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A cyclic MAC scheduler for collecting data from heterogeneous sensors

Chun-Yu Lin a,, Chen-Lung Chan b, Chung-Ta King a, Huang-Chen Lee b

a Department of Computer Science, National Tsing Hua University, Taiwanb Computer and Communication Research Center, National Tsing Hua University, Taiwan

a r t i c l e i n f o

Article history:

Received 27 November 2009

Received in revised form 27 February 2011

Accepted 28 February 2011

Available online 5 March 2011

Keywords:

Wireless sensor networks

Data collecting system

Time division multiple access

Cyclic schedule

Distance constrained task set

a b s t r a c t

Many wireless sensor networks applications, e.g., structural health monitoring (SHM), require the sensors

to construct a multihop network to collect the environmental data in real-time. These sensors generallygenerate sensing data in fixed rates, so their transmission schedules can be deterministically listed. Time

division multiple access (TDMA) is especially appropriate for these applications because it can prevent

radio interference, thereby reducing the transmission power and maximizing wireless spectrum reuse.

However, to reserve sufficient bandwidths on distinct links of a heterogeneous WSN, a complex TDMA

schedule is necessary, and a sensor node might need to keep a large TDMA schedule table in its tiny mem-

ory. To prevent a large size TDMA schedule table, this paper proposes a CyclicMAC scheduler that assigns

each node a temporal transmission pattern which is merely parameterized by period and phase. The

CyclicMAC scheduler determines the period to satisfy the bandwidth requirement of the node, and

adjusts the phase to achieve collision-freeness and reduce the end-to-end latency as well. The end-

to-end latency of the resulting schedule is proven to be optimal if the wireless links only interfere with

their parent link andsibling links. As far as we know, CyclicMAC is the first that simultaneously addresses

the three design issues of TDMA scheduling, which satisfies heterogeneous bandwidth requirements,

minimizing schedule table size, and reducing end-to-end latency, for multihop wireless sensor networks.

2011 Elsevier B.V. All rights reserved.

1. Introduction

Structural health monitoring(SHM) refers to a collection of tech-

nologies that monitor and diagnose the health state of an architec-

tural structure in real-time. Typically, heterogeneous sensors are

deployed inside and around the structure to periodically collect

various types of data relevant to the health state. For example,

to monitor a bridge, engineers must deploy sensors such as

accelerometers, strain gauges, displacement transducers, level

sensing stations, anemometers, temperature sensors and dynamic

weight-in-motion sensors. These sensors measure everything from

tarmac temperature, wind speed, deflection and rotation of cables,

and movement of the bridges desks. Different measurements have

different characteristics and need to be sampled and reported at

different rates, e.g., temperature may be reported once every few

minutes, while vibration and movement may need to be reported

several hundred times per second. Since most existing SHM

systems rely on wired sensors, the cost of deployment and mainte-

nance is usually very high. The massive advances in the develop-

ment of wireless sensor networks (WSN) in recent years offer new

opportunities to the SHM applications. Wireless communication

eliminates the cost of deploying wires and increases the scalability

of the SHM systems.

Wireless sensor nodes are usually powered by batteries. Short-

range communication is more appropriate for transmitting sensed

data because it requires less energy than long-range communica-

tion. It also enables spatial reuse of the radio spectrum, and there-

by increases the throughput of network. For these reasons, sensors

usually use multihop transmission, which utilizes a series of short-

range communication links to send data back to the control center,

called a sink. In WSN applications, the multihop networks are

usually built based on either CSMA or TDMA MAC protocols. In

CSMA-based protocols, such as S-MAC [1] and T-MAC [2], when a

sensor node needs to transmit a data packet, it and the other sen-

sor nodes in the same network exchange messages or use Clear

Channel Assessment (CCA) hardware components to grant the

right to access the channel and prevent the packet collision. But

in TDMA-based protocols, the sensor nodes transmit data packets

according to a predefined schedule that will never cause the packet

collision. In general, a CSMA-based protocol is suitable for a dy-

namic environment in which the wireless links between the sensor

nodes are easily broken or the sensor nodes will generate data in

unstable rates. However, such overhead on energy consumption

is unnecessary if the system environment is relatively stable. For

0140-3664/$ - see front matter 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.comcom.2011.02.012

Corresponding author at: Room 734, EECS Building, No. 101, Section 2, Kuang-

Fu Road, Hsinchu 30013, Taiwan. Tel.: +886 3 5715131x33906; fax: +886 3

5723694.

E-mail addresses: [email protected] (C.-Y. Lin), [email protected]

(C.-L. Chan), [email protected] (C.-T. King), [email protected] (H.-C. Lee).

Computer Communications 34 (2011) 16301644

Contents lists available at ScienceDirect

Computer Communications

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m c o m
http://dx.doi.org/10.1016/j.comcom.2011.02.012mailto:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.comcom.2011.02.012http://www.sciencedirect.com/science/journal/01403664http://www.elsevier.com/locate/comcomhttp://www.elsevier.com/locate/comcomhttp://www.sciencedirect.com/science/journal/01403664http://dx.doi.org/10.1016/j.comcom.2011.02.012mailto:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.comcom.2011.02.012

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example, in most SHM applications, each sensor node is mounted

on the structures and transmits sensed data regularly. Such stable

system characters lead to a static network topology and static data

rates that are appropriate to the TDMA-based protocols.

Consider a wireless sensor network with a set of sensor nodes.

We assume that a pair of sensor nodes has a wireless link if they

are in the radio range of each other. If a group of nodes are in range

of each other, their data packets will collide if these packets are

transmitted simultaneously. To prevent the potential radio inter-

ference, the transmissions of these wireless links must be stag-

gered into different times. In a TDMA-based MAC protocol, the

TDMA scheduler determines the times to transmit packets of each

wireless link to prevent radio interference. Assuming the timeline

is slotted, the TDMA scheduler assigns each wireless link a series of

timeslots on which it can transmit the data packets. The assign-

ments are stored in the TDMA schedule tables of the two sensor

nodes connected by the wireless link. The sensor nodes can thus

turn on/off their radio interfaces according to their TDMA sched-

ules to save energy. Due to its simplicity and efficiency on energy

consumption, TDMA-based protocols have been widely applied in

many WSN applications.

However, when applying TDMA to a multihop wireless sensor

network that supports real-time SHM applications, the TDMA

scheduler should further take the following three practical design

issues into account:

Satisfying bandwidth requirement: The available bandwidth of a

wireless link is determined by the number of transmission

timeslots allocated to the link, and the bandwidth should be

sufficiently large to not only transmit the data packets gener-

ated by the sensor nodes connected by the link but also relay

the traffic from the upstream links. Thus, the TDMA scheduler

should assign sufficient timeslots to each link according to its

aggregated bandwidth requirement so that all the sensed/

relayed data packets can be collected in time.

Minimizing TDMA schedule table: The TDMA schedule table spec-

ifies when the wireless links will be activated in a given period.The sensor node must store the TDMA schedule in its main

memory, which is a resource as scarce as the battery power.

Therefore, the TDMA schedule should be compact enough so

that the remaining memory space can be used by other critical

tasks, such as queuing the sensing data.

Reducing the end-to-end latency: When using WSN in an emer-

gency application, the underlying wireless network should have

similar performance as a wired network, i.e., data packets

should be delivered to the sink immediately after they are

generated. Note that in a multihop wireless network, the end-

to-end latency of a data packet will be increased if the transmis-

sion of the packet is interrupted to wait for the active timeslot

of an intermediate wireless link. Thus, to reduce the end-to-end

latency, the TDMA scheduler must arrange the transmissiontimeslots of this packet link by link along the end-to-end path

to ensure the timeslots are consecutive.

Many previous works have addressed some of these design is-

sues of TDMA scheduling for wireless sensor networks. However,

to the best of our knowledge, none of these works fulfills all the

above three issues simultaneously. Some TDMA schedulers [48]

take the bandwidth requirement into account by allocating each

sensor node a contiguous timeslot whose length is proportionally

fair to its bandwidth requirement. However, such design does

not consider the consecutiveness of the allocated timeslots along

the end-to-end path from a sensor to the sink, and therefore could

lead to a considerable end-to-end latency of transmitting a data

packet. The EDF-based TDMA schedulers [911] enumerate everyintending packet transmission and schedule the transmissions

based on Earliest Deadline First policy to reduce the end-to-end

latency. These approaches consider both different bandwidth

requirements and low end-to-end transmission latency. However,

the TDMA schedule tables in these approaches must include the

enumeration of all the packet transmissions, so these approaches

tend to generate a huge schedule table when the sensor nodes have

deviated sensing rates, or when the network size is large. The

resulting TDMA schedule table might be too enormous for sensor

nodes to store in their tiny memory. Some TDMA schedulers

[12,1519] generate a round-robin TDMA schedule table, which

is simple and small. However, these TDMA schedulers do not con-

sider the different bandwidth requirements of the sensor nodes

and the end-to-end latency in a data collecting system.

