DTIC ADA461671: A New Approach to Channel Access Scheduling for Ad Hoc Networks

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by  Defense Technical Information Center

A New Approach to Channel Access Scheduling
(cid:3)
for Ad Hoc Networks
Lichun Bao J.J. Garcia-Luna-Aceves
ComputerScienceDepartment ComputerEngineeringDepartment
UniversityofCalifornia UniversityofCalifornia
SantaCruz,CA95064 SantaCruz,CA95064
[email protected] [email protected]
ABSTRACT within the e(cid:11)ective range of the transmissions in the time
Three typesof collision-free channel access protocols for ad and frequency axes. TDMA, FDMA, CDMA, SDMA, and
hoc networks are presented. These protocols are derived their combinations are widely deployed in cellular systems
from a novel approach to contention resolution that allows [1] [11]. However,thesesolutionsrequireacentralbasesta-
eachnodetoelect deterministically oneormultiplewinners tion, and the peer-to-peerscheduling neededin ad hocnet-
forchannelaccessinagivencontentioncontext(e.g.,atime works is muchharder to solve.
slot),giventheidenti(cid:12)ersofitsneighborsoneandtwohops
away. The new protocols are shown to be fair and capable Thequestforoptimalsolutionstochannelaccessscheduling
ofachievingmaximumutilizationofthechannelbandwidth. in ad hoc networks (i.e., multihop packet radio networks)
The delay and throughput characteristics of the contention often results in NP-hard problems in graph theory (such as
resolution algorithms are analyzed, and the performance of k-colorability on nodes or edges) [8] [9] [22]. In some cases,
the three types of channel access protocols is studied by however, the problems can be solved by reducing them to
simulations. simplercasesforwhichpolynomialalgorithmsareknownto
achieve suboptimal solutions using randomized approaches
1. INTRODUCTION orheuristicsbasedonsuchgraphattributesasthedegreeof
thenodes.
Channelaccessschemesforadhocnetworkscanbecontention-
basedorscheduled. Theadvantageofcontention-basedschemes
Manysolutionshavebeenproposedcombiningbothrandom
isthattheyarerelativelyeasytodeploy;thishasresultedin
and scheduled access approaches [4] [5] [24]. Speci(cid:12)cally,
many contention-based schemes for ad hoc networks being
a few time slot assignment algorithms were presented by
proposed based on carrier sense multiple access with colli-
Cidon and Sidi [6], and Pond and Li [20] using a dedicated
sion avoidance (CSMA/CA), and the success of the IEEE
controlsegmentofthechanneltoresolveconflictsandbroad-
801.11(b)standardforwirelesslocalareanetworks[7]. Collision-
cast channel reservations. However, the complex resolution
avoidance schemes are attractive for ad hoc networks, be-
of neighbor schedules via message exchanges in the chan-
cause they attempt to eliminate collisions of data packets,
nelconsumeaconsiderableportionofthescarcebandwidth
which degrade network performance. However, collision-
and introduce long delays to obtain the correct schedule.
avoidance schemes cannot prevent collisions of data pack-
Several channel scheduling and reservation protocols have
ets resulting from near-far phenomena, fading, and capture
been proposed based on in-band signaling (phased dialogs
e(cid:11)ects on the channel [12, 14]. In addition, it is di(cid:14)cult
or RTS/CTS handshakes) before transmissions [25] [27] to
to provide quality of service or fairness with these channel
secure a temporary schedule for channel access. Because of
access schemes. This points to the need for channel access
the in-band signaling required, these protocols su(cid:11)er from
methods based on scheduling.
unused time slots when signals collide because of their ran-
domness.
Scheduled access schemes prearrange or negotiate a set of
timetablesforindividualnodesorlinks,suchthatthetrans-
Topology-transparent scheduling methods have been pro-
missionsfromthesenodesorontheselinksarecollision-free
posed by Chlamtac and others [3] [17] to avoid the need
(cid:3)
This work was supported by the Defense Advanced Research forthein-bandsignalingoftheabove\topology-dependent"
ProjectsAgency(DARPA)underGrantNo. F30602-97-2-0338. schemes. Thebasicideaofthetopology-transparentschedul-
ing approach is for a node to transmit in a number of time
slots in each time frame. The times (slots) when node i
transmitsinaframecorrespondstoauniquecodesuchthat,
for any given neighbor k of i, node i has at least one trans-
mission slot during which k and none of k’s own neighbors
are transmitting. Therefore, within any given time frame,
any neighbor of i can receive at least one packet from i
collision-free. The limitation of the topology-independent
scheduling approaches described to date is that the sender
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1. REPORT DATE 3. DATES COVERED
2001 2. REPORT TYPE 00-00-2001 to 00-00-2001
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
A New Approach to Channel Access Scheduling for Ad Hoc Networks
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Engineering,Santa Cruz,CA,95064
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unclassified unclassified unclassified
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
isunabletoknowwhichneighbor(s)cancorrectlyreceivethe Given a set of contenders, Mi, against an entity
packet it sends in a particular slot. This implies that the i in contention context t, how should the prece-
senderhastosenditspacketinthevariousslotsinaframe, dence of i be arbitrated in the set Mi[fig, such
makingtheframelength(numberofslots)muchlargerthan that every other contender yields to i whenever i
thenumberofnodesinatwo-hopneighborhoodanddepen- derivesitselfasthewinnerforthecommonchan-
dent on thenetwork size, which is less scalable. nel?
