Self-stabilizing TDMA Algorithms

for Dynamic Wireless Ad-hoc Networks

∗

Pierre Leone

and Elad M. Schiller

Computer Science Department, University of Geneva, Geneva Switzerland

Computer Science Department, Chalmers University of Technology, G

oteborg, Sweden

Keywords:

Self-stabilization, Dynamic Networks, MANETs, VANETs, MAC.

Abstract:

In dynamic wireless ad-hoc networks (DynWANs), autonomous computing devices set up a network for the

communication needs of the moment. These networks require the implementation of a medium access control

(MAC) layer. We consider MAC protocols for DynWANs that need to be autonomous and robust as well as

have high bandwidth utilization, high predictability degree of bandwidth allocation, and low communication

delay in the presence of frequent topological changes to the communication network. Recent studies have

shown that existing implementations cannot guarantee the necessary satisfaction of these timing requirements.

We propose a self-stabilizing MAC algorithm for DynWANs that guarantees a short convergence period, and

by that, it can facilitate the satisfaction of severe timing requirements, such as the above. Besides the con-

tribution in the algorithmic front of research, we expect that our proposal can enable quicker adoption by

practitioners and faster deployment of DynWANs, such as the IEEE 802.11p for mobile ad hoc networks

(MANETs) and vehicular ad-hoc networks (VANETs).

1 INTRODUCTION

Dynamic wireless ad-hoc networks (DynWANs) are

autonomous and self-organizing systems where com-

puting devices require networking applications when

a ﬁxed network infrastructure is not available or not

preferred to be used. In these cases, computing de-

vices may set up a short-lived network for the com-

munication needs of the moment, also known as, an

ad-hoc network. Ad-hoc networks are based on wire-

less communications that require implementation of a

Medium Access Control (MAC) layer. We consider

MAC protocols for DynWANs that need to be au-

tonomous, robust, and have high bandwidth utiliza-

tion, a high predictability degree of bandwidth al-

location, and low communication delay in the pres-

ence of frequent changes to the communication net-

work topology. Existing implementations cannot

guarantee the necessary satisfaction of timing require-

ments (Bilstrup et al., 2008; Bilstrup et al., 2009).

∗

This work was partially supported by the EC, through

project FP7-STREP-288195, KARYON (Kernel-based AR-

chitecture for safetY-critical cONtrol), see (Casimiro et al.,

2012). A technical report version of this work appears

in (Leone and Schiller, 2012a), and a brief announcement

version is in (Leone and Schiller, 2012b).

This work proposes an algorithmic design for self-

stabilizing MAC protocols that guarantees a short

convergence period, and by that, can facilitate the sat-

isfaction of severe timing requirements. The proposed

algorithm possesses a greater degree of predictabil-

ity, while maintaining low communication delays and

high throughput.

The dynamic and difﬁcult-to-predict nature of

wireless ad-hoc networks gives rise to many fault-

tolerance issues and requires efﬁcient solutions. Dyn-

WANs, for example, are subject to transient faults due

to hardware/software temporal malfunctions or short-

lived violations of the assumed settings for model-

ing the location of the mobile nodes. Fault tolerant

systems that are self-stabilizing (Dolev, 2000) can re-

cover after the occurrence of transient faults, which

can cause an arbitrary corruption of the system state

(so long as the program’s code is still intact), or the

model of dynamic networks in which communication

links and nodes may fail and recover during normal

operation (Dolev and Herman, 1997). The proof of

self-stabilization requires convergence from an arbi-

trary starting system state. Moreover, once the system

has converged and followed its speciﬁcations, it is re-

quired to do so forever. The self-stabilization design

criteria liberate the application designer from dealing

119

Leone P. and M. Schiller E..

Self-stabilizing TDMA Algorithms for Dynamic Wireless Ad-hoc Networks.

DOI: 10.5220/0004231401190124

In Proceedings of the 2nd International Conference on Sensor Networks (SENSORNETS-2013), pages 119-124

ISBN: 978-989-8565-45-7

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

with low-level complications, such as bandwidth allo-

cation in the presence of topology changes, and pro-

vide an important level of abstraction. Consequently,

the application design can easily focus on its task –

and knowledge-driven aspects.