In this paper, we propose a TDMA scheduler called CyclicMAC

that fulfills all the above design issues in multihop wireless sensor

networks. CyclicMAC scheduler specifies a cyclic link schedule

parameterized only by period and phase for each wireless link,

where the period is the time interval between two consecutive

packet transmissions and the phase is the initial delay time to

transmit the first packet. Undoubtedly, the size of the TDMA sche-

dule table in CyclicMAC can be effectively reduced since it only

needs to store two parameters for each wireless link, instead of

the timetable of each individual packet transmission. The band-

width requirement of a wireless link can be satisfied by setting

an appropriate period, and the end-to-end latency of a data packet

can be minimized by adjusting the phase. We also prove that in an

ideal case in which the wireless links only interfere with their par-

ent links and sibling links, CyclicMAC scheduler will generate a

TDMA schedule with an optimal end-to-end latency, i.e., the time-

slot length multiplies the number of intermediate links from

source node to sink. Such ideal case is reasonable in a sparsely de-

ployed wireless sensor network. We also prove that in a densely

deployed network, the end-to-end latency is still bounded. There-

fore, CyclicMAC is considered to be an ideal MAC scheduler to WSN

applications whose data sampling rates are static.

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

lists the previous works related to our research. In Section 3, weformally describe the system model of TDMA over a multihop

wireless sensor network. Section 3.1 introduces the proposed

CyclicMAC scheduler. In Section 5, we present some performance

evaluations of the proposed scheduler via simulation. Section 6

gives some concluding remarks.

2. Related works

In this paper, we focus on the design of a TDMA scheduler that

generates a small TDMA schedule to support both the bandwidth

requirement and latency minimization for a data collecting system

over a multihop wireless sensor network. While some famous

works, such as B-MAC [1] T-MAC [2], Dozer [3], target at support-ing general purpose WSN applications which might be highly

dynamic, we only target at the data collection system whose

network condition is stable, rather than dynamic.

Some previous works [48] propose TDMA schedulers that sup-

port the bandwidth requirements by achieving the fairness of

bandwidth allocation. Sridharan and Krishnamachari [4] proposed

a method that determines the number of time slots allocated to the

sensor nodes proportionally according to their bandwidth require-

ments. Wang et al. [5], Zheng et al. [7], and Rajendran et al. [8] de-

fine the timeslot allocation as an optimization problem that

maximizes the throughput. Soldati et al. [6] further defines an opti-

mization problem that considers the end-to-end bandwidth alloca-

tion over a multihop network. In general, these TDMA schedulers

allocate timeslots for the sensor nodes according to their samplingrates to ensure bandwidth fairness among the nodes. These

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schedulers usually allocate some consecutive timeslots to each

node according to its bandwidth requirement. However, such con-

secutive allocation could easily induce additional transmission la-

tency in a multihop wireless sensor network. In a multihop

wireless sensor network, a data packet is transmitted by the source

sensor node, relayed by several intermediate sensor nodes, and

then delivered to the sink. If the timeslot allocation does not con-

sider the order of packet transmission carefully, the data packet

might need to be queued in an intermediate node because the cur-

rent timeslot has been allocated to another neighbor node. This

undoubtedly lengthens the end-to-end latency, and once the queue

has overflowed, the packets will be dropped and therefore cause

packet loss.

A TDMA scheduler that only considers the bandwidth require-

ment is insufficient. In a static data collecting system such as a

SHM application, the sensor nodes usually sample the environ-

ment and transmit the sample data to the sink at regular rates.

Therefore, the TDMA scheduler can deterministically enumerate

all the packet transmissions in a given time interval and then sche-

dule the packet transmission times to satisfy various designated

goals, such as real-time [911]. For example, both Li et al. [9]

and Stankovic et al. [10] schedule packet transmissions, in a multi-

ple hop and a single hop network respectively, via the Earliest-

Deadline-First(EDF) scheduling algorithm, which has been proven

effective in both satisfying bandwidth requirements and reducing

end-to-end latency [12]. Chipara et al. [11] schedules the transmis-

sions of the messages responding to a specific query with deadline,

in a multiple hop wireless sensor network. However, in a network

consisting of many sensor nodes with heterogeneous sampling

rates, enumerating the packet transmissions requires both inten-

sive computation and memory overhead. Even if the scheduler is

executed on a powerful server to eliminate the computation over-

head on the sensor nodes, it still has to announce a huge schedule

table to the entire network. Undoubtedly, to broadcast such a large

schedule table to a multihop wireless sensor network requires con-

siderable energy consumption on the sensor nodes. Besides, to

keep this schedule table in the wireless sensor network requiresthe sensor nodes to allocate an excessive amount of memory for

storage, which might not be feasible for resource constrained sen-

sor nodes.

An interesting approach to reduce the size of TDMA schedule ta-

bles is to let the wireless links transmit data packets in a round-ro-

bin schedule [1319]. These works assume that the system

execution timeline is equally divided into many periods, with each

period being composed of a set of equally-sized timeslots with

identifiers. Then, a round-robin scheduler allocates each node a

timeslot ID that indicates the node can periodically be active to

transmit data at that timeslot in each period. By the round-robin

schedule, each sensor node could only use the timeslot id and total

timeslot number to determine the activation of its wireless link so

that the sensor nodes could keep a small schedule table. DMAC[13] further staggers the activation of sensor nodes to reduce the

end-to-end latency. Mao et al. [15] proposes a TDMA scheme

which employs machine learning model to find the time-optimal

solution for such staggered TDMA schedule. Song et al. [16] ana-

lyzes the time-optimality of such staggered schedule in typical tree

routing structure. Some of these previous works [1719] employ

the graph coloring algorithm to determine the order of transmis-

sion timeslots of wireless links. The coloring algorithm also allows

spatial reusability when scheduling the transmissions of a multi-

hop wireless network, thus improving the throughput of the net-

work. Li et al. [17] provides a general coloring model for

scheduling the transmissions, and extends the model to consider

the transmission latency in multihop network. Gandham et al.

[18] devises a distributed coloring algorithm for link scheduling.Lu et al. [19] analysis delay efficiency of a coloring based sleep

scheduling algorithm. However, these round-robin-based TDMA

schedulers basically assign the bandwidth evenly to the adjacent

wireless links according to the network topology. When the sensor

nodes have heterogeneous bandwidth requirements, such even

bandwidth allocation could allocate too many timeslots to low

data rate wireless links but insufficient timeslots to high data rate

wireless links. If the network is single hop, previous work proposed

by Carley et al. [20] could be a good reference to solve such band-

width allocation problems. In their work, a contention-free peri-

odic message scheduler is proposed to support heterogeneous

bandwidth allocation by giving each wireless link a cyclic schedule

that is parameterized by a period and a phase. However, their

scheduling algorithm can only be applied in single hop networks,

so it still cannot benefit data collecting systems generally imple-

mented over multihop networks. However, the idea behind this

previous work is interesting, and this triggers our work on devel-

oping CyclicMAC, which extends the concept of cyclic scheduling

to support multihop wireless sensor networks.

3. System models

In this section, we formulate the system model of a WSN-based

data collecting system. We assume the topology of the data collect-

ing system is static and consists of total m wireless sensor nodes

N= {n0, n1, . . . , nm} to collect sampling data. Among the sensor

nodes, n0 is the sink, and it collects the sampling data from the

other sensor nodes {n1, n2, . . . , nm}. To address the heterogeneity,

each sensor node has its own designated sampling rate. Let

S= {s1, s2, . . . , si, . . . , sm} denote the sampling rates of the sensor

nodes, where si indicates the sampling rate of the sensor node ni.

A data collecting tree E= {e1, e2, . . . , ei, . . . , em} is a collection of wire-

less links rooted on n0, where the routing structure ofEis assumed

to be a given parameter, which is determined based on the appli-

cation requirements, such as energy efficiency, latency efficiency

or load balance. Each wireless link ei is a directional link whose

source node is ni and destination node is the parent node of ni inthe data collecting tree E. Since the data collecting tree defines

the precedence relationships among links when they collect sam-

pling data, we can say that each link has a parent link and a set

of child links. That is, Parenti denotes the next link of ei to the sink

in E, while Childreni denotes the preceding links whose destination

nodes are ni. Fig. 1 illustrates a data collecting system. {n0, n1, n2,

n3, n4, n5, n6} are the sensor nodes that collect structure health data.

They form a data collecting tree, illustrated in solid links, to deliver

their sample data to the sink node n0. As mentioned, the data col-

lecting tree also defines the precedence relationship of the wireless

links. Take e4 in Fig. 1 as an example; thus Children4 is {e3, e2} and

both Parent3 and Parent2 are e4.

In a wireless network, two wireless links cannot be scheduled

for transmission at the same time if their radio interfaces interferewith each other. In Fig. 1, the dashed lines illustrate the interfer-

ence between two wireless links. To represent this schedule con-

straint, an interference graph I is introduced to represent the

interference between the wireless links. The vertices of I indicate

the wireless links of E, e.g., the vertex e1 in I is the wireless link

e1 in E. If ei and ej interfere with each other, there will be an edge

between them. The interference graph I can be represented as a

m m matrix I= {Iij j Iij = 1 if ei and ej interfere with each other;

otherwise, Iij = 0}.