A uni(cid:12)ed framework for channel assignment in time, fre-
quency, and code division multiple access called UxDMA Todescribeoursolutiontotheproblem,weassumethatpri-
was described byRamanathan [21] tocomputeak-coloring maryoperantsinmathematicalformulasareof(cid:12)xedlength,
ofanarbitrarygraphwithinpolynomialsteps. Theheuristic and the sign ‘(cid:8)’ lends to carrying out concatenation oper-
was to begin coloring nodes or edges randomly or sequen- ation on its operants. During the contention context t, the
tiallyaccordingtovertexdegrees,andconcludewithamin- solutiontotheproblemisthefollowingNeighborhood-aware
imumnumberofcolorssuchthatasetofconstraintsonthe Contention Resolution (NCR) algorithm:
nodes orlinksare satis(cid:12)ed. Theconstraints on thecoloring
pattern include commonly known interferences, such as di- NCR(contention context t):
rect and hidden-terminal interferences [26]. A limitation of
this and similar schemes based on k-colorings of graphs is
that, inherently,topology information needsto becollected 1. Compute apriority ptk for each memberk in set Mi[
fig:
and frequent schedule broadcasts have to be carried out in
dynamic networks, which would consume a signi(cid:12)cant por- ptk =Rand(k(cid:8)t)(cid:8)k;k2Mi[fig (1)
tion of thescarce wireless bandwidth.
where function Rand(x) is a pseudo-random number
Toavoidtherepetitiousscheduleadjustmentsorredundant generator that produces a uniformly distributed ran-
multipletransmissionsofdatapacketsduetothevolatilityof dom numberusing therandom-seed x.
wireless network topologies, we propose that local topology
2. Exit if Eq. (2) is not true.
beanintegralingredientofthechannel-accessschedulingfor
each node of an ad hocnetwork. 8j 2Mi;pti >ptj (2)
Section2showsthattheschedulingproblemsfornode-activation 3. i may access thecommon channelduringt. 2
and link-activation channel access can be approached as a
2-coloring problem on graphs. It presents a new contention
Note that, while the Rand function can generate the same
resolution algorithm called neighborhood-aware contention
number on di(cid:11)erent inputs, each priority number is unique
resolution (NCR) by: (a) each node maintaining the iden-
ti(cid:12)ers of its one- and two-hop neighbors, and (b) making a sinceptk;k2Mi[figisappendedwithktothecorrespond-
ing Rand(k(cid:8)t).
newnodeorlink activation decision duringeach contention
context (e.g., each time slot). Section 3 addresses the per-
Describing NCR in termsof a two-coloring problem, an en-
formance of NCR, its fairness, and its proper operation.
tityigivesitselfcolorrifitshasthehighestpriorityamongst
Section 4 describes three channel access protocols based on
itscontendersinacontentioncontext;otherwise,icolorsit-
node-activation and link activation-schemes. Section 5 dis-
selfwith b. Nodesincolor r areactiveinthecorresponding
cusses the neighbor protocol for handling mobility. Section
contention context. The color r is extensively used in each
6 addresses theperformance of theseprotocols by means of
contention situation to the maximal degree without colli-
simulation experiments. Section 7 concludes the paper.
sions.
