acquisition due to the adaptive

procedures employed for adjusting the threshold values at

nodes in our protocols. Note that the enforcement of local

queries at source nodes is not counted. In Fig. 3, we can see

200

400

600

800

0.1 0.2 0.3 0.4 0.5 0.6

Mobility ratio

Netw

ork

Lif

etim

e( s

eco

nd

)

MREP SEADSR

Fig. 2 Network lifetime by different protocols versus mobility ratio innetworks wherein no transmission power adjusting capabilities assumedat nodes

Springer

492 Wireless Netw (2006) 12:481–494

Two-Ray model

20

40

60

80

100

0.1 0.2 0.3 0.4 0.5 0.6

Mobility ratio

(No

rmal

ized

)C

on

t ro

lp

ow

er

con

sum

edp

erro

ute

acq

uis

itio

n

SEADSR

PANDA-TP

MREP

HEAP-1

HEAP-2

MLRP

Free-space model

40

60

80

100

0.1 0.2 0.3 0.4 0.5 0.6

Mobility ratio

(No

rmal

ized

)C

on

tro

lp

ow

er

con

sum

edp

erro

ute

acq

uis

itio

n

SEADSR

PANDA-TP

MREP

HEAP-1

HEAP-2

MLRP

Fig. 3 Control power consumed per route acquisition by using different protocols versus mobility ratio in different propagation models

clearly that the route acquisition latency due to our design

is quite low. The simulated protocols from the lowest to the

highest with respect to route acquisition latency are: MREP,

HEAP-1, HEAP-2, and MLRP. Note that although the num-

ber of searching rounds per request by using SEADSR or

PANDA-TP is always one (not shown), different deferring

approaches in their implementations are to be enforced at in-

termediate nodes for high-quality paths to be selected. Such

intentional deferring at intermediate nodes can increase the

route acquisition latency. In our designs, such intentional de-

ferring at intermediate nodes is not needed. Therefore, the

performance of the simple methods that we provided for

adaptively adjusting the threshold values at nodes is quite

satisfying. In addition, in our simulations, the route acquisi-

tion latency does not change significantly with propagation

models.

1

2

0.1 0.2 0.3 0.4 0.5 0.6

Mobility ratio

Av

erag

eN

um

ber

of

sear

chin

gro

un

ds

per

rou

teac

qu

isit

ion

MLRP

HEAP-2

HEAP-1

MREP

Fig. 4 Avg. route acquisition latency (measured in number of searchingrounds) per request by using different protocols versus mobility ratio

In summary, from the above simulation results, we draw

the following conclusions. In terms of the network lifetime,

MREP outperforms MLRP in the free-space model, which

is the opposite in the two-ray model. MLRP outperforms

MREP in terms of communication overhead while MREP

achieves lower route acquisition latency. For the hybrid pro-

tocols, HEAP-2 outperforms HEAP-1 with respect to both

network lifetime and communication overhead, and HEAP-

1 achieves slightly lower route acquisition latency as com-

pared with HEAP-2. Overall speaking, HEAP-2 is suitable

for different propagation models for prolonging the network

lifetime and reducing the communication overhead.

8. Conclusions

Energy use is in many cases the most crucial issue in design-

ing wireless ad hoc networks. In this paper, we presented

the design of several on-demand energy-aware routing proto-

cols. Our protocols work to find energy-efficient routes while

minimizing the overhead incurred in acquiring such routes in

networks wherein no topological information stored at nodes.

To achieve this objective, our design is to adaptively select

the subset of network nodes required to involve in a route-

searching process (measured in nodal remaining energy) or

the degree (measured in transmission power) to which in-

termediate nodes are required to participate in searching for

such a path. We respectively designed protocols by consider-

ing nodal remaining energy and/or link transmission power

to prolong network lifetime through balancing energy drain-

ing among nodes. We provided detailed analytical results

related to the designed protocols. Detailed designs were pro-

vided for nodes in network to adaptively and independently

adjust key parameters in the respective protocol implemen-

tations without topological information at nodes. Simulation

results demonstrate that the designed protocols can achieve

Springer

Wireless Netw (2006) 12:481–494 493

prolonged network lifetime and can greatly reduce the com-

munication overhead consumed in acquiring energy-efficient

paths.