Fig. 2 shows the corresponding interference graph of the exem-

plary network in Fig. 1. The interference graph Ican be built using

the theoretical [21,22] or empirical interfering model [23,24].

Maheshwari et al. [25] study the impact of interference estimation

algorithms by evaluating packet reception rate under variouslevels of radio interference. They especially compare the packet

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reception rates of a TDMA MAC under several famous interference

estimation models. Their work is helpful for the readers to under-

stand the practical issues in details.

3.1. TDMA scheduling model and constraints

Based on the above model, the TDMA scheduler still needs to

determine the active times of the wireless links in E. Let the system

execution timeline be divided into a set of timeslots numbered

incrementally from 0. The length of a timeslot tk is the time re-

quired to transmit a single sample packet completely. The TDMA

schedule can then be represented as a mapping function f(tk, ei) 2

{0,1}, where each f(tk, ei) determines the state of a wireless link eiin a specific timeslot tk. That is, f(tk, ei) = 1 indicates that ei can be

active to transmit data from ni to its parent at time tk, while

f(tk, ei) = 0 indicates the ei is silent.

A feasible TDMA schedule for a static data collecting systemshould satisfy the two requirements below:

Collision-free requirement: The TDMA schedule should stagger

the packet transmission times of interfering wireless links.

Bandwidth requirement: The TDMA schedule should allocate suf-ficient timeslots to each wireless link according to its aggre-

gated bandwidth requirement.

A TDMAschedule is said to be collision free if no two interfering

wireless links are active at the same time. The collision-free

requirement is formally defined as below, given any timeslot tk:

8ei; ej 2 E and Iij 1;ftk; ei ftk; ej 5 1: 1

Furthermore, a wireless link might deliver the data packets gener-

ated by the source node of the link or forwarded from the children

links. The TDMA schedule should allocate sufficient timeslots to

each wireless link in order to ensure the wireless link has sufficient

bandwidth to deliver these data packets. Formally, given a period T

and the TDMA schedule of a wireless link ei, the bandwidth require-ment is formulated as below:

XT0tk 0

ftk; eiP T si X

ej 2Childreni

XTtk0

ftk; ej; 2

where si is the sampling rate of ni, and Tsi is the total number of

data packets generated by ni. The left hand side of Eq. (2) is the total

timeslots that ei owns to transmit data during T, and the right hand

side is the sum of the total data that ei receives from its children

links and itself. Note that to keep the discussion clear, we default

assume that one packet contains one sample data (i.e., without data

aggregation) and the packet size equals to the maximum sample

size. Therefore, the length of a timeslot will be equal to the time re-

quired to completely transmit a single packet. Of course, Eq. (2) canalso be applied in the scenario where one data packet contains more

Fig. 1. An example of a WSN-based data collecting system.

e2

e3

e4

e5

e6

e1

Fig. 2. The interference graph of the network in Fig. 1.


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than two samples by adjusting the sampling rate, if the samples can

be fitted into a packet. But if the required packet size increases (e.g.,

the maximum sample size increases), the system must be resched-

uled. However, this exception should rarely happen in a static WSN.

3.2. Problems of timetable-based implementation

In a static data collecting system, the sensor nodes generate thesensing data in static sampling rates. Therefore, the aggregated

transmission pattern will repeat in every hyper-period, which

is the least common multiple of all the sensor nodes sampling

periods. For such a static system, a TDMA schedule can be imple-

mented via a timetable that specifies the transmission timeslots

of each wireless link during a hyper-period. The timetable is then

distributed to all the sensor nodes, and a sensor node will follow

the TDMA sub-schedules of the wireless links connected to it to

transmit its data packets. After the current hyper-period is fin-

ished, the sensor node will re-execute the schedule.

Although the timetable-based approach is easy to implement, it

intends to construct a huge schedule table. We illustrate such a

problem by estimating the space complexity of the timetable. Con-

sider a data collecting system with n sensor nodes. Assume that adata packet generated by a sensor node ni is relayed by hi number

of wireless links, i.e., total hi number of packet transmissions will

be generated. In addition, the hyper-period T is the least common

multiple of all the sensor nodes sampling periods. During each hy-

per-period T, the sensor node will generate Tsi data packets be-

cause its sampling rate is si. Therefore, in a TDMA schedule table,

the number of the timetable entries for the wireless link ei will

be hi T si. Based on the above, the number of the entries in the

complete TDMA schedule table will bePn

i1hi T si. Furthermore,

the hyper-period T intends to be large in a data collecting system

with heterogeneous sensor nodes because the sampling rates of

the sensor nodes are deviated. In the worst case, Tmight be as large

as the production of all the sampling periods, and such a large hy-

per-period will undoubtedly lead to a large TDMA schedule table.

As we mentioned above, a huge TDMA schedule table will occu-

py considerable memory space, which might not be affordable in

resource limited sensor nodes. Besides, to broadcast such a huge

TDMA schedule table to the entire network will cause a lot of en-

ergy consumption on the sensor nodes. Due to the above two dis-

advantages, a timetable-based TDMA scheduler is considered to be

less efficient for a resource-limited WSN.

4. CyclicMAC: collision free cyclic TDMA scheduler

To minimize the size of the TDMA schedule table, in this paper

we propose a TDMA scheduler that specifies a cyclic schedule to

each wireless link of a given data collecting tree. A cyclic schedule

is parameterized by a period, which is the time interval betweentwo consecutive transmissions, and a phase, which is the initial

delay time of the first transmission. This kind of TDMA schedule re-

quires a tiny memory space because only two parameters are

needed to be stored. Broadcasting such a small TDMA schedule

to the entire network also requires much less energy consumption

than broadcasting a timetable-based TDMA schedule. Note that the

concept of cyclic schedule is introduced by Carley et al. [20], but

the scheduler they proposed can only be applied to single hop net-

works. This paper adapts such a concept and proposes a new cyclic

scheduler that not only supports multihop wireless networks but

also takes the bandwidth and the end-to-end latency requirements

into account.

4.1. Cyclic TDMA scheduling problem

To simplify the notations, we let the schedule that specifies the

transmission timeslots of a wireless link be referred to as a cyclic

linkschedule,and welet theaggregationof the cyclic linkschedules

of the entire network be referred to as a cyclic TDMA schedule.

More specifically, letqi and/i bethe periodandthe phase ofa wire-less link eis cyclic link schedule, respectively. That is, ei will initially

pause for /i timeslots and then periodically transmit a data packet

everyqi timeslots. Fig. 3 shows an example of a data collecting treethat uses a cyclic TDMA schedule for data transmissions. In this

example, the cyclic link schedule of wireless link e2 is hq2,/2 i =h6,4i; hence, e2 will transmit data at timeslots {4,10,16, . . .}. Simi-

larly, e3 will transmit data at timeslots {9,19,29, . . .} and e4 will

transmit data at timeslots {3,13, 23,33, . . .}. Formally, assuming

the timeslots are numbered incrementally from zero, the cyclic link

schedule of a wireless link ej is defined as below:

fti; ej 1 ifti /i%qi 0;

0; otherwise:

3

The previous section has demonstrated that the TDMA schedule for

a data collecting system based on WSN should fulfill both collision-

free and bandwidth requirements. Eq. (1) illustrates the condition

of the collision-free requirement for a TDMA schedule. We extend

Eq. (1) to derive the condition that a collision-free cyclic TDMA

schedule must satisfy. Let ei and ej be two wireless links that inter-

fere with each other, i.e., Iij = 1. A TDMA schedule will lead them to

actually collide with each other if f(tk, ei) +f(tk, ej) > 1 at a certain

timeslot tk, i.e., both their cyclic link schedules allocate timeslot tkto transmit the data packet. This collision condition can be formu-

lated as below:

/i g qi tk;

/j h qj tk;

(

where both g and h are non-zero positive integers. The formulation

can be reduced as follows:

/i g qi /j h qj;

) /i /j h qj g qi:

n1

n2

n3 n4

(6, 4)

(10,9) (10, 3)

e2

e3

e4

0 1 2 3 4 5

e3 e4

e2

6 7 8 9 10 11 12 13 14 15

2

3

4

2

4

3

2

16

4

Fig. 3. An example of a cyclic TDMA schedule.


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Moreover, let gcd (qi,qj) be the greatest common divider of qi and

qj. Hence, let u qi

gcdqi ;qjand z

qjgcdqi ;qj

, and then the above equa-

tion can be simplified as below:

/i /j h u gcdqi;qj g z gcdqi;qj:

Let another non-zero positive integer k represent h u g z, and

the above equation can be reduced as below:

/i /j k gcdqi;qj for k h u g z: 4

Eq. (4) shows that the cyclic schedules of ei and ej, i.e., hqi,/ii andhqj,/ji, will use the same timeslot to cause a collision if we can finda certain non-zero positive integer k that makes the Eq. (4) be true.