2. NEIGHBORHOOD-AWARE
ThedescriptionofNCRprovidedthusfarassumesthateach
CONTENTIONRESOLUTION node requires the same amount of bandwidth. In practice,
Inmultihopwirelessnetworks,contendingentitiesarenodes tra(cid:14)c demands at di(cid:11)erent nodes can vary, which requires
orlinks(edges)betweennodes. Weassumethateveryentity di(cid:11)erent nodes to receive di(cid:11)erent amounts of bandwidth.
knowsthesetof itscontendersbysomeappropriatemeans, Variable bandwidth requirements are easily accommodated
suchaseachnodeperiodicallybroadcastingtheidenti(cid:12)ersof in NCR by assigning multiple pseudo identities to each en-
itsone-hopneighborsifcontendingentitiesarenodes,orthe tity, with each entity being assigned up to a maximum of
identitiesoflinksinitstwo-hopneighborhood ifcontending Lpi pseudo identities.
entitiesarelinks. Wealsoassumethateachcontentioncon-
textisidenti(cid:12)able,whichisreasonableinnetworksbasedon A pseudo identity of an entity is identi(cid:12)ed by the concate-
a time-division multiple access or frequency hopping. nation of theidenti(cid:12)erassigned totheentityand a number
identifying one of the one ore more pseudo identities as-
Given the knowledge of contenders for an entity i, the con- signedtotheentity. Ifanentityiclaimspii2[0;Lpi]pseudo
tention resolution algorithm must decide whether i is the identities,thel-thpseudoidentityisdenotedasi(cid:8)l,where
winnerinthecontentioncontext. Theproblemofcontention 1(cid:20)l(cid:20)pii.
resolutionwithneighborhoodinformationcanthusbestated
as follows: Consequently,NCRmodi(cid:12)edformultipleidentitiesforeach
node (NCR-MI)is thefollowing:
NCR-MI (contention context t): Anadhocnetworkhasa(cid:12)nitenumberofentities;therefore,
NCRalwaysproducesoneormultiplewinnersforeachcon-
tention context since NCR gives a unique priority number
1. Computetheprioritynumbersonthepseudoidentities to each entity and multiple locally maximal priorities exist
ofeachmemberk2Mi[fig,thel-thprioritynumber in the network. Accordingly, NCR allows live utilization of
of which is denoted as ptk(cid:8)l: thecommon channel.
ptk(cid:8)l= Rkan2d(Mk(cid:8)i[lf(cid:8)igt;)1(cid:8)(cid:20)kl(cid:8)(cid:20)l;pik (3) 3.2 Performance
When the arrival rate of the queuing system in a channel
2. Exit if Eq. (4) is not true. access scheduling system is bellow the service rate, we can
analyze the delay properties of the queuing system using a
8j 2M ;9 m; pt >pt ;
i i(cid:8)m j(cid:8)n (4) steady-stateM/G/1 queuewithservervacations, wherethe
1<m<pii;1<n<pij: single server is an entity (node/link).
3. i may access the common channelduring t. 2 Wesupposethatdatapacketsarriveatanentityiaccording
to a Poisson process with rate (cid:21)i and are served by (cid:12)rst-
come-(cid:12)rst-serve (FIFO) strategy. Server i takes a vacation
The portion of thecommon channelavailable toan entity i
for V of one time slot when there is no data packet in the
is
queue; otherwise, i looks for the next available time slot to
pi
qi = k2Mi[ifigpik: (5) ttrhaenrsamnidtotmhene(cid:12)srssitnpNacCkRetawnaditNinCgRin-MthI,ethqueenuuem. bBeercoafusteimoef
slots towait before transmission is ageometric distribution
P with parameter 1−qi, where qi is the probability of the
Note that NCR is the special case of NCR-MI with the re- entity i winning a contention context (Eq. (6) and (5)).
striction 8k 2Mi[fig;pik = 1. For simplicity, the rest of Therefore, the service time Xi for a data packet is Yi+1,
this paper addresses only NCR. where PfYi =kg=qi(1−qi)k−1.
3. BEHAVIOROFNCR The mean and second moments of random variable Xi are:
3.1 Correctness 1
Oncethenodesofanadhocnetworkhaveconsistentknowl- Xi =Yi+1= qi
edge of their two-hop neighborhood, NCR achieves the fol-
lowing three goals: Xi2 =Yi2+2Yi+1= qi2−q22qi+2
i
1. Avoidunintentionalcollisionsfromsimultaneoustrans-
missions. And the mean and second moments of random variable V
are: V =V2 =1.
2. Fair sharing of network bandwidth for each node, so
astoavoid theresource starvation problem presentin So that theextended Pollaczek-Kinchin formula
contention-based schemes.
(cid:21)X2 V2
W = + ;
3. Allowconstantbandwidthutilization,evenunderheavy 2(1−(cid:21)X) 2V
tra(cid:14)c load, so as to keep network data transmission
forM/G/1 systemwithvacationsreadilyyieldstheaverage
live at all times.
waiting time in thequeueat entity i:
Because it is assumed that contenders have mutual knowl- Wi= (cid:21)i(2qqi2i(−qi2−qi(cid:21)+i)2) + 12
edge and t is synchronized, the order of contenders based
on the priority numbers is consistent at every participant.
