A Communication Mechanism using Traveling Wave Phenomena
for Wireless Sensor Networks
Yoshiaki Taniguchi, Naoki Wakamiya, Masayuki Murata
Graduate School of Information Science and Technology, Osaka University
1-5 Yamadaoka, Suita, Osaka 565-0871, Japan{y-tanigu, wakamiya, murata}@ist.osaka-u.ac.jp
Abstract
In this paper, we propose and evaluate a self-organizing
communication mechanism for wireless sensor networks
where a large number of sensor nodes are deployed. To
accomplish application-oriented periodic communication
without any centralized controls, we adopt traveling wave
phenomena of a pulse-coupled oscillator model by regarding sensor nodes as oscillators and emission of radio signals as firing. Through simulation experiments, we confirm
that our mechanism delivers sensor information to / froma designated node in a more energy-efficient manner thanother method, although it takes time to generate a traveling wave. In addition, we implement our mechanism using
MOTE MICAz and verify its practicality.

1 Introduction
The development of low-cost microsensor equipments
having the capability of wireless communication has caused
sensor network technology to attract the attention of many
researchers and developers. It is possible to obtain information on behavior, condition, and position of elements in a
local or remote region by deploying a network of batterypowered sensor nodes there. Each sensor node in such asensor network has a general purpose processor with a limited computational capability, a small memory, and a radiotransceiver.
Due to several restrictions including limited battery capacity, random deployment, and a large number of fragile
sensor nodes, a communication mechanism should be energy efficient, adaptive, robust, fully distributed, and selforganizing. Furthermore, it should be able to handle various types of communication, i.e., diffusion and gathering,
involving the whole network in accordance with application’s requirements. For example, a sensor node detecting an emergency would distribute the information over thewhole sensor network to alert the other nodes and makethem cooperatively react to the emergency. On the contrary,a sensor node detecting an uncertain condition would collect and aggregate sensor information of the other nodes tohave a more precise view of the environment by conjecturing from collected information.
Most of communication schemes cannot adopt to dynamically changing application’s requirements. For example, directed diffusion [1] also considers both types of communication, i.e., pull and push. In the two-phase pull diffusion, sinks first emit an interest message to find sources.
Interest messages are flooded across a network, and matching sources periodically send exploratory data to the sinkalong paths that interest messages traversed. After the initial exploratory data come, the sink chooses one and reinforces the corresponding paths to sources so that following
data traverse them to the sink with the smallest latency. The
pull-type communication is shown to be appropriate for acase with many sources and few sinks. On the contrary, inthe push diffusion, sources first send exploratory data to notify possible sinks of the existence of data. The push-typecommunication is good for a case with many sinks and few
sources. Although directed diffusion can support two different application’s requirements, these mechanisms cannot
be used simultaneously and the mechanism to employ must
be determined in advance taking into account expected conditions, including the number of sources and sinks and theircommunication frequency.
To answer dynamically changing application’s requirements, a communication mechanism should handle bothtypes of communication, especially in an autonomous andself-organizing manner. In addition, taking into account the
insufficient computational capability and memory capacityof inexpensive small sensor nodes, the mechanism must be
as simple as possible. A simple mechanism can also avoid
introducing programming and operational errors.
For this purpose, we adopt a pulse-coupled oscillator(PCO) model based on biological mutual synchronizationsuch as that observed in flashing fireflies [2, 3]. In a PCO