MAC algorithms. ALOHAnet and its synchronized

version Slotted ALOHA (Abramson, 1985) are pio-

neering wireless systems that employ a strategy of

“random access”. Time division multiple access

(TDMA) (Schmidt, 1974) is another early approach,

where nodes transmit one after the other, each using

its own timeslot, say, according to a deﬁned schedule.

The scheduled approach offers greater predictabil-

ity of bandwidth allocation and communication de-

lay, which can facilitate fairness (Herman and Tixeuil,

2004) and energy conservation (Ye et al., 2002).

There are two well-known approaches for deal-

ing with contention (timeslot exhaustion): (1) em-

ploying policies for administering message priority,

or (2) adjusting the nodes’ individual transmission

signal strength or carrier sense threshold (Yu and

Biswas, 2007; Scopigno and Cozzetti, 2009). The

former approach is widely accepted and adopted by

the IEEE 802.11p standard (see Section 4), whereas

the latter has only been evaluated via computer simu-

lations (Scopigno and Cozzetti, 2009).

STDMA (Yu and Biswas, 2007) and Viqar and

Welch (Viqar and Welch, 2009) consider scheduling

that is based on Global Navigation Satellite System

(GNSS).

Related Work. We propose a self-stabilizing TDMA

algorithm that does not require GNSS accessibility or

knowledge about the node trajectories. Rather it con-

siders an underlying self-stabilizing local pulse syn-

chronization, such as (Mustafa et al., 2012).

When using collision-detection at the receiving-

side (Scopigno and Cozzetti, 2009; Cozzetti and

Scopigno, 2009; Yu and Biswas, 2007; Tadokoro

et al., 2008; Lenoble et al., 2009), it is up to the

receiving-side to notify the sender about collisions

via another round of collision-prone transmissions,

and by using FI (frame information) payload ﬁelds

that includes T entries, where T is the TDMA frame

size. Thus far, FI-based protocols study the stochas-

tic resolution of message collision via computer net-

work simulations (Yu and Biswas, 2007; Abrate et al.,

2011; Scopigno and Cozzetti, 2010; Cozzetti et al.,

2009; Tadokoro et al., 2008; Lenoble et al., 2009).

Simulations are also used for evaluating the

heuristics of MS-ALOHA (Scopigno and Cozzetti,

2009) for dealing with contention (timeslot exhaus-

tion) by adjusting the nodes’ individual transmission

signal strength and / or carrier sense threshold.

We do not consider lengthy frame information (FI)

ﬁelds, which signiﬁcantly increase the control infor-

mation overhead, and yet we provide provable guar-

antee regarding the convergence time. Further anal-

ysis validation of the proposed algorithm via simu-

lations and test bed implementation can be found in

Section 5, and respectively, in (Mustafa et al., 2012).

The proposed algorithm does not consider

collision-detection mechanisms that are based on sig-

nal processing or hardware support, as in (Demirbas

and Hussain, 2006). Rather, it employs a variation

on a well-known strategy for eventually avoiding con-

current transmissions among neighbors. This strategy

allows the sending-side to eventually observe the ex-

istence of interfering transmissions. Before sending,

the sender waits for a random duration while perform-

ing a clear channel assessment. A channel is consid-

ered to be used once the detected energy levels reach

a threshold in which the radio unit is expected to suc-

ceed in carrier sense locking (details appear in Sec-

tion 2 and (Leone and Schiller, 2012a)).

The proposed MAC algorithm can be entirely

based on the carrier sensing of message transmission,

as in (Cornejo and Kuhn, 2010), which focuses on fair

bandwidth allocation, but does not consider dynamic

networks or self-stabilization.

There are several proposals related to self-

stabilizing MAC algorithms (Kulkarni and Aru-

mugam, 2006; Arumugam and Kulkarni, 2005; Aru-

mugam and Kulkarni, 2006; Lagemann et al., 2009;

Herman and Tixeuil, 2004; Jhumka and Kulkarni,

2007); however, none of them consider dynamic net-

works and their frame control information is quite ex-

tensive. In (Leone et al., 2009a; Leone et al., 2010;

Mustafa et al., 2012; Leone et al., 2009b), we con-

sider a MAC algorithm that uses convergence from a

random starting state (inspired by self-stabilization),

were as here we consider self-stabilizing MAC algo-

rithms. An extended survey of the related work ap-

pears in (Leone and Schiller, 2012a).