When entity i has the highest priority in the set Mi[fig, Adding the average service time to the queuing delay, we
each k 2 Mi respects the right of i, and allows i to access get theoverall delay in thesystem:
the common channelcollision-free. Ti=Wi+Xi = (cid:21)iq2i(+qi2−(1(cid:21)+i)qi) + 32 (7)
NCR basically generates a permutation of the contending
members, the order of which is decided by the priorities
of all participants. Since the priority is a pseudo-random Let (cid:21)i=0, theleast expected system process latency is:
number generated from a seed that changes from time to
time,thepermutationalsobecomesrandomsuchthatihas Ti=1=qi+2:5 (8)
certain probability,commensurate to its contention level,
Dependingonwhethertheentityisanodeorlink,theprob-
1
qi = jM [figj (6) abilities of the entity winning a contention context are dif-
i
ferent, so are thedelays of data packetsgoing through that
to win in each contention context. entity. Figure 1 shows the average delay of a packet in the
Average Packet Delays in the System
60
qi=0.05
50
(a) Hidden Terminal Problem
me Slots)40
Delay in System T (Tii2300 qi=0.10 (b) Direct Interference (c) Self Interference
qi=0.20
10 qi=0.50 Figure 2: Examples of Collision Types
00 0.05 0.1 0.15Arriva0l. 2Rate li 0(P.2a5cket/Tim0.e3 Slot)0.35 0.4 0.45 0.5 Tinhgetfhoalltownoindgeschaalrnenaedlyackcneoswsptrhoetiorcnolesigahrbeodrehsocoridb,edi.ea.,sstuhmey-
have exchanged the necessary information about their two-
Figure 1: Average System Delay of Packets
hop neighborhood.
4.1 Node ActivationProtocol
queuing system at an entity i with di(cid:11)erent channel access
probability qi and arrival rate (cid:21)i. To keep the queuingsys- We (cid:12)rst present theNAMA (Node-Activation Multiple Ac-
tem in a steady state, it is necessary that(cid:21)i <qi. cess)protocol,whichisbasedonNCR,nodeactivation,and
a distributed time division multiplexing scheme.
BecauseofthecollisionfreedomofNCR,thecommonchan-
Wedonotaddress hownodesare timesynchronized inthis
nel can serve certain load up to the maximum channel ca-
paper. Thiscan beachievedbyeither: (a) listeningtodata
pacity. Thatis,thethroughputoverthecommonchannelis
tra(cid:14)c in the network, and aligning time slots to the latest
the summation of arrival rates at all competing entities as
starting point of a complete packet transmission by one-
long as the queuing system at each entity remains in equi-
hop neighbors; or (b) other means, such as GPS (global
librium on the arrival and departure events. We have the
following system throughput S from each and every entity positioning systems) timing signals.
k that competes for the common channel:
Block
0 1 S -1
S = min((cid:21)k;qk) (9) b
Membership
k Section
X Section
where qk is the probability that k may access the common 0 1 Ps-1
channel, and (cid:21)k is thedata packet arrival rate at k.
Part
0 1 Tp-1
4. CHANNELACCESSPROTOCOLS
Time Slot
For simplicity, we abstract the topology of a packet radio
network as an undirected graph G = (V;E). V is the Figure 3: Time Division in NAMA
set of nodes, each mounted with an omnidirectional radio
transceiverandassignedauniqueIDnumber. E (cid:18)V (cid:2)V is A time slot is the smallest time unit for transmitting one
the set of links between nodes. Unless noti(cid:12)ed otherwise, a ormorecompletedatapackets. InNAMA,weimposemore
link (u;v)2E indicates nodeu and v are within thetrans- structures on time slots such that the combination of Tp
mission rangeofeachothersothattheycanexchangeradio consecutive time slots forms a part, Ps consecutive parts
packetviathecommonchannel,inwhichcasethetwonodes form a section, and Sb consecutive sections give the largest
are called one-hop neighbors. Two distinct nodes having a unit of time, block, as illustrated in Figure 3. Given the
common one-hop neighbor are called two-hop neighbors to current time slot number t, we derive the current time slot
each other. The set of d-hop neighbors of a speci(cid:12)c node i number of a part, the current part and section numbers as
is denoted by Nid, where d=1;2. Note that Ni1\Ni2 may follows:
not beempty. t0=t mod Tp
p0=(t=Tp) mod Ps (10)
Inmultihopwirelessnetworks,asingleradiochannelisspa- s0 =[t=(Tp(cid:2)Ps)] mod Sb
tially reused at di(cid:11)erent parts of the network. Collisions
happen in three cases as illustrated in Figure 2 [23]. It is where mod is a modular operator, and all operants are in-
su(cid:14)cient for collision-freedom if nodes within two hops do tegers.