global synchronizationtime
non-firing node

traveling wave

time
firing node

Figure 1. Global synchronization and traveling wave

model, synchronous behavior of a group of oscillators is
considered. Each oscillator operates on a timer. When thephase of the timer reaches one, an oscillator fires. Oscillators coupled with the firing oscillator are stimulated andthey shift the phase of timers by a small amount. Throughmutual interactions by stimuli among oscillators, they eventually reach a synchronized behavior. There are several
papers which employ a PCO model to make sensor nodes
operate in synchrony, e.g., clock synchronization, througha distributed and self-organizing control mechanism [4–6].
In [6], we proposed a data gathering scheme which employ synchronized behavior of a PCO model, and confirmedthat it worked in a fully-distributed, self-organizing, robust,
adaptive, scalable, and energy-efficient manner.
In our previous research work [7], in contrast to theother works, we focused on another phenomenon observedin a PCO model. In a PCO model, it is shown that not
only the global synchronization where all oscillators firesynchronously, but a traveling wave, where oscillators behave synchronously but with fixed phase difference, appears(Fig. 1) [3]. By adjusting parameters and functions of a
PCO model, we can control the frequency, form, and direction of a wave. We proposed a new simple communication
mechanism which can organize a variety of communication,i.e., diffusion and gathering, depending on application’s requirements. The desired pattern of message propagation
emerges through reactions of sensor nodes to surrounding
conditions and local and mutual interactions among sensor
nodes, that is, by self-organization. We investigated conditions of a phase response curve (PRC) with which a wireless sensor network reached a preferred phase-lock condition from arbitrary settings of the initial phase of sensor
nodes. In addition, we proposed a self-organizing communication mechanism which generated concentric travelingwaves centered at a sensor node, which wanted to gather
information from all sensor nodes or diffuse information to
all sensor nodes. We further confirmed the basic behaviorof our mechanism through simulation experiments. In our
mechanism, each sensor node broadcasts its sensor information in accordance with the phase of its own timer. Whena sensor node receives a radio signal of others, it shifts

the phase of its timer. Through mutual interactions amongneighboring sensor nodes, they reach the state, called phaselock, where the phase differences among sensor nodes are
kept constant, and they emit sensor information alternately.
In this paper, we evaluate our mechanism through additional
simulation experiments. Furthermore, we implement ourmechanism using MOTE MICAz [8], and verify that themechanism can work on real wireless environment.
The rest of this paper is organized as follows. First, inSection 2, we briefly introduce how to generate travelingwaves in a pulse-coupled oscillator model. Next, we introduce our communication mechanism for wireless sensor
networks in Section 3, and show simulation results in Section 4. In Section 5, we implement our mechanism andconfirm the feasibility and availability of the mechanism.
Finally, we conclude the paper and describe future researchworks in Section 6.

2 Traveling waves in a pulse-coupled oscillator model
A pulse-coupled oscillator model is developed to explain synchronous behaviors of biological oscillators suchas pacemaker cells, fireflies, and neurons [3]. Consider
a set of N oscillators. Each oscillator i has phase φi ∈[0, 1] (dφi /dt = 1). As time passes, φi shifts toward
one and, after reaching it, the oscillator fires and the phasejumps back to zero. Oscillator j coupled with the firing oscillator i is stimulated and advances its phase by an amount∆(φj ). Thus, we have
φj → φj + ∆(φj ),(1)

where ∆(φ) is called a phase-response curve (PRC). For
example, for the quadratic integrate-and-fire (QIF) model,∆QIF (φ) = −a sin 2πφ and for the radial isochron clock(RIC) model, ∆RIC (φ) = a(1 − cos 2πφ) [3]. Here, an
oscillator ignores all stimuli at the moment of firing, andan oscillator identifies multiple stimuli received at the sametime as one stimulus.
Through mutual interactions, a set of oscillators reach either of the global synchronization where they have the same
phase and fire all at once, or the phase-lock condition wherephases are different among oscillators with a constant offset
as shown in Fig. 2. In the case of the phase lock, the geographic propagation of firings seems like a traveling wave asshown in Fig. 1. Whether a network reaches the global synchronization or the phase-lock depends on the initial phaseof timers or properties of the PRC [9].
We have investigated conditions of PRC that led to desired phase-lock condition regardless of the initial phase [7].
We first consider a traveling wave in a PCO network where
oscillators are arranged in a line. We assume a pacemaker,

phase1firingfiring

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Figure 3. PRC ∆S of Eq. (3)For example, the following PRC function satisfies Eq. (2).
a sin∆(φ)=00that is an oscillator which dominates and controls a firing
pattern on a PCO network. A pacemaker is different fromother oscillators only in a point that it will not be stimulated
by other oscillators and thus fires at its own periodic timing,
which corresponds to the data gathering or diffusion cycle
in a wireless sensor network. Therefore, there is no centralized control over a wireless sensor network and the model isself-organizing. Furthermore, we consider that an oscillator
is stimulated only by its neighboring oscillators which arecloser to the pacemaker.
In a PCO network, to generate a desired traveling wave
where oscillators fire from a pacemaker toward the edge atconstant phase-difference τ regardless of the initial phaseof oscillators, a PRC function must satisfy the following
conditions.
 0 < ∆(φ) ≤ 1 − τ − φ (0 ≤ φ < 1 − τ )∆(φ) = 0(φ = 1 − τ )(2)