Our Contribution. This work proposes a self-

stabilizing MAC algorithm that demonstrates rapid

convergence without the extensive use of frame con-

trol information (Section 2). Our analysis shows that

the algorithm facilitates the satisfaction of severe tim-

ing requirements for DynWANs (Section 3).

We start by considering transient faults and topo-

logical changes to the communication network, i.e.,

demonstrating self-stabilization. We then turn to fo-

cus on bounding the algorithm’s convergence time af-

ter an arbitrary and unbounded ﬁnite sequence of tran-

sient faults and changes to the network topology. In

particular, equation (2) shows that the expected lo-

cal convergence time is brief, and equation (3) for-

mulates the expected global convergence time. More-

SENSORNETS2013-2ndInternationalConferenceonSensorNetworks

120

Constants, variables, macros and external functions

2 MaxRnd (n in the proofs) : integer = bound on round number

s : [0, T-1] ∪ {⊥} = next timeslot to broadcast or null, ⊥

4 signal : boolean = trying to acquiring the channel

unused[0,T-1] : boolean = marking unused timeslots

6 unused set = { k : unused[k] = true } : unused timeslot set (macro)

MAC fetch()/MAC deliver() : MAC layer interface

8 transmit/receive/carrier sense : communication primitives

10 Upon receive(< DATA, m> ) do MAC deliver(< m> )

12 Upon carrier sense(t) (∗ defer transmission during t ∗)

if s = t ∧signal then s := ⊥ (∗ mark that the timeslot is not unique ∗)

14 (signal, unused[t ]) := (false, false) (∗ quit the competition ∗)

16 Function select unused(set) (∗ select an empty timeslot ∗)

if set =

0 then return ⊥ else return uni f orm select(set)

Upon timeslot(t)

20 if t = 0 ∧s = ⊥ then s := select unused(unused set)

(unused[t], signal) := (true, false) (∗ remove stale information ∗)

22 if s 6= ⊥∧t = s then send(MAC fetch())

24 Function send(m) (∗ send message m to p

s neighbors ∗)

for ((signal, k) := (true, 0); k := k + 1; k ≤ MaxRnd) do

26 if signal then with probability ρ(k) = 1/(MaxRnd −k) do

signal := false (∗ quit the competition ∗)

28 transmit(< BEACON> ) (∗ try acquiring the channel ∗)

wait until the end of competition round (∗ exposure period alignment ∗)

30 if s 6= ⊥ then transmit(< DATA, m> ) (∗ send the data packet ∗)

Figure 1: Self-stabilizing TDMA-based MAC algorithm, code of node p

over, for a given probability, the global convergence

time is calculated in equation (4).

We protocol implementations that deal with sit-

uations in which there is a non-constant number of

transmitting and neighboring terminals (Section 4).

Lastly (Section 5), we explain that when allow-

ing a fraction of the bandwidth to be spent on frame

control information and when considering any given

probability to converge within a bounded time, the

proposed algorithm demonstrates a low dependency

degree on the number of nodes in the network.

Due to the space limit, the proofs appear in (Leone

and Schiller, 2012a).

2 ALGORITHM DESCRIPTION

The system consists of a set, P, of N anonymous com-

municating entities, which we call nodes. Denote ev-

ery node p

∈ P with a unique index, i.

TDMA protocols divide the radio time into

frames, which are then divided in to T broadcasting

timeslots, where T is an upper bound on the number

of concurrently transmitting terminals in any given

neighborhood. We call N

the (interference) neigh-

borhood of node p

∈ P and d

= |N

| is named the

(interference) degree of node p

The MAC algorithm in Fig. 1 assigns timeslots to

nodes after the convergence period. We assume that

the MAC protocol is invoked periodically by synchro-

nized common pulse that aligns the starting time of

the TDMA frame (Mustafa et al., 2012). The term

(broadcasting) timeslot refers to the period between

two consecutive common pulses. In our pseudo-code,

we use the event timeslot(t) that is triggered by the

common pulse.

Nodes raise the event carrier sense() when they

detect that the received energy levels have reached a

threshold in which the radio unit is expected to suc-

ceed in carrier sense locking. We assume that times-

lots allow the transmission of DATA packets using the

transmit() and receive() primitives. Moreover, we

consider signaling (beacons) as short packets that in-

clude no data load, rather their carrier sense delivers

important information. Before the transmission of the

DATA packet in timeslot t, the scheme uses beacons

for singling the node intention to transmit the packet

within t.