Hence, let L = {hq1,/1i, hq2,/2 i, . . ., hqi,/ii, . . . , hqm,/mi} be a cyclicTDMA schedule, where m is the number of sensor nodes. L will

not lead each pair of interfering wireless links to actually interfere

with each other if the below condition is true:

8ei; ej 2 E&Iij 1;/i /j k gcdqi;qjfor all integer k;

5

In addition to the collision-free requirement, the cyclic TDMA

schedule should also satisfy the bandwidth requirement that is

formulated by Eq. (2). A cyclic TDMA schedule should allocate suf-

ficient timeslots in each link according to its bandwidth require-

ment. Let T be an arbitrary time period. The number of timeslots

in which a wireless link ei will transmit data isTqi

j k. Then the band-

width requirement can be formulated asXTtk0

ftk; ei T

qi

; 6

where qi is the period of the wireless link ei. In other words, qidetermines the bandwidth allocated to the wireless link ei and it

should satisfy eis bandwidth requirement. Eq. (2) can be reduced

by substituting

PTtk 0

ftk; ei withTqi

j k:

XTtk0

ftk; eiP T si X

ej 2Childreni

XTtk0

ftk; ej

)T

qi

P T si

Xej2Childreni

T

qj

$ %

)1

qi

P si

Xej 2Childreni

1

qj

$ %:

Finally, we can derive that the cyclic TDMA schedule L can ensure

each wireless link satisfies the bandwidth requirement if the below

condition is true:

8ei 2 E; qi 61

si Pej 2Childreni1qj

: 7

Hence, we define a TDMA scheduling problem as below:Collision-free cyclic link scheduling for data collecting: Given a data

collecting system consisting of:

m sensor nodes N= {n1, n2, . . . , nm} with sampling rates S= {s1,

s2, . . . , sm}, and

a data collecting tree E= {e1, e2, . . . , em} with interference graph I

determine a cyclic TDMA schedule L = {hq1,/1i, hq2,/2i, . . .,hqi,/ii, . . . hqm,/mi}, in which qi and qi are the period and thephase of a wireless link e0is cyclic link schedule, that satisfies the

below two conditions:

8ei;ej 2 E&Iij 1;/i /j k gcdqi;qj for all integer k

8ei 2 E;qi 61

si P

ej 2Childreni1qj

4.2. CyclicMAC scheduler

In this subsection, a cyclic TDMA scheduler, called CyclicMAC, is

introduced to solve the problemofcollision-free cyclic link scheduling

for data collecting. CyclicMAC generates a cyclic TDMA schedule

that consists of a set of cyclic link schedules for the wireless links

in the data collecting tree. The CyclicMAC scheduler works in two

stages: (1) period determination, and (2) phase determination. Inthe period determination stage, CyclicMAC determines the periods

of the wireless links cyclic link schedule according to their band-

width requirements. That is, the bandwidth of each wireless link

cannot be smaller than the summation of its sampling data rate

and the bandwidth requirements of its children wireless links, as

Eq. (7) describes. CyclicMAC scheduler traverses the data collecting

tree fromleaves to root and initiates each wireless link a cyclic link

schedule whose period satisfies the bandwidth requirement. Let L

be the resulting cyclic TDMA schedule, and let hqi ;/i i be the cyclic

link schedule for a wireless link ei after the period determination,

while /i is set to zero initially. In the phase determination stage,

the CyclicMAC scheduler first sorts all the cyclic link schedules

(i.e., hqi ;/i i ) in L

by the order of the period lengths (i.e., qi )and then determines the phase of each

hq

i;/

j ithat does not violate

the collision-free requirement as Eq. (5) depicts.

Finding the phases that make L collision-free is not trivial. The

first reason is that such collision-free phases might not exist at all.

Recall that Eq. (5) describes the collision-free requirements of the

wireless links. If gcdqi ;q

j 1 , no matter which values of the

phases /i and/j are selected, we can always find an integer k that

lets wireless links ei and ej be active in the same timeslot. There-

fore, if ei and ej interfere with each other, their packets will

undoubtedly collide in this case. The second reason is that the

search space of finding collision-free phases for L could be enor-

mous. Consider L as set of periodic tasks that periodically perform

transmission jobs; then the period of a cyclic link schedule is re-

ferred to as the period of a periodic task. If we let L be referred to

as a set of periodic tasks whose phases are not determined yet, pre-

vious work [20] in real-time systems has concluded that the num-

ber of possible phase assignments for L will beQm

i1qi , which is

exponential.

In this paper, we employ the Distance Constraint scheduler(DCS)

[26] to derive a collision-free phase assignment. The Distance Con-

straint scheduler (DCS) targets the real-time scheduling problem

named Distance Constraint Task System (DCTS). A DCTS refers to

a set of periodic tasks that contend for CPU resources, and each

of these tasks should be executed periodically in a fixed interval.

The fixed interval that each task periodically executes is called

the distance constraint of the task. By conclusion of [26], a DCTS

has a collision-free phase assignment if their periods are har-

monic. The word harmonic means that, in a set of periods, one

period is always divisible by all the other periods that are shorter

than it. Similarly, we can let the cyclic link schedule of a wirelesslink ei be referred to as a periodic task with distance constraint qi ,and then the cyclic TDMA schedule L can also be transformed to a

DCTS in which a set of wireless links contend for access to the

wireless channel for periodically transmitting data packets in

fixed intervals. However, in a practical data collecting system, it

is almost impossible to guarantee the periods generated in the

period determination stage are harmonic if the sampling rates of

the sensor nodes are arbitrary. Hence, to force the periods to be

harmonic, we let the CyclicMAC scheduler automatically trans-

form the periods into numbers in powers of 2. That is, let qi bethe period of eis cyclic link schedule determined by Eq. (7); then

we have

qi 2 log2

qi

2j k

: 8


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Note that the transformed period will be smaller or equal to the ori-

ginal one in order to fulfill the bandwidth requirement. Due to the

harmonic transformation of the periods in Eq. (8), the resulting cyc-

lic link schedules might allocate more timeslots than the actual

requirement. Hence, using DCS for phase determination seems to

easily degrade the utilization of the wireless channel, and thus de-

creases the system throughput. However, this problem is not too

critical of the CyclicMAC scheduler because these over-allocated

timeslots still have the chance to be reallocated to the other wire-

less links that does not interfere with the current one. Remind that

a timeslot can only be allocated to one of the wireless links that

interference with each other, to prevent packet collision. That is,

we can say that a timeslot is shared among these wireless links

that does not interfere with each other. Even if the current link allo-

cates more timeslots than its demand, the over-allocated timeslots

can be reallocated to the others that have not been scheduled yet.

Table 1 shows the function CyclicMAC-Schedulerwhich summa-

rizes howthe CyclicMAC scheduler determines the phases of a cyc-

lic TDMA schedule. Assume L is the cyclic TDMA schedule

determined in the period determination stage. From line 2 to line

5, the periods of the cyclic link schedules in L are all transformed

into harmonic numbers based on 2 according to Eq. (8). Fromline 6

to line 9, the CyclicMAC scheduler determines the phases of the

cyclic link schedules according to an increasing order based on

their period lengths. Line 8 is the procedure to determine the

phases according to the collision-free requirement, and the func-

tion Collision-Free-Phase-Determinationillustrated in Table 2 details

the steps. The phase of a wireless links cyclic link schedule is the

initial delay time to transmit the first packet. Undoubtedly, the ini-

tial delay time is smaller than the length of a period, i.e., the phase

ranges from 0 to qi 1 the length of the period. Therefore, theCyclicMAC scheduler exhaustively goes through the phases from

0 to and picks the first met phase that will not cause the wireless

link ei to interfere with other wireless links that have been sched-

uled, as the function Collision-Free-Phase-Determination does. The

procedure IsCollisionFree illustrated in Table 3 checks if the candi-

date phase conflicts with the cyclic link schedules which have beenscheduled, via the facilitation of interference graph I.

The operation of the proposed CyclicMAC scheduler has been

introduced as shown above. However, a TDMA scheduler might fail

to determine a schedule for a data collecting system whose band-

width requirements of some wireless links are too high or the link

degree of some nodes are too dense. In this case, we say that the

system is not schedulable. We then derive the essential conditions

to formulate the schedulability of a data collecting system that ap-

plies the CyclicMAC scheduler. We start the derivation from the

simplest case that the interference graph of a data collecting sys-

tem is a complete graph. In this case, because only one wireless

link can be active at any timeslot, we can use the total bandwidth

requirement of the data collecting system to determine whether

the system is schedulable or not. Let L be the cyclic TDMA schedule

of the data collecting system. Given a time period T, the number oftimeslots allocated by L is Tq1

Tq2 Tqm. Thus, the schedulability

condition for L will be as below:

Xmi1

T

qi6 T )

Xmi1

1

qi6 1: 9

If the above condition is not true, this implies that L allocates times-

lots more than actual availability, which also implies that L is not

schedulable.