1 − τ − φ ≤ ∆(φ) < 0 (1 − τ < φ < 1).

=∆(φ)=1-τ−φ

0.2

-0.2

Figure 2. Global synchronization and phaselock∆S (φ)

0.4

0

∆(φ )

0

a=0.1, b=0.5
a=0.05, b=0.3

0.6

time
firing

1

φj

0.8

∆(φ)

global synchronization(3)

Here, a and b are parameters which determine characteristics of the PRC. Figure 3 illustrates PRC ∆S (φ) for two
different settings of a and b when τ = 0.2. Two dot-anddash lines stand for ∆(φ) = 0 and ∆(φ) = 1 − τ − φ,respectively. The curve of PRC satisfying Eq. (2) must lie
between these two lines. As parameters a and b increase,a traveling wave emerges more rapidly. Especially, a traveling wave emerges by only one interaction, i.e., stimulus,
with a = 0 and b = 1. However, such aggressive setting
spoils the resilience of the mechanism against a failure ofnode, skewness of a timer, and unexpected influence fromthe environment, since a single firing emitted at a wrong
timing will drastically change the state of the whole system. Therefore, a PRC function and its parameters should

be appropriately determined taking into account the tradeoff between the speed that a traveling wave emerges and theresilience against failures.
PRC ∆S can generate both types of traveling wave. By
setting τ as τ < 0.5, a traveling wave from the peacemakertoward the edge of a PCO network with constant phasedifference can be organized. On the contrary, with τ > 0.5,
a traveling wave moves from the edge of a PCO network toward the peacemaker. The same PRC can also be applied tothe case of two dimensional arrangement of oscillators bymaking a tree whose root is the pacemaker. In a tree, an oscillator is stimulated by its parent, i.e., an oscillator closer tothe pacemaker. Although any routing protocol for wirelesssensor networks is viable to organize such tree-type topology and it can be combined with our mechanism, a simple
way of setting such relationship among oscillators will begiven in the next section.

3 A distributed and self-organizing communication mechanism
In this section, we briefly introduce our fully-distributedand self-organizing communication mechanism for wirelesssensor networks [7]. In our mechanism, any sensor node
can gather or diffuse information in accordance with an application’s requirements. In our mechanism, a node fromwhich messages are disseminated or to which messages aregathered is called a core node and plays a role of a pacemaker in the PCO model.
Sensor node i (1 ≤ i ≤ N ) has a timer with phase φi ∈[0, 1]. It maintains PRC function ∆(φ), level value li , session identifier si , direction δi , and offset τ (0 < τ < 0.5).
Initially a level value, a session identifier, and a direction
are set to zero. A level value corresponds to the number ofhops from the core node and it is used to define the relationship among sensor nodes in stimulation. The PRC function
and offset are determined at the deployment phase, but theoffset can be dynamically adjusted as explained later. In thispaper, based on Eq. (3), we use the following PRC function