References

1. Q. Li, J. Aslam, and D. Rus, Online power-aware routing in wirelessad-hoc networks, in Proc. ACM Mobicom’01 (2001) pp. 97–107.

2. J.-H. Chang, and L. Tassiulas, Energy conserving routing in wirelessad-hoc networks, in Proc. IEEE INFOCOM’00 (2000) pp. 22–31.

3. C.E. Perkins, E.M. Royer, and S. Das, Ad hoc on demand distancevector routing, in Proc 2ndIEEE Workshop on Mobile ComputingSystems and Applications (1999) pp. 90–100.

4. D.B. Johnson, and D.A. Maltz, Dynamic source routing in ad hocwireless networks, in Mobile Computing, edited by T. Imielinskiand H. Korth, chapter 5, Kluwer Academic Publishers (1996) pp.153–181.

5. X.-Y. Li, P.-J. Wan, and Y. Wang, Power efficient and sparse spannerfor wireless ad hoc networks, in Proc. IEEE ICCCN’01 (2001) pp.564–567.

6. N. Li, J. Hou, and, L. Sha, Design and analysis of an MST-basedtopology control algorithm, in Proc. IEEE INFOCOM’03 (2003).

7. J. Wu, F. Dai, M. Gao, and I. Stojmenovic, On calculating power-aware connected dominating sets for efficient routing in ad hoc wire-less networks, IEEE/KICS Journal of Communication Networks,vol. 4, no. 1 (2002) pp. 59–70.

8. J. Li, and P. Mohapatra, A novel mechanism for flooding basedroute discovery in ad hoc networks, in Proc. IEEE GLOBECOM’03(2003) pp. 692–696.

9. S. Doshi, S. Bhandare, and T.X. Brown, An on-demand mini-mum energy routing protocol for a wireless ad hoc network, ACMSIGMOBILE Mobile Computing and Communications Review, vol.6, no. 3 (2002) pp. 50–66.

10. M.C. Domingo, D. Remondo, and O. Leon, A simple routingscheme for improving ad hoc network survivability, in Proc. IEEEGLOBECOM’03 (2003) pp. 718–723.

11. B. Zhang, and H.T. Mouftah, Adaptive energy-aware routing pro-tocols for wireless ad hoc networks, in Proceedings of the FirstInternational Conference on Quality of Service in HeterogeneousWired/Wireless Networks (QShine) (2004) pp. 252–259.

12. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network Flows: Theory,Algorithms, and Applications, Englewood Cliffs, NJ: Prentice Hall(1993).

13. Z. Wang and J. Crowcroft, Quality-of-service routing for support-ing multimedia applications, IEEE Journal on Selected Areas inCommunications, vol. 14, no. 7 (1996) pp. 1228–1234.

14. V. Rodoplu, and T.H. Meng, Minimum energy mobile wireless net-works, IEEE J. Sel. Areas Comm., vol. 17, no. 8 (1999) pp. 1333–1344.

15. S. Narayanaswamy, V. Kawadia, R.S. Sreenivas, and P.R. Kumar,Power control in ad-hoc networks: Theory, architecture, algorithmand implementation of the COMPOW protocol, in Proc. EuropeanWireless Conference (2002) pp. 156–162.

16. V. Kawadia, and P.R. Kumar, Power control and clustering in adhoc networks, in Proc. IEEE INFOCOM’03 (2003) pp. 459–469.

17. J. Gomez, A.T. Campbell, M. Naghshineh, and C. Bisdikian, PARO:Conserving transmission power in wireless ad hoc networks, inProc. IEEE ICNP’01 (2001) pp. 24–34.

18. B. Zhang, and H.T. Mouftah, Localized power-aware routing forwireless ad hoc networks, in Proc. IEEE ICC’04 (2004) pp. 3754–3758.

19. Y. Xue, and B. Li, A Location-aided power-aware routing protocolin mobile ad hoc networks, in Proc. IEEE Globecom’01 (2001) pp.2837–2841.

20. S.-Y. Ni, Y.-C. Tseng, Y.-S. Chen, and J.-P. Sheu, The broad-cast storm problem in a mobile ad hoc network, in Proc. ACMMOBICOM’99 (1999) pp. 151–162.