However, in a multihop wireless network, the interference

graph is not necessary to be a complete graph. Inspirited from

[5], we derive the schedulability condition of such a general case

based on the maximal cliques of interference graph. A set of nodes

and edges is called a clique if it induces a complete sub-graph. A

maximal clique is a complete sub-graph that does not contain

any other complete sub-graph. Undoubtedly, a clique in the inter-

ference graph I refers to a set of wireless links that interfere with

each other; therefore, the cyclic link schedules of these wireless

links should satisfy the schedulability condition (Eq. (9)). Hence,

the schedulability of L can be verified by the following lemma:

Lemma 1. Assume I = {C1, C2, . . ., Ck}, in which Ck is a maximal clique

of I. A cyclic TDMA schedule L is schedulable if the below condition is

true:

8Ck 2 I;Xei2Ck

1

qi6 1:

When the system is not schedulable, it means that the sensorsmight send out too many packets so that the resulted traffic

exceeds the capacities of the wireless channels. Undoubtedly, the

data collecting system cannot work perfectly because the band-

width requirement is higher than the upper bound that the net-

work can support. The only solution to let the system workable

is to reduce the amount of packets, e.g., adopting the solutions

fromcongestion control, such as [46], to adjust the periodin order

to meet the schedulable condition.

4.3. Toward end-to-end latency efficiency

For data collecting systems that collect environmental data dur-

ing emergencies, the end-to-end latency of a data packet is also a

critical optimization goal. The end-to-end latency of a data packetis the time interval from the time the packet leaves the source node

Table 1

Main function of CyclicMAC scheduler.

Function CyclicMAC-Scheduler (L, I): L

1 let L :{};

2 for each < qi;0 >2 L do

3qi : 2

log2q

i2

j k;

4 put < qi,0> into L;5 end for;

6 sort all < qi,0 >2 L by qi in ascending order;

7 for each < qi,0 >2 L do8 invoke Collision-Free-Phase-Determination (ei, < qi, 0 > ,L,I);9 end for;

10 return L;

Table 2

The function to determine a collision-free phase for wireless link

ei.

Function Collision-Free-Phase-Determination

(ei, hqi,0i ,L, I)

1 for j = 0 to qi 1 do2 if IsCollisionFree(j,qi, L, I) then3 /: =j;

4 end if;

5 end for;

Table 3

The function to inspect whether the given phase is

collision-free.

Function IsCollisionFree (/,qi,L, I): Boolean

1 for each < qj,/j >2 L and /j 0 do2 if (/%qj = /j) and Iij then3 return FALSE;

4 end if;

5 end for;


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to the time it is received by the sink. In a multihop network, the

end-to-end latency of a data packet is the summation of the trans-

mission times and the queuing times in the intermediate nodes. The

total transmission time depends on the number of wireless links to

relay the data packet, and it can be effectively reduced by applying

a routing structure with fewer intermediate hops from the source

node to the sink, e.g., a balanced routing tree with small tree

height. The total queuing time depends on the transmission sched-

ules of two consecutive wireless links. That is, if two consecutive

wireless links are active discontinuously, the data packet from

the incoming wireless link will be queued in the intermediate node

to wait for permission to use the outgoing wireless link. In a data

collecting tree, the data packets are transmitted in the direction

from the leaves to the roots. Hence, given a data path from the

source node to the sink, the optimal case is that the transmission

timeslots of any two consecutive wireless links are always contin-

uous to eliminate the queuing time. In this subsection, we improve

the collision-free phase determination toward minimizing the

queuing time to reduce the end-to-end latency.

The phases of the cyclic TDMA schedule are the primary factors

that affect the queuing time. Consider two consecutive wireless

links, ei and ej, where ej is the parent ofei (i.e., the data packets will

be delivered from ei to ej). Let hqi,/ii and hqj,/ji be the cyclic linkschedules of ei and ej, respectively. Recall that the source nodes

of ei and ej are ni and nj, respectively. Hence, the data packets of

ni will be transmitted through ei and possibly be queued in nj to

wait for the transmission timeslot to access ej. Consider an exam-

ple thathqi,/ii = h32,16i and hqj,/ji = h4,1i. If we unroll these twocyclic link schedules, the transmission timeslots of ei and ej will

be {16,48,80,. . .} and {5,9,13,17, . . .,49, . . . ,81, . . .}, respectively.

Note that in this case, every data packet transmitted by ei will be

immediately relayed by ej in the subsequent timeslot, i.e., the pack-

et will not be queued in the intermediate node nj. However, if

hqi,/ii = h32,15i, the unrolled transmission timeslots of ei will be{15,47,79, . . . }, so the data packets transmitted by ei will be queued

for 1 timeslot in nj. In cyclic TDMA schedule, the queuing time is

deterministic if the periods are harmonic. Assuming qi > qj, thequeuing time between hqi,/ii and hqj,/ji can be computed asbelow:

QueueTimehqi;/ii; hqj;/ji

/j

/iqj

j k 1

qi /i 1; if/i%qj > /j

/j /iqj

j k qi /i 1; otherwise:

8>: 10

Consider the first transmission period {0,1, . . . ,qi} ofei. The case that(/i%qj) > /j means that when the first packet transmitted by thechild link ei was received by the source node of the parent link ej,

the parent link ej has already used its active timeslot of the current

period, i.e., the/iqjj kth

period, to transmit other packets. Hence, thepacket from ei must be queued in the intermediate node nj to wait

for the next period. Thus, the next closest active timeslot of ej will

be /j /iqj

j k 1

qi , so the queuing time will be /j

b/iqjc 1

qi /1 1. In the other case where (/i%qj)6 /j, the

parent link ej has not used its active timeslot of the current period,

so the queue time will be /j b/iqj

c

qi /i 1.

By using Eq. (10), the function Latency-Efficient-Phase-Determi-

nation depicted in Table 4 can greedily pick the phases that induce

a minimum queuing time. From line 1 to line 12 in the function

Latency-Efficient-Phase-Determination, the CyclicMAC scheduler

determines the phase of a wireless link eis cyclic link schedule.

Let ej be the parent link ofei (Line 1). In line 3 to line 11, the Cyclic-MAC scheduler greedily searches the phase that is collision-free

and induces the smallest queuing time among all the candidate

phases. The function ends after all the phases are checked (Line

12).

4.4. Latency analysis

In this subsection, we analyze the end-to-end latency of a given

cyclic schedule generated by the CyclicMAC scheduler. Recall that

the end-to-end latency of a data packet is the time interval from

the timethe packet leaves the source node to the timeit is received

by the sink, and let Queue Time(hqi,/ii, hqj,/ji) represent the queu-ing time of a packet from a wireless link ei to its parent link ej. In a

data collecting tree, a data packet will be relayed by several inter-

mediate wireless links before arriving at the sink node. The end-to-

end latency of a data packet will be the summation of the trans-

mission times of the wireless links and the queuing times in the

intermediate nodes during the transmission. Let a sensor node nibe i hops away from the sink n0, and let P= {ei, ei1, . . ., ej, . . ., e2, e1}

be the end-to-end path that relays the data packets from thesource node ni to the sink n0, where each ej 2 Eand is the jth inter-

mediate link of P from the sink to the source node ni. Due to the

basic principle of TDMA summarized in Section 3, a wireless link

will spend one timeslot to transmit a data packet, so the total

transmission time of the wireless links will be jPj timeslots, where

jPj is the number of intermediate links from the source node ni to

the sink n0. Hence, let Latency(jPj) denote the end-to-end latency

(in number of timeslots) of a data packet along the path

P;Latency(jPj) is computed as below:

LatencyjPj X

ek ;ek12P

QueueTimehqk1;/k1i; hqk;/ki jPj:

Based on the latency metric, we then discuss the end-to-end latency

of the CyclicMAC scheduler in the sparsely deployed data collectionsystem, and in the densely deployed data collection system.

[Sparsely deployed data collection system]. A sparsely deployed

data collection systemrefers to the data collection system in which

a wireless link is only interfered by its parent and sibling links. For

a wireless link, the CyclicMAC scheduler must pick the phase that

will not conflict with the schedules of its parent and sibling links.

In addition, as the phase will affect the length of queuing time,

CyclicMAC scheduler should carefully determine the phase for each

wireless link in order to minimize the end-to-end latency. We will

show that, with the heuristic, Latency-Efficient-Phase-Determina-

tion, the CyclicMAC will generate a schedule that lets the queuing

time of a packet transmission on each hop be zero in sparsely de-

ployed data collection system. Because the transmission time can-

not be eliminated, such a schedule leads to an optimal end-to-endlatency. The proof is as below:

Table 4

Determine the phase with consideration of end-to-end latency.