nottransmitatthesametime. Hence,contentionsatanode
i should be resolved on thesubgraph derived from thetwo- Anodeichooses only onepartpi,duringwhich tocontend
hop neighbors of i, i.e., Ni1 [Ni2, depending on node/link for a time slot to transmit data packets. The choice of a
activation schemes and signal coding methods as shown in part isdependenton thedensity ofneighbors already using
the following protocols. that part, usually decided when thenode joins a network.
Time-slot where priority pt is obtained from Eq. (1) for k, and
k
0 1 2 St-2 St-1 pk is the part numberchosen bynode k.
Segment 8. Exit if Eq. (2) does not hold for node i.
frameType srcID #nbrUpd nbrUpds 9. Accessthecommon channelincurrenttimeslottand
Signal Format exit.
. . . . . .
nbrID nxtPartNo 10. Exit if
9k;k2Ni1[Ni2 and pk =p0 and (ptk mod Tp)=t0:
Figure 4: Signal Frame Format in Membership Sec-
tion 11. The set of contending neighbors of node i now be-
comes:
Formanagementpurposes,thelastsectionofablockisallo- Mi =fkjk2Ni1[Ni2 and pk =p0g
catedformembershipmaintenanceandiscalledmembership
section. New neighbors that did not transmit but listened Compute anotherpriority numberptk0 as follows:
inprevioussectionstransmitsignalsinthemembershipsec-
tfuiornth.erFdoirvitdheids ipnutropSostes,egtmimeentsslootfseqinuatlhdeulraasttiosnecftoironsenadre- ptk0 =Rand(k(cid:8)t(cid:8)t0)(cid:8)k; k2Mi[fig (11)
ing signals. Each signal contains the sender’s ID and the
12. Exit if
part number that the node is willing to use in the coming
blocks (Figure 4). 9j 2Mi; pti0 6>ptj0 (12)
frameType src ID dst ID #NbrUpdNbrUpds payload 13. Access thecommon channelin time slot t. 2
Regular Data Frame
. . . . . . 4.2 Link ActivationProtocol
nbrIDcurPartNonxtPartNo TheLAMA(LinkActivation MultipleAccess) protocolisa
time-slotted code division medium access scheme using di-
rect sequencespread spectrum (DSSS)together with NCR.
Figure 5: Data Frame Format in Regular Sections
In DSSS, code assignment can adopt transmitter-oriented,
Inordertoobtaintwo-hopneighborinformation,everynode
receiver-oriented or a per-link oriented coding schemes [13]
broadcastsitsone-hopneighborIDsandcorrespondingpart
[16][19]. Achannelaccessschedulingbasedontransmitter-
numbers whenever necessary. Portion of the header (cid:12)eld
oriented code assignment handles very much the same case
of each data frame and signal frame is allocated for this
asNAMA,becausebothapproachesadvocatethebroadcast
purpose (Figure 4 and 5). Depending on the payload of
natureof transmission.
a data frame, neighbors exchange their one-hop neighbor
updates in a single or multiple data frames. The signal
In LAMA, we opt for a receiver-oriented code assignment,
alsocontainsasmanyaspossibleone-hopneighborIDsand
whichissuitableforunicastingusingalink-activationscheme.
corresponding part numbers.
Althoughmanycollisionresolutionprotocolscateredtocode
In NAMA, the contender set Mi of node i is a subset of assignmentalgorithmstoeliminatepacketcollisions[2][15],
Ni1 [Ni2, and changes from section to section in time as the code assignment for LAMA is relatively static and ran-
dom, and the contentions for transmission on the code of
described in thefollowing algorithm:
theintendedreceiverareresolved byothercomputations in
LAMA.