for all sensor nodes.
∆(φ)= a sinπ
φ + b(g − φ),g(4)Here, g is defined as (1 − δi τ ) mod 1. δi is a parameter
which controls the direction of information propagation. It
is set at 1 for diffusion and −1 for gathering.
Basic behavior of a sensor node is as follows. A sensor
node wakes up when its phase is at 1−τ , and then it receives
and processes messages as needed. When its phase reaches
one, a sensor node broadcasts a message. A message that
sensor node i emits contains level value li , session identifier si , direction δi , and its information aggregated withother sensor’s information which it kept in its buffer. After
that, it keeps awake for τ to receive and process messages
as needed, and then goes to sleep. τ should be appropriately determined considering trade-off between the rate ofsuccessful message reception and the lifetime of sensor network. The smaller τ is, the smaller the probability of successful message reception by missing messages delayed bycollisions in radio signals. At the same time, a smaller τ
leads to longer lifetime of sensor network, since a node isawake for the duration of 2τ in one communication cycle.
To initiate a new communication, a core node broadcasts
a message containing a new session identifier set at the current value plus one, a level value of zero, the direction, andinformation to disseminate or gather. Now, sensor node i
receives a message from sensor node j. If session identifier sj is larger than si , sensor node i considers that a newcommunication begins. Therefore, it sets its level value li at
lj +1, session identifier si at sj , and direction δi at δj . Then,
it is stimulated to join a new traveling wave. This mechanism means that the current communication is terminatedby a newly initiated communication. To avoid unintended
termination of communication by other sensor nodes, a corenode might advertise its desired communication period in a
message it emits. However, it requires an additional mechanism such as clock synchronization, and it is left as oneof future research issues. If session identifiers are the sameamong sensor nodes i and j but the level value lj is smaller
than li , sensor node i sets its level value li at lj + 1, direction δi at δj , and it is stimulated. Stimulated sensor node i
shifts its phase based on the PRC function. As in the PCOmodel, a sensor node is not stimulated by messages fromsensor nodes with a smaller level value during the following duration of τ when it has already been stimulated, toavoid being stimulated by deferred messages. If the session
identifier is the same and level value lj is li − δ, sensor node
j is an upstream node of sensor node i. Therefore, to relay
information of sensor node j to the next downstream node,sensor node i deposits the received information in its local
buffer. Information aggregation can be done at this time orjust before next message emission. If a message does notsatisfy the above conditions, sensor node i ignores it. We

should note here that a sensor node only emits a message inaccordance with the phase of its timer. No additional message is required to organize a traveling wave.
Although we do not describe details due to limitation of
the space, our mechanism also considers additional deployment and removal of sensor nodes, multiple core nodes, andnode failures [7].

4 Simulation experiments
We first evaluate our communication mechanism throughsimulation experiments. We consider wireless sensor networks of 100, 900, and 2500 sensor nodes randomly distributed in 10×10, 30×30, and 50×50 region, respectively.
The range of radio signal is fixed at 2 units of length. Initial
phase of sensor nodes is set at random. A core node is randomly chosen for data gathering. A sensor node consumes
81 mW for transmission, 30 mW for receiving and idle, and
0.003 mW for sleep [8]. Initial energy is 50 J for all nodes.
We use Eq. (4) with a = 0.01 and b = 0.5 as the PRC function and τ is set at 0.1. For comparison purposes, we also
conduct simulation experiments for the directed diffusion.
All results are averaged over 100 simulation experiments.
Figure 4 shows comparison with the directed diffusion
where per-hop delay is set at 0.1 time units. The responsetime indicates the duration from emission of an interest ora message with a new session identifier to reception of sensor information from all nodes. The topology time indicates the duration from emission of an interest or a message
with a new session identifier to reception of reinforcement
messages at all nodes or to establish the phase-lock condition. The number of messages indicates the average numberof messages that a node sends and receives during the response time or the topology time. In Fig. 4 (a), both of the
response time and topology time with our mechanism are
longer than those with the directed diffusion. A travelingwave is generated thorough local and mutual interactions,whereas the directed diffusion relies on message flooding.
However, the overhead in terms of the number of messages
is much smaller with our mechanism. It is only 1 to 6 %of the directed diffusion in the response time and 4 to 26 %in the topology time as shown in Fig. 4 (b). Since a sensor node emits a message per cycle in our mechanism, thenumber of message increases in proportional to the response
and topology time. As described in Section 2, the responsetime and topology time can be reduced by adjusting a PRC
function and its parameters.
Figure 4 (c) shows results for the case of information
diffusion, where a randomly chosen node diffuses information to the whole sensor network. When comparing to thepush diffusion of the directed diffusion, our proposal takes
longer to diffuse information to all nodes. Differently fromthe data gathering scenario, the overhead is larger with ournumber of messages