Function Latency-Efficient-Phase-Determination

(ej, hqi,0i ,L, I)

1 let ej be the parent link of ei, i.e., Parenti;

2 MinQueueTime :MAXVALUE;

3 for h = 0 to qi 1 do4 if IsCollisionFree(h, qi, L, I) then

5 tmp : QueueTime (qi, h,qj,/j);6 if tmp < MinQueueTime then

7 MinQueueTime : tmp;

8 /i : h;

9 end if;

10 end if;

11 end for;

12 puthqi, /ii into L;


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Theorem 1. In a data collecting system, if

(a) the periods of a cyclic TDMA schedule L satisfy the bandwidth

requirementsof the wireless links i:e:;8ei 2 E;qi 61

siP

ej 2Childreni

1qj

!,

(b) the periods in L are schedulable, and

(c) each wireless link only has interference with its parent link and

its sibling links,

the function Latency-Efficient-Phase-Determination can always

find phases for the cyclic TDMA schedule L to ensure the end-to-end

latency of a data packet will always be equivalent to the link count

from the source node to the sink, in units of timeslot. The above

condition can be formally represented as below:

LatencyP jPj;

where P is an end-to-end path in the data collecting system.

Proof. The theorem is proven if we can show that the queuing

time of any pair of consecutive wireless links is zero so that the

end-to-end latency of Pwill be equal to the number of its wireless

links, i.e., jPj. Therefore, the goal is to prove the queue time will be

zero. That is,Xek ;ek12P

QueueTimehqk1;/k1i; hqk;/ki 0:

Remember that we have assumed that the wireless links do not

have any interference relationship except their parent links and

their sibling links. Therefore, we can derive the end-to-end latency

of a data packet under distinct numbers of intermediate links (i.e.,

distinct values of jPj) to prove Theorem 1, as below:

jPj = 1: The total transmission time will be one timeslot if the

source node n1 is the one hop neighbor of the sink node.

Besides, the end-to-end latency of the data packet from n1 will

be zero because the wireless link e1 can only interfere with itssibling links. Note that the sibling links of e1 with shorter peri-

ods than q1 will be scheduled prior to e1, e.g., ek and el in Fig. 4have been scheduled. In addition, because all the periods are

harmonic, q1 will be an integral multiple of the hyper-periodofqk and ql. This implies that in a period of e1, the cyclic linkschedules of these sibling links will repeat several times. That

is, in each period q1, the timeslot allocations for ek and el will

be the same, as illustrated in Fig. 4. Hence, once CyclicMAC

can pick an initial offset /1 in the first period to be the phases

ofe1, the timeslots {/1 + q1,/1 + 2 q1,/1 + 3 q1, . . .} will alsobe available for e1. But if no such available timeslot is found in

the first period, CyclicMAC will also be unable to find such a

timeslot in the following periods. This implies that q1 is notschedulable, which violates assumption (b). Based on the above,

we have proven that if the periodq1

is schedulable, no queuing

time will be necessary to transmit a packet from n1 to the sink.

jPj = 2: The total transmission time will be two timeslots if the

source node ni is two hops away from the sink node. We then

prove that a data packet from ni will be transmitted to the sink

in two timeslots.

Assume P= {e1,e2} is an end-to-end path from a node n2 to the

sink n0. Let q2 be the period of the cyclic link schedule of e2,and letq1 be the period of the cyclic link schedule ofe1. The goalis to determine a phase /2 for e2 in the range from0 toq2 1 sothat, Queue Time(hq2,/2i, hq1,/1i) = 0. Which implies that thedata packets can be transmitted to the sink in 2 timeslots.

Because e1 will not only transmit its own data packets but also

relay the data packets from its child link e2

, the period rho1

must

be equal to or shorter than q2. Note that e2 might interfere withits parent link (i.e., e1) and sibling links. Thus, when determin-

ing the phase of the link e2, the phases of (1) the parent link

e1, (2) e1s sibling links with shorter periods than q2, and (3)e2s sibling links with shorter periods than must have been

determined. Therefore, there is no need to prove that in each

period q2, the timeslot allocations for these scheduled links willbe the same, as illustrated in Fig. 5. Hence, once CyclicMAC can

pick an initial offset /2 in the first period to be the phases ofe2,

the timeslots {/2 + q2,/2 + 2 q2,/2 + 3 q2, . . .} will always beavailable for e2. Thus, we have proven that if the period q2 isschedulable, no queuing time will be necessary to transmit a

packet from e2 to e1.

jPj =f: Assume that the above condition is fulfilled for an end-

to-end path whose length is f; in other words, there are fwire-

less links in P (i.e., P= {ef, ef1, . . . , e1}), and the end-to-end

latency of P will be f timeslots. Fig. 6 illustrates such an

example.

jPj =f+ 1: An end-to-end path P= {ef+1,ef, ef1, . . ., e1} whose

length is P =f+ 1 must include an end-to-end path

{ef, ef1, . . ., e1} whose length is f. Based on the above induction,

the end-to-end latency of the path {ef, ef1, . . ., e1} will be f.

Fig. 4. The timeslot allocation that allows the data packets from n1 to be immediately transmitted to the sink.

Fig. 5. The timeslot allocation that allows the data packets from e2 to be transmitted by e1 immediately.


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Hence, if we can find a phase for ef+1 that will let a packet from

ef+1 be transmitted by ef immediately, the end-to-end latency of

jPj will be f+ 1. Note that ef is the first link of the path

{ef, ef1, . . ., e1} and also the second link of P= {ef+1, ef, ef1, . . ., e1}.

Hence, qf, which is the period of ef, will be allocated with ashorter period than the period ofef+1. Note that ef+1 might inter-

fere with its parent link (e.g., ef) and sibling links. Thus, when

determining the phase of ef+1, (1) the parent link ef and its sib-

ling links with shorter periods than qf+1, (2) efs downstreamlinks and their sibling links with shorter periods than qf+1,and (3) ef+1s sibling links with shorter periods than qf+1 musthave been determined. Because the periods are all harmonic,

the period qf+1 will be an integral multiple of the hyper-periodof (1)qf , (2) the periods of efs sibling links with shorter periodsthan qf+1, (3) the periods of efs downstream links and their sib-ling links with shorter periods than qf+1, and (4) the periods ofef+1s sibling links with shorter periods than qf+1. Once Cyclic-MAC can pick an offset /f+1 to be the phase of ef+1, the timeslots

{/f+1 + qf+1, /f+1 + 2 qf+1, /f+1 + 3 qf+1 , . . .} will always beavailable for ef+1. Otherwise, this implies that qf+1 is not sched-ulable, which violates assumption (b).

Based on the above induction, we have proven that the function

Latency-Efficient-Phase-Determination will pick phases for a cyclic

TDMA schedule to obtain an optimal end-to-end latency if all the

wireless links only interfere with their parent links and sibling

links. Such ideal case is although restricted but still reasonable in

a sparsely deployed wireless sensor network.

[Densely deployed data collection system]In case of densely de-

ployed data collecting system, a wireless link interferes with not

only the parent and sibling links, but also the wireless links of

the other sub-trees. That is, when determining the phase for a

wireless link, CyclicMAC scheduler might not be able to assign

the phase leading to zero queuing time to the wireless link because

such phase might conflict with the cyclic link schedule of a nearby

link. In that case, the function Latency-Efficient-Phase-Determina-

tion (line 4 to line 10) will greedily select the phase that will queue

the data packet for just one timeslot. If no such phase is available,

the function Latency-Efficient-Phase-Determination will select the

phase that queues the data packet for two timeslots. This phase

determination process will continue until a phase is selected or

the phase offset exceeds the period length. Such additional latency

will be at most the number of its interfering neighbor wireless

links. That is, assuming the data collecting system is schedulable,

the resulted end-to-end latency of schedule L will be as below:

max8P2E

jPj Xej 2P

jIjj where jIjj is the number of ejs neighbor in I

0@

1A;

where Pis an end-to-end path in a data collecting tree E, and Iis the

corresponding interference graph.

5. Simulation results

In this section, we evaluate the performance of the CyclicMACscheduler via simulation. We use TOSSIM-CC2420 [27] to simulate

a network containing some sensor nodes equipped with a Chipcon

CC2420 wireless transceiver. We compare CyclicMAC with three

popular MAC mechanisms, which are commonly used on wireless

sensor networks as follows:

EDF-based TDMA: EDF-based TDMA is a typical timetable-

based TDMA scheduler. It lists the transmissions within the

hyper-period of the sampling periods of the sensor nodes. Note

that the total packet transmissions include those directly

launched by the sensor nodes and the corresponding relaying

transmission. Then, EDF-based scheduler specifies a timeslot

to every packet transmission according to the Earliest Deadline

First policy. Notably, EDF-based scheduler has been proven to

be optimal in reducing end-to-end latency[12].

Coloring TDMA: In Coloring TDMA, each wireless link is

assigned a timeslot ID, which indicates a color in the coloring

algorithm. The coloring algorithm is executed based on the

interference graph of the network so that two wireless links

that interfere with one another will not be assigned to the same

timeslot. The order of color assignment is in the order of Depth

First Search (DFS) from the sink to the leaf nodes in order to

minimize the end-to-end latency. That is, during traversing of

the data collecting tree, each visited wireless link will be

assigned a timeslot that is closest to the timeslot assigned to

its parent.