NAMA:
Weassumethatapoolofwell-chosenquasi-orthogonalpseudo-
1. Computethecurrentpartnumberp0 accordingtoEq. noise codes, the set of which is denoted as Cpn = fckg,
(10). are available for each node to choose from. The pseudo-
2. Exit if (p06=pi) is true. cn0oi<secc1o<des::i:n<sidcejCCpnpnj−1a.reAsorretceedivaecrciorisdiansgsigtonetdheairpvsaeuludeos-:
3. Compute thepriority pti using Eq. (1). noise code ci from Cpn by the following hashing operation,
whichutilizesthepseudo-randomnumbergeneratorusedin
4. Assign node i to time slot ti=pti mod Tp. Eq. (1):
5. Compute the current time slot t0 in part p0 using Eq. ci =ck; k=Rand(i) mod jCpnj (13)
(10).
6. If (ti6=t0) then proceed to Step 10. LAMA establishes a channel access schedule for each indi-
vidualtimeslot. Havingtheknowledgeofone-hopneighbors
7. Compute theset of contendingneighbors
is su(cid:14)cient for a node to avoid collision of type (b) in Fig-
Mi =fkj k2Ni1[Ni2 and pk =p0 and ure 2, and knowledge of its two-hop neighbors is enough to
(ptk mod Tp)=t0g eliminate collision of type(a) and (c).
Becausewehavealimitednumberofpseudo-noisecodesfor in PAMA.Linksare directed in PAMAto signify transmis-
assignment, it is possible that multiple nodes to share the sion directions. Each undirected link is represented by two
same code. If we denote the set of i’s one-hop neighbors directed linksin opposite directions.
assigned with codecas n1i;c,ourgoal in LAMAis todecide
whether node i can activate a link on a code c and send AsinLAMA,weassumeapoolofquasi-orthogonalpseudo-
packet to one of the receivers in n1i;c during time slot t. noise codes, Cpn =fckg. A pseudo-noise code cu from Cpn
Therefore, the set of contenders to node i includes one-hop isassignedtoadirectionallink(u;v)attimeslottaccording
neighborsofiandone-hopneighborsofnodesinthesetn1i;c to thefollowing hashing function:
excluding nodei itself, as shown in the following formula: cu =ck; k=Rand(u(cid:8)t)(cid:8)u mod jCpnj: (15)
Note that it is unnecessary to involve v in the code assign-
Mi=Ni1[ Nk1 −fig: (14) ment, because of the simple fact that a node can activate
0k2n1 1 only onelink at a time.
i;c
[
B C
@ A LikeLAMA,thetwo-hopneighborinformation ispresumed
LAMA: to be available in PAMA by the appropriate integration of
NAMA and PAMA.
1. Compute the priority ptk of every node k 2 Mi[fig PAMA decides whether a directed link (u;v) can be acti-
using Eq. (1). vatedbynodeuintimeslott. Thesetofcontenderstolink
(u;v)aretheincidentlinksofuandvexcluding(u;v)itself,
2. If Eq. (2) holds, then activate link (i;j);j 2 n1i;c in i.e.,
time slot t. 2
M(u;v) = f(x;y)j(x;y)2E;x2fu;vg g[
f(x;y)j(x;y)2E;y2fu;vg g−f(u;v)g:
Non-contending Link
Contending Link
Active Link 1d b c
5
a 14 19 k d
x j e k
11 23 a
b i
8 21
c x k 20 Figure 7: An Example of HiddenTerminal Problem
f
In PAMA
6
g Whenalink(u;v)isactivated,therearepossiblehiddenter-
minal conflicts from one-hop neighbors of v if any outgoing
Figure 6: An Example of Contending Resolution linkontheone-hopneighborsofnodevisassignedthesame
code as (u;v). Figure 7 illustrates that a collision happens
Figure6exempli(cid:12)esacontentionsituation at nodeiduring at node b when link (a;b) and (c;d) are activated using the
timeslott. Thetopologyisanundirectedgraph. Thenum- same code k. PAMA is able to deactivate link (a;b) for the
ber beside each node represents the current priority of the current time slot as described in the following algorithm:
node. Node j and k happen to have the same code x. To
determineificanactivatelinkson code x,wecomparepri- PAMA:
oritiesofnodesaccordingtoLAMA.Nodeihasthehighest
pjraionrditkyawsitwheinlloanset-hheoipronneeig-hhobpornse,iagnhdbohrisg.hTerheprreifoorritey, ithcaann 1. Cf(oum;vp)ugteustihnegpEriqo.ri(ty16p)t(:x;y)ofeverylink(x;y)2M(u;v)[
activate either (i;j) or (i;k) in the current time slot t de-
pending on back-logged data flows at i. In addition, node pt(x;y)=Rand(x(cid:8)y(cid:8)t)(cid:8)x(cid:8)y (16)
e may activate link (e;d) if d is assigned a code other than
2. Exit if Eq. (17) does not hold.
code x.