During the convergence period several nodes can

be assigned to the same timeslot. The algorithm

solves such timeslot allocation conﬂicts by letting the

node p

and p

to go through a (listening/signaling)

competition before transmitting in its broadcasting

timeslot. The competition rules require each node

to choose one broadcasting timeslot out of n listen-

ing/signaling periods. This implies that among all

the nodes that attempt to broadcast in the same times-

lot, the ones that select the earliest listening/signaling

period win this broadcasting timeslot and access the

communication media. Before the winners access

their timeslots, they signal to their neighbors that they

won by sending beacons during their chosen signaling

periods. When a node receives a beacon, it does not

transmit during that timeslot, because it lost this com-

petition. Instead, it randomly selects another broad-

casting timeslot and competes for it on the next broad-

casting round.

3 CORRECTNESS

The proof starts by considering no changes to the net-

work topology and that the ratio between the node

extended degree and the frame size is less than one,

i.e., ∀p

∈P : 1  T /d

(see Section 4 for extensions).

We continue by focusing on the converge period for

a single neighborhood and the entire network. These

convergence estimations facilitate the exploration of

important properties for dealing with changes in the

Self-stabilizingTDMAAlgorithmsforDynamicWirelessAd-hocNetworks

121

5 10 15 20 25 30 35 40 45 50

0.2

0.4

0.6

0.8

max convergence time

probability

Observation of the max convergence time, N=500, r=0.1

empirical

theoretical bound

(a)

5 10 15 20 25 30 35 40 45 50

0.2

0.4

0.6

0.8

max convergence time

probability

Observation of the max convergence time, N=2500, r=0.1/sqrt(5)

empirical

theoretical bound

(b)

5 10 15 20 25 30 35 40 45 50

0.2

0.4

0.6

0.8

max convergence time

probability

Observation of the max convergence time, N=5000, r=0.1/sqrt(10)

empirical

theoretical bound

(c)

Figure 2: Numerical validation of equation (3), which bounds the network-wise convergence time. We compare the bound,

P(t

max

< k) = (1 −(1 −q)

)

, with the numerical results, which consider random geometric graphs in which the nodes are

randomly placed on the unit square. The charts considers N ∈ {500, 2500, 5000} nodes (from left to right). All experiments

considered 2 listening/signaling periods, interference range of 0.1/

(

500

), which result in an average extended degree of 15,

/T = 1 on average, and q

= 1/4.

network topology. Due to the space limit, the proofs

appear in (Leone and Schiller, 2012a).

The proof delineates the different states at which

a node can be in relation to its neighbors, and groups

these states into three categories of relative states: (1)

Ready to be allocated, when the node state depicts

correctly its neighbor states, (2) Obtaining a timeslot,

when the node is competing for one, but there is no

agreement with its neighbor states, and (3) Allocated

to a timeslot, when the node is the only one to be al-

located to a particular timeslot in its neighborhood.

The self-stabilization proof shows that, start-

ing from an arbitrary starting conﬁguration, each

node eventually reaches the relative state Allocated.

OnlyOne

(x) is the probability that a node enters the

relative state Allocated from either Ready or Obtain-

ing, where n is the number of listening/signaling pe-

riods, T the TDMA frame size, d

is p

’s extended

degree, and ρ

= 1/MaxRnd = 1/n is p

’s probability

to select the k-th listening/signaling period for trans-

mitting its beacon.

OnlyOne

(x) ≥

∑

k=1

1 −

∑

`=1

(1)

Neighborhood Convergence The expected time, S

for node p

∈ P to reach the relative state Allocated

satisﬁes equation (2). Note that S

≤4 when the num-

ber of listening/signaling periods is n ≥ 2. Namely,

the proposed algorithm convergence with a neighbor-

hood is brief.

≤ min{



n −1



+ 1



n −1



} (2)

Network Convergence. The expected number of re-

transmissions is smaller than



n−1



d/T

− 1, where

d = max({d

: p

∈ P}). Hence, we have that the ex-

pected number of broadcasting rounds, S, that guar-

antee that all nodes reach the relative state Allocated

satisﬁes equation (3).