CSMA: The default MAC mechanism supported by TOSSIM-

CC2420 is CSMA. Before transmitting a packet, a sensor node

will wait for a random period and then assess the channel con-

dition via a Channel Clear Assessment (CCA) hardware compo-

nent to ensure the channel is clear for transmission. If the

channel is not clear, the sensor node will wait for an additional

random period and check the CCA again to see if the channel is

clear to send.

We then conduct several simulations with distinct sampling

rates and deviations to evaluate the performances of the above

schedulers. In each simulation, we assume that the timeslot lengthis 4 ms, which is capable of transmitting one 42-byte packet with a

29-byte payload. The data packets are not aggregated by the inter-

mediate nodes due to their heterogeneous nature. Additionally, the

queue size of each sensor node is 420 bytes, i.e., capable to queue

10 packets. If the queue is full, the oldest data packet will be

dropped and considered as a lost packet. The simulation is re-

peated for three rounds; in each round, the simulation lasts for

5 min and then generates the following performance metrics:

Delivery rate: The ratio of the packets successfully received by

the sink.

End-to-end latency of a data packet: The duration between the

time that a data packet leaves the source node to the time that

it is received by the sink node.

5.1. Table size

In the previous section, we analyzed the space complexity of a

timetable-based TDMA schedule. For a static data collecting sys-

tem, the length of the hyper-period (i.e., the least common multi-

ple) of the sampling periods affects the size of the timetable. The

worst case of the table size will be the production of all the sam-

pling periods, which will be exponential, and such a large table

could be too large for practical WSN-based applications. But if

the sampling periods are in harmonic form, the length of the hy-

per-period will be equal to the longest period. In this subsection,

we will demonstrate how the sampling rates and their deviations

impact the timetable size via simulation. In the following simula-tions, we randomly generate 4, 8, 12, 16, 20, 24, and 30 sensor

nf+1 n0...

f+1 hops

fhops

efef+1e1

n1nf

Fig. 6. An end-to-end path with f intermediate links.


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nodes, and a minimum hop tree is constructed above the sensor

nodes. We compare the maximum size of the TDMA schedule ta-

bles generated by the EDF-based TDMA scheduler and CyclicMAC.

In the EDF-based TDMA schedule, each table entry specifies a

transmission timeslot for a wireless link, and the size of a table en-

try is 5 bytes, i.e., 1 byte for the wireless link id and 4 bytes for the

timeslot id. We also assume that a sensor node only keeps the nec-

essary entries that specify its transmission timeslots of its adjacent

wireless links.

In the first simulation, the average sampling rate of the sensor

nodes is set to 2.5 Hz (i.e., the corresponding sampling period is

100 timeslots). We define the deviation as the difference between

the upper bound and the average, the same to the difference be-

tween the lower bound and the average. The deviation of the sam-

pling rate in this simulation is set to 50%, i.e., the possible sampling

periods range from 50 to 150 timeslots. As mentioned above, the

schedule table of a sensor node in EDF-based TDMA should specify

sufficient transmission timeslots to transmit the data packets of

the sensor itself and its upstream nodes. The number of entries

in the schedule table of the node is primarily determined by three

major factors: the number of upstream nodes, the sampling rates

of the node and its upstream nodes, and the length of the hyper-

period of the sampling periods of these nodes. The worst case of

the table size will happen if the following three conditions are all

satisfied: (1) the sink has only one child node, (2) all the other sen-

sor nodes are the children of this child node, and (3) the sampling

periods of these nodes are all prime numbers. In our simulation,

the average sampling rate is 2.5 Hz (i.e., the average sampling per-

iod of the sensor nodes is 100 timeslots), and the largest number of

sensor nodes is 30. Since the deviation of the sampling rates is 50%,

the worst case in such a scenario happens when the sampling peri-

ods of these 30 sensor nodes are the largest 30 prime numbers in

the range from 50 to 150 timeslots. Since the size of a table entry

is 5 bytes, the size of the entire schedule table in the worst case

will be tens of Gigabytes, which is an incredible large storage

requirement. Fig. 7(a) illustrates our simulation results that dem-

onstrate the relationship between the maximum TDMA scheduletable size and the number of sensor nodes in EDF-based TDMA

and CyclicMAC. As expected, when the number of sensor nodes in-

creases, the schedule table size will grow exponentially. When the

number of sensor nodes increases up to 30, the size of the EDF-

based TDMA schedule table will be larger than 350 M bytes.

In the next simulation, we still set the average sampling rate to

2.5 Hz and then vary its deviation to 10%, 20%, 30%, 40%, and 50%.

Fig. 7(b) illustrates the relationship between the table size and the

deviation of sampling rate in EDF-based TDMA and CyclicMAC.

This figure illustrates an apparent trend that a larger deviation of

the sampling rate implies a larger EDF-based schedule table.

Hence, we conclude that, in a data collecting system, the table size

is primarily affected by the number of sensor nodes, the sampling

rates, and the deviation of sampling rates. The simulation resultsalso demonstrate that the EDF-based TDMA schedule is only

affordable to a data collecting system containing just a few sensor

nodes, and all of these nodes must operate homogeneously. Both

the figures also show that under all the above configurations, the

CyclicMAC scheduler always generates a constant and small-sized

schedule table, which is more desirable to the sensor nodes with

limited resources.

5.2. Performance evaluation

In this subsection, we evaluate the performance of CyclicMAC

when the sampling rates of the sensor nodes are in different levels

of deviation. In detail, the average sampling rates of the sensor

nodes are set to 2.5 Hz, 1.3 Hz, 0.8 Hz, 0.6 Hz, or 0.5 Hz, and thedeviation of its sampling rate is set to 10%, 20%, 30%, 40%, or 50%.

We generate ten topologies, which all contain 30 sensor nodes that

are randomly separated in a field of 290 235 square meters. Fig. 8illustrates one of these network topologies in the simulation. We

let the transmission range of CC2420 radio be 50 m, because it

can achieve 99% delivery rate if no interference happens under this

configuration. We build the underline network topology based on

this information, above which we build a routing tree whose tree

height equals 7 hops. For convenience, the interference graph of

the network topology is also built based on the distance based

interference model. That is, two wireless links will interfere with

each other if (1) the distance between their source nodes is shorter

than or equal to 50 m, or (2) the distance between the destination

node of one wireless link and the source node of the other wireless

link is shorter than or equal to 50 m.

Fig. 9(a) compares the average system delivery rates of EDF-

based TDMA, Coloring TDMA, CSMA, and CyclicMAC under differ-ent sampling rates over the randomly generated networks. In gen-

eral, the delivery rates of the three TDMA-based protocols are

much better than that of the CSMA protocol. This is because CSMA

highly suffers the hidden station problem [28]. Even if the sam-

pling rate is low, the hidden station problem also incurs extensive

packet collisions. Moreover, the Coloring TDMA performs poorly

when the sampling rate is high. This is because the Coloring TDMA

scheduler allocates the transmission timeslots based on the inter-

ference graph rather than the bandwidth requirements of the wire-

less links. Hence, when the sampling rate is high, a lot of data

packets will be queued too long in the sensor nodes and finally

could be dropped, thus decreasing the packet delivery rate.

Fig. 9(b) illustrates the average delivery rates of the nodes with dif-

ferent distances to sink node. The delivery rates of the TDMA-basedschedulers are still higher than the CSMA protocol. However, we

Fig. 7. The size of TDMA schedule tables generated by different schedulers: (a) the

number of sensor nodes vs. maximum table size; (b) the deviation of sampling rate

vs. maximum table size.


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also observe that as the distance increases, the delivery rate of Col-

oring TDMA significantly decreases. This is also because Coloring

TDMA does not consider the heterogeneous bandwidth require-

ments on wireless links. In overview, the EDF-based scheduler per-

forms similarly to CyclicMAC on the delivery rate. However, as

mentioned in the previous sub-section, the overhead on schedule

table size of EDF is much larger than that of CyclicMAC.

Fig. 9(c) shows the comparisons on the end-to-end latenciesand the corresponding deviations in EDF-based TDMA, Coloring

TDMA, and CyclicMAC. As we mentioned in the previous subsec-

tion, the mechanism of CSMA differs too much from those of the

other TDMA-based schedulers, and the delivery rate of CSMA is

also too low, so we just ignore CSMA in this simulation. Obviously,

the end-to-end latency of Coloring TDMA is the worst among the

three TDMA schedulers. This is also because the Coloring TDMA

does not consider the heterogeneous bandwidth requirements on

wireless links, so the queuing time lengthens the end-to-end la-

tency. On the other hand, the end-to-end latency of EDF-based

TDMA is slightly shorter than that of CyclicMAC; however, the

extensive table size of EDF-based TDMA makes it infeasible to be

applied in a resource limited WSN. In addition, the deviations of

the end-to-end latency of CyclicMAC are slightly smaller thanthose of EDF-based TDMA. This result shows that the CyclicMAC

induces amore static behavior in packet deliveries, which is bene-

ficial to the management of the sensor data. As CyclicMAC has a

delivery rate, an end-to-end latency similar to EDF-based TDMA,

and a static packet delivery behaviors but requires much less stor-

age overhead on TDMA schedule tables, CyclicMAC is considered as

the most balanced solution among these TDMA schedulers.