8(x;y)2M(u;v); pt(u;v)>pt(x;y) (17)
4.3 PairwiseLinkActivationProtocol
3. Computethepriorityofeachtwo-hopneighborofnode
ThePAMA(Pairwise-link ActivationMultipleAccess) pro- u, that is:
tocolisalsoatime-slottedlinkactivationprotocolbasedon
a code division multiplexing scheme using DSSS. The dif- ptk =Rand(k(cid:8)t)(cid:8)k; k2Nu2 (18)
fterraennscmeitwteitrh-reLcAeiMveAr piasirt,haatndaccoomdpeuitsedasesivgenreydtifmore-aslogti,vesno 4. Compute the code assignment ck on node k;k 2 Nu2
using Eq. (15).
that the contention situation is di(cid:11)erent from time slot to
time slot. 5. Activatelink (u;v) in time slot t if:
Unlike NAMA and LAMA in which contending entities are 8k2Nu2 and cu =ck;ptu >ptk (19)
nodes, links are the entities competing for channel access 2
5. NEIGHBORPROTOCOL When the time for the membership section comes, the new
Becausecollision-freetransmissionschedulingbasedonNCR member randomly selects a segment within the section to
depends on accurate two-hop neighborhood information, it transmit its signal, which contains its ID number and part
is critical for a node to realize and incorporate neighbor- numberand those of its one-hop neighbors (Figure 4). It is
hood changes promptly. A neighbor protocol handles these expectedthatallone-hopneighborsofthenewmemberhear
changesinareliablefashionforNAMA,LAMAandPAMA. thesignalandincorporatethenewmemberintheirone-hop
We describe briefly the mechanisms provided in NAMA to neighbor set.
deal with topology changes.
Therecouldbecollisionswhenmultiplenewmemberswithin
We rely on the membership section of each block to accept two hopstryto notify thenetworkin exactly thesame seg-
newmemberstochannelaccessscheduling. Nodesaredi(cid:11)er- ment of the membership section. We resolve these hidden-
entiated in terms of those that are already participating in neighbor relations by thenext case.
the channel access scheduling and those that are not. The
former nodes are silent during the membership section of When two nodes become one-hop neighbors, they need to
a block, when latter nodes announce their existence using (cid:12)rstly recognize each other and then to synchronize their
signal frames. one-hop neighbor information. We name such two nodes a
andb,respectively,andconsidertherecognitionofbbyain
Anewmember(cid:12)rstlistenstothenetworktra(cid:14)cforatleast two cases.
acompleteblockbeforeittriestoparticipateintheschedul-
ing. Thedurationofablock,whichisSb sections,isderived
such that it ishighly probablethat every two-hop neighbor (cid:15) areceivesacompletedataframefromb. Inthiscase,a
ofthenewmembertransmitsatleastonceintheblock. We sendsoutaneighborupdateinitsnextdataframere-
consider two-hop instead of one-hop neighbors because the gardingthestatusofb. Unlessbsendsbackaneighbor
probability of each node being activated is the reciprocal update about a, a sends out a signal in the member-
of the number of its two-hop neighbors. This situation has shipsection likeanewmemberdoesandwaitsforthe
been formulated as an occupancy problem in combinatorial acknowledgment from b. The process is repeated un-
mathematics[10][18],whichpursuestheprobabilityofhav- til b recognizes a, when a and b exchange complete
ingmemptycellsafterrandomlyplacingrballsintoncells, one-hop neighbor information.
wherer correspondstotheblocksize,andncorrespondsto
(cid:15) a does not receive a complete data frame from b, but
the number of two-hop neighbors of a new member. We
detects collisions in some time slots. In this case, a
use the result on the probability of leaving exactly m cells
sendsoutasignalinthefollowingmembershipsection
empty,which is:
like a new member does. Aslong as collisions exist, a
n−m keepssendingsignalsinthemembershipsection. Once
pm(r;n)=n−r mn (−1)v n-vm (n−m−v)r (20) a is recognized by b, b follows the process as in the
v=0 previous case.