S ≤



n −1



d/T

(3)

Moreover, given that there are N nodes in the net-

work and α ∈ (0, 1), the network convergence time is

bounded by equation (4) with probability 1 −α.

k = 1 +

log



1 −

√

1 −α



log



1 −



n−1





(4)

This means that with probability α all nodes are al-

located with timeslots in maximum k broadcasting

rounds, see Fig. (3).

We numerically validate equations (3) and (4) in

Fig. 2, and respectively, Fig. 3. Note that these exper-

iments show that the average convergence time of the

network is below the upper bound of equation (3).

4 IMPLEMENTATION

We mention mechanisms for dealing with timeslot ex-

haustion, see details in (Leone and Schiller, 2012a).

Peritonized Listening/Signaling Periods. One

can consider listening period parameters, [LSP

start

LSP

end

], that refer to the ﬁrst, and respectively, the last

listening/signaling periods that a node can use when

attempting to acquire a broadcasting timeslot. E.g.,

suppose that there are six listening/signaling periods,

SENSORNETS2013-2ndInternationalConferenceonSensorNetworks

122

and that nodes with the highest priory may use the

ﬁrst three listening/signaling periods, [0, 2], and nodes

with the lowest priority may use the last three, [3,5].

In the case of two neighbors with different listening

period parameters, say [0,2] and [3,5], that attempt

to acquire the same broadcasting timeslot, the highest

priority node always attempts to broadcast before the

lowest priority one.

Global convergence time if T=1 with prob. 0.99

2 3 4 5 6 7 8 9 10

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Figure 3: Contour plot of equation (4) for s = d/T = 1. The

contour lines connect values of k(n,N) that are the same

(see the text tags along the Contour lines), where N is the

number of nodes and n is the number of signaling periods.

TDMA-based Back-off. Let us consider two back-

off parameters, CW

start

and CW

end

, that refer to the

maximal and minimal values of the contention win-

dow. Before selecting an unused timeslot, the proce-

dure counts a random number of unused ones. Fig. 4

presents an implementation of the select unused()

function that facilitates back-off strategies as an al-

ternative to the code presented in Fig. 1.

The statically allocated variable count records

the number of backoff steps that node p

takes un-

til it reaches the zero value. Whenever the func-

tion select unused() is invoked with count

= 0,

node p

assigns to count

a random integer from

[CW

start

,CW

end

]. Whenever the value of count

is not

greater than the number of unused timeslots, the re-

turned timeslot is selected uniformly at random. Oth-

erwise, a ⊥-value is returned after deducting the num-

ber of unused timeslots during the previous broadcast-

ing round.

5 DISCUSSION

Thus far, both schedule-based and non-schedule-

based MAC algorithms could not consider timing re-

quirements within a provably short recovery period

that follows (arbitrary) transient faults and network

topology changes. This work proposes the ﬁrst self-

stabilizing TDMA algorithm for DynWANs that has

a provably short convergence period. Thus, the pro-

posed algorithm possesses a greater degree of pre-

dictability, while maintaining low communication de-

lays and high throughput.

In this discussion, we would like to point out

the algorithm’s ability to facilitate the satisfaction

of severe timing requirements for DynWANs by nu-

merically validating equations (3) and (4). As a

case study, we show that, for the considered settings

of Fig. 2, the global convergence time is brief and

deﬁnitive. Fig. 3 shows that the proposed algorithm

demonstrates a low dependency degree on the num-

ber of nodes in the network even when considering

10,000 nodes by merely using small fraction of the

bandwidth to be spent on frame control information

(say 3 listening/signaling periods) and when consid-

ering 99% probability to convergence within 30 to 35

TDMA frames.

We have implemented the proposed algorithm, ex-

tensively validated our analysis via computer simula-

tion, and tested it on a platform with more than two

dozen nodes, see (Mustafa et al., 2012). These results

indeed validate that the proposed algorithm can in-

deed facilitate the implementation of MAC protocols

that guarantee satisfying these severe timing require-

ments, such as MANETs and VANETs.

Addtional constants and variables

2 CW

start

and CW

end

: backoff parameters

count : statically allocated variable that counts the backoff steps

Function select unused(set)

6 let rtn val = ⊥v // indicate busy channel (default return value)

if count ≤ 0 then count ← uni f orm select([CW

start

,CW

end

])

8 count ← count− | set |

if count ≤ 0 then (count, rtn val) ←(0,uni f orm select(set))

10 return rtn val

Figure 4: select unused() with TDMA-based back-off

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