21. Z.J. Haas, J.Y. Halpern, and L. Li, Gossip-based ad hoc routing, inProc. IEEE INFOCOM’02 (2002) pp. 1707–1716.

22. B. Williams, and T. Camp, Comparison of broadcasting techniquesfor mobile ad hoc networks, in Proc. ACM MOBIHOC’02 (2002)pp. 194–205.

23. L. Bao, and J.J. Garcia-Luna-Aceves, Topology management in adhoc networks, in Proc. ACM MOBIHOC’03 (2003) pp. 129–140.

24. J.E. Wieselthier, G.D. Nguyen, and A. Ephremides, On theconstruction of energy-efficient broadcast and multicast treesin wireless networks, in Proc. IEEE INFOCOM’00 (2000) pp.585–594.

25. J. Cartigny, D. Simplot, and I. Stojmenovic, Localized minimum-energy broadcasting in ad-hoc networks, in Proc. IEEEINFOCOM’03 (2003) pp. 2210–2217.

26. V. Bharghavan, A.J. Demers, S. Shenker, and L. Zhang, MACAW:A media access protocol for wireless LAN’s, in Proc. ACMSIGCOMM’94 (1994) pp. 212–225.

27. IEEE Computer Society LAN MAN Standards Committee, Wire-less LAN Medium Access Protocol (MAC) and Physical Layer(PHY) Specification, IEEE Std 802.11-1997. The Institute of Elec-trical and Electronics Engineers (1997).

Baoxian Zhang received his B.S., M.S., andPh.D. degrees in Electrical Engineering fromNorthern Jiaotong University, Beijing, Chinain 1994, 1997, and 2000, respectively. FromJanuary 2001 to August 2002, he was work-ing with Department of Electrical and Com-puter Engineering at Queen’s University inKingston as a postdoctoral fellow. He is cur-rently a research scientist with the Schoolof Information Technology and Engineering

(SITE) of University of Ottawa in Ottawa, Ontario, Canada. He haspublished over 40 refereed technical papers in international journalsand conference proceedings. His research interests include routing al-gorithm and protocol design, QoS management, wireless ad hoc andsensor networks, survivable optical networks, multicast communica-tions, and performance evaluation. He is a member of the IEEE.bxzhang@site.uottawa.ca

Hussein Mouftah joined the School of Infor-mation Technology and Engineering (SITE) ofthe University of Ottawa in September 2002as a Canada Research Chair (Tier 1) Profes-sor in Optical Networks. He has been with theDepartment of Electrical and Computer En-gineering at Queen’s University (1979-2002),where he was prior to his departure a Full Pro-fessor and the Department Associate Head. Hehas three years of industrial experience mainly

at Bell Northern Research of Ottawa, now Nortel Networks (1977-79).He has spent three sabbatical years also at Nortel Networks (1986-

87, 1993-94, and 2000-01), always conducting research in the area ofbroadband packet switching networks, mobile wireless networks andquality of service over the optical Internet. He served as Editor-in-Chiefof the IEEE Communications Magazine (1995-97) and IEEE Commu-nications Society Director of Magazines (1998-99) and Chair of theAwards Committee (2002-2003). He is a Distinguished Speaker of theIEEE Communications Society since 2000.

Dr. Mouftah is the author or coauthor of five books, 22 book chaptersand more than 700 technical papers and 8 patents in this area. He is the re-cipient of the 1989 Engineering Medal for Research and Development of

Springer

494 Wireless Netw (2006) 12:481–494

the Association of Professional Engineers of Ontario (PEO), and the On-tario Distinguished Researcher Award of the Ontario Innovation Trust.He is the joint holder of the Best Paper Award for a paper presented atSPECTS’2002, and the Outstanding Paper Award for papers presentedat the IEEE HPSR’2002 and the IEEE ISMVL’1985. Also he is the jointholder of a Honorable Mention for the Frederick W. Ellersick Price Pa-per Award for Best Paper in the IEEE Communications Magazine in

1993. He is the recipient of the IEEE Canada (Region 7) OutstandingService Award (1995). Also he is the recipient of the 2004 IEEE Com-munications Society Edwin Howard Armstrong Achievement Award,and the 2004 George S. Glinski Award for Excellence in Research of theFaculty of Engineering, University of Ottawa. Dr. Mouftah is a Fellowof the IEEE (1990) and Fellow of the Canadian Academy of Engineering(2003).

Springer