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Figure 4. Comparison among proposal and directed diffusion through simulation experiments
mechanism. It is 220 to 790 % of the directed diffusion in
response time and 718 to 877 % in topology time as shownin Fig. 4 (d). In the case of diffusion, only one source node
floods exploratory data to all other nodes in the push diffusion, but our mechanism takes time to generate a travelingwave and thus requires much message exchanges.
Figure 4 (e) shows the data gathering ratio against thepacket loss probability in a 10×10 network. The data gathering ratio is defined as the ratio of data reached to a corenode or a sink node to the number of nodes. A sensor noderandomly fails in transmitting a message at the packet loss
probability shown on the x-axis. In Fig. 4 (e), our mechanism always achieves higher data gathering ratio than the
directed diffusion with the same packet loss probability.
In our mechanism, broadcasting contributes to achieving
multi-path effect and this leads to the higher gathering ratio.
Finally, we verify energy efficiency of our mechanism
from a viewpoint of a lifetime of a sensor network of 100
nodes. The lifetime is defined as the duration from emissionof an interest or a message with a new session identifier todeath of any sensor node due to depletion of energy. As
shown in Fig. 4 (f), the lifetime with our mechanism is 1577
time units whereas that with the directed diffusion is 265
time units. Furthermore, by using a power-saving mode [7],the lifetime with our mechanism becomes as long as 2733
time units wheres that with the directed diffusion is 304 timeunits.

5 Implementation and evaluation
We implement our mechanism using a commercial sensor unit MOTE MICAz [8]. It has an omni-directional antenna and employs IEEE 802.15.4 MAC protocol on 2.4
GHz bandwidth for radio communication. A 10-seconds
timer is implemented by shifting phase φi by 0.01 at every
100 milliseconds. A message is 40 bits long where the first
4 bits are for level value, 1 bit for δ, 3 bits reserved, 16 bits
for session identifier, and the last 16 bits for data.
We confirm basic behavior of our mechanism on a sensor
network consisting of 16 nodes arranged in a grid as shownin Fig. 5 (a). To maintain the stable network topology, we
introduce a filter with which a node ignores messages from
non-neighboring nodes. A pair of nodes connected by asolid line in Fig. 5 (a) exchange messages. Since the filter is implemented on the application layer, collisions ofradio signals among non-neighboring nodes occur. A cycle of data gathering or dissemination is set at 10 seconds.
Other parameters and settings are the same as those used forthe simulation experiments in the previous section. First,
all sensor nodes periodically broadcast messages independently from each other. At time 100 seconds, sensor node 6
becomes a core node and initiates a data diffusion session.
Then, at time 200 seconds, sensor node 11 initiates a newdata session for data gathering.
Figures 5 (b) and 5 (c) show how the sensor network

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Figure 5. Experimental evaluation
reached the phase-lock condition. Each mark stands for an
instant when a sensor node emitted a message. For easier
understanding, sensor nodes are sorted in order of the hopcount from the core node. At first, all sensor nodes independently emit messages. However, by exchanging messages,
the phase-lock condition for information diffusion eventually appears at about 130 seconds. Figure 5 (b) shows that
sensor nodes emit messages in order of the hop count fromthe core node, and thus information propagates from sensor node 6 to the edge of sensor network. From time 200,
the phase-lock condition for information diffusion is firstbroken by initiating a new session. Then, the new phaselock condition for information gathering appears at about
250 seconds, where information propagates from the edgeof sensor network towards the sensor node 11.

6 Conclusion and future work
In this paper, we first briefly introduced our fullydistributed and self-organizing communication mechanism.
We conducted simulation and practical experiments to verify the effectiveness and practicality of the proposal. As
future research works, we consider additional experiments
to improve our mechanism under a larger network environment with more randomly deployed sensor nodes, more obstructions, more interference, and more collisions.

Acknowledgment
This work was partly supported by “Special Coordination Funds for Promoting Science and Technology: Yuragi
Project”, Grant-in-Aid for Scientific Research on Priority
Areas 18049050, and a Grant-in-Aid for Scientific Research(A)(2) 16200003 of the Ministry of Education, Culture,
Sports, Science and Technology in Japan.

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