Finally, we evaluate the improvement on end-to-end latency

caused by the proposed latency minimization function Latency-

Efficient-Phase-Determination. Without the proposed latency mini-

mization function, the consecutive wireless links might not be able

to transmit data in contiguous timeslots. This implies that a data

packet might be queued for a while in an intermediate link, and

thus the end-to-end latency will increase. The simulation resultillustrated in Fig. 10 conforms to our expectation. With the

proposed latency minimization function, the end-to-end latency

can be reduced to around half of the original.

5.3. Bridge monitoring: a case study

In this section, we evaluate CyclicMAC using the configuration of

a practical bridge monitoring application. This bridge monitoring

system is to monitor the health state of the Chun-Chen Bridge,which connects Taipei City and Taipei County in Taiwan. Table 5

illustrates both the placements of the sensor nodes on the bridge

and the topology of the underlying wireless networks. The length

of the Chun-Chen Bridge is 400 meters, and the distance of farthest

pair of sensor nodes are 50 m. Table 5 lists the sensors used in this

scenario, including their locations and sampling rates. Note that the

accelerometers are placed on positions {1, 9, 10, 11, 12}, which are

close to thesink, and these sensors generate an extensiveamountof

sample data which is not affordable to the wireless channel. Recall

that the payload of a packet in our simulator is 29 bytes, so we let

these high sampling rate sensor nodes continuously feed the sam-

ple data to the payload of a packet and transmit the packet until

the payload is full, thus reducing the packet transmission rates.

However, even with this down-sampling mechanism, the bridgemonitoring system still has some challenges with packet transmis-

sion. Apparently, the traffic in the area near to the sink node is hea-

vy, implying that a large amount of packet collisions might occur. If

a MAC protocol does not arrange the packet transmission well, the

packet delivery rate will decrease dramatically, whilst the end-to-

end latency will increase significantly.

Fig. 11(a) shows the resulting delivery rates of EDF-based

TDMA, CSMA, Coloring TDMA, and CyclicMAC scheduler. The deliv-

ery rate of CSMA is only about 30% and is the worst among the four

MAC protocols. This is because the traffic around the sink is so

crowded that the CCA of each sensor node in this area is usually

aware of the transmissions of data packets, thus the sensor node

usually cannot send its packets. This, therefore, lets the packets

be easily queued too long in some intermediate nodes and finallyleads to packet loss due to queue overflowing. In addition, even

Fig. 8. The network topology used in the simulation.


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if the CCA acknowledges that the channel is clear to send, packet

collision still could happen due to the hidden station problem

[28]. Coloring TDMA prevents packet collision, so it has a higherdelivery rate than CSMA. However, the coloring algorithm assigns

the timeslots based on the network topology rather than the band-

width requirements of the wireless links, so we expect that the

data packets might be queued in some intermediate nodes too

long, even being dropped due to queue overflowing. As we ex-

pected, Fig. 11(a) shows that Coloring TDMA can only successfully

deliver 77% of the data packets. This figure also illustrates that both

EDF-based TDMA and CyclicMAC can deliver almost 100% of the

data packets, which are the best in this application.

The bridge monitoring system must collect the sample data for

alarming the emergencies, like bridge breaking, so the end-to-end

latency is also important. Because the mechanism of CSMA differs

too much from those of the other TDMA-based schedulers, and the

delivery rate of CSMA is also too low, we just ignore CSMA in thissimulation. Fig. 11(b) shows the end-to-end latencies of EDF-based

TDMA, Coloring TDMA, and CyclicMAC. With the same results in

the previous subsection, the latency of Coloring TDMA is the worst

among the three TDMA schedulers, and the latencies of EDF-basedTDMA and CyclicMAC are very similar in this scenario. CyclicMAC

only performs slightly worse than EDF-based TDMA on the nodes

whose distances from the sink are 7 and 8 hops, respectively.

The above simulation results demonstrate that the EDF-based

TDMA seems a suitable solution to a static data collecting system

because it can support both the highest delivery rate and the short-

est end-to-end latency. However, the simulation results in Section

5.1 have demonstrated that the EDF-based TDMA will generate a

huge TDMA schedule table that is not affordable to resource-lim-

ited sensor nodes. On the other hand, the delivery rate and the

end-to-end latency of CyclicMAC are almost the same as the

EDF-based TDMA. Besides, unlike the EDF-based TDMA, CyclicMAC

just requires a tiny TDMA schedule table. Hence, CyclicMAC seems

to provide a more practical solution to a WSN-based data collectingsystem.

0%

20%

40%

60%

80%

100%

0.5 0.6 0.8 1.3 2.5

DeliveryRate(%)

Sampling Rate (Hz)

CyclicMAC

EDF

Coloring

CSMA

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8

DeliveryRate(%)

Distance (hops to sink)

CyclicMAC

EDF

Coloring

CSMA

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

1 2 3 4 5 6 7 8

End-to-EndLatency(seconds)

Distance (hops to sink)

CyclicMAC

EDF

Coloring

Deviation (%)

ops 1 2 3 4 5 6 7 8

Cyc icMAC 0.0% 0.1% 1.8% 6.2% 10.1% 7.1% 14.1% 11.3%

EDF 0.0% 11.2% 12.0% 20.9% 12.5% 14.9% 12.5% 21.5%

Co oring 88.5% 88.5% 86.8% 51.7% 48.7% 46.7% 44.7% 42.8%

(a)

(b)

(c)

Fig. 9. Network performance of different schedulers: (a) delivery rates vs. sampling rates; (b) delivery rates vs. the distances from the nodes to the sink; (c) average end-to-

end latencies vs. the distances from the nodes to the sink.


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6. Conclusion and future works

In this paper, we have proposed a TDMA scheduler, called

CyclicMAC scheduler, that fulfills the three design issues of a struc-

tural health monitoring (SHM) application over a multihop wire-

less sensor network. For a given routing structure and bandwidthrequirement of each wireless link, CyclicMAC scheduler can gener-

ate a cyclic TDMA schedule with minimum end-to-end latency. A

cyclic TDMA schedule only occupies a small amount of memory

space, and this advantage makes it suitable to be stored and ex-

changed in a resource limited wireless sensor network. Besides,

the schedule not only satisfies the heterogeneous bandwidth

requirements of distinct wireless links but also reduces the end-

to-end latency of transmitting a data packet. We have proven that

in an ideal case where each wireless link only interferes with its

parent link and sibling links, the schedule will not induce any

queuing time so that the end-to-end latency of transmitting a

packet is optimal. Such ideal case is although restricted but still

reasonable in a sparsely deployed wireless sensor network. And

in other cases, our schedule also results in a bounded end-to-endlatency of transmitting a packet. We have compared the perfor-

mance of CyclicMAC with those of an EDF-based TDMA, Coloring

TDMA, and CSMA over 10 randomly deployed networks and a real

bridge monitoring system. Simulation results have demonstrated

that the EDF-based TDMA scheduler has both the highest packet

delivery rate and the shortest end-to-end latency, but it might gen-

erate a huge TDMA schedule table that is not affordable to a re-

source-limited sensor node. In addition, CyclicMAC scheduler

performs almost as efficiently as the EDF-based TDMA scheduler

but requires only a tiny TDMA schedule table. With these advanta-

ges, CyclicMAC is considered to be an ideal MAC scheduler to real-time WSN applications whose data sampling rates are static.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

1 2 3 4 5 6 7 8

End-to-EndLatency(seconds)

Distances (hops to sink)

With latency minimization

Without latencyminimization

Deviation (%)hops 1 2 3 4 5 6 7 8

With latencyminimization

0.0% 0.1% 1.8% 6.2% 10.1% 7.1% 14.1% 11.3%

Without latencyminimization

0.0% 0.1% 2.0% 7.0% 10.1% 8.1% 14.0% 11.0%

Fig. 10. Effectiveness of different phase determinations on the end-to-end latency.

Table 5

A Topology of a bridge monitoring system.List of sensor nodes.

Sensor type Sampling

rate (Hz)

Data size for

a sample

Location

Accelerometer 100 6 bytes 1, 9, 10

Thermal sensor 1 1 byte 2, 3, 4, 5, 6, 11, 12

Settlement Gauges 1 1 byte 13

Inclinometer 0.125 1 byte 7, 8, 14

Fig. 11. Network performances of different MAC schedulers: (a) delivery rate; (b)average end-to-end latencies vs. the distances from the nodes to the sink.


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To extend CyclicMAC, we will further explore a number of is-

sues. The first is to improve the utilization of the timeslots. Recall

that in CyclicMAC, the lengths of the periods are transformed into

harmonic numbers so that the timeslots can be scheduled via the

Distance Constraint scheduler. The transformed periods must be

shorter than or equal to the original ones; hence, there might be

some wastage in utilization because the number of allocated

timeslots might exceed the actual requirement. This problem is

actually not too critical in CyclicMAC because these timeslots still

have a second chance to be allocated to other links, as we have

mentioned in Section 4. However, a more accurate period assign-

ment still could

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