(cid:18) (cid:19) (cid:18) (cid:19)
X
Given theaverage numberof two-hop neighbors n in a net- Inthesecondcase,collisionsmayalsobecausedbytwoone-
work, we search for such an r that p0(r;n) > 0:99, which hopneighborsofanotknowingeachother,whichrequiresa
promises 99% probability ofhavingeverytwo-hop neighbor
tosendoutupdatesaboutone-hopneighborsinthecolliding
transmit at lease once in a block. Figure 8 shows the mini-
part to resolve conflicts.
mum numbers of balls (block size) to allow p0(r;n)>0:99,
given di(cid:11)erent numbers of cells (two-hop neighbors). In re- Ontheotherhand,anodeadetectsthedisappearanceofits
ality, we put an upper and a lower bound on the block size existing one-hopneighborb ifneitherdataframe norsignal
such that less time is spent on neighbor coordination while is received from b for a couple of blocks, in which case a
new members still can quicklynotify thenetwork. deletes b from its one-hop neighbor set as well as one-hop
neighborsreportedbyb. Nodeageneratesaneighbor-delete
200 updateto notify its one-hop neighbors about thechange.
Neighbor update information requires reliable propagation,
s150 thus acknowledgment and retransmission mechanisms are
Ball integralpartsofneighborprotocol, which wedonotspecify
of in thispaper.
er 100
b
m
6. PERFORMANCE
u
N
50
6.1 Expected Performance Differences
InNAMA,contendingmembersarenodeswithin twohops,
0 andtheyareassigned intothedi(cid:11)erentpartsandtimeslots
0 5 10 15 20 25
Number of Cells of a section. Therefore, the average number of contending
nodes for each time slot becomes
Figure8: NumberofBallsvs. NumberofCellsSuch jN1[N2j
i i
That p0(r;n)>0:99 P (cid:1)T
s p
Although contention is less than the number of two-hop (cid:15) Bandwidth of a radio transmission is up to 2 Mbps.
neighbors, the chances of transmission are also diminished
by thesame factor. (cid:15) A time unit in the simulation equals one time slot. A
timeslotlast8millisecondsincludingguardtime,long
In LAMA, contentions happen on each code. When a node enough to transmit a 2KB packet.
i tries to transmit on a code to one of its neighbors, con-
tentionscomefrombothi’sone-hopneighborsandtheone- (cid:15) In NAMA, the number of time slots within a part is
hop neighbors of the receivers possessing the code. So the Tp = 5, and the number of parts within a section is
average numberof contenderstoi on a code c is: Ps =3. Thus, a section lasts 120 milliseconds.
(cid:15) InNAMA,thelowerandupperlimitsontheblocksize
jNi1[ Nj1 j−1 are 31 and 97, respectively.
0 1
j2n1
i;c
B [ C (cid:15) InLAMAandPAMA,30pseudo-noisecodesareavail-
accordingtoEq. (14). T@houghtheAcontentionlevelishigher able for code assignments, i.e., jCpnj=30.
than NAMA,nodescompete for every time slot.
(cid:15) Allnodeshavethesame packetarrival rate(cid:21)i ineach
PAMAismoretopology-dependentthantheothertwopro- simulation. Unless otherwise speci(cid:12)ed, the destina-
tocols. Not only two-hop neighbors, but also links between tions of the generated packets are evenly distributed
two-hopneighborsbecomethecontentionsources. Thecon- on all outgoing links.
tendersofalink in PAMAareabout twiceas manyasthat
of LAMA because of the directional treatment of links in (cid:15) PacketsareservedinFirst-InFirst-Out(FIFO)order.
PAMA.
(cid:15) Thedurationofthesimulationis800seconds(equalto
Above all, the density of packet radios placed in an ad- 100000 time slots) in thefully connectedscenario and
hoc network and the transmission range of the radios de- 400seconds(equalto50000timeslots)inthemultihop
termine contention levels in these protocols. Suppose that networkscenario,longenoughtocomputethemetrics
the network nodes are uniformly distributed on an in(cid:12)nite of interests.
plane with density (cid:26), and all nodes have the same e(cid:11)ec-
tive transmission range r. A node in NAMA has approxi-
mately 4(cid:26)(cid:25)r2−1 contendingnodes with regard to two-hop 6.2.1 FullyConnectedScenario:
neighbors. In LAMA,a node would havearound 2(cid:26)(cid:25)r2−1 Inthefullyconnectedscenario,simulationswerecarriedout
contending nodes for activating a link, considering the two infourcon(cid:12)gurations: 2-,5-,10-,20-nodenetworks,toman-
endpointsofthelink,ifweassumeone-hopneighborsofthe ifestthee(cid:11)ectsofdi(cid:11)erentcontentionlevels. Figure9shows
endpoints are assigned distinctive codes. While in PAMA, the delay values under di(cid:11)erent loads in the four cases as
the number of contending links of each link activation is well asatheoretical curvederivedfrom Eq. (7)withqi val-
4(cid:26)(cid:25)r2−2 because of thedirectional treatment of links. ues as shown in the (cid:12)gures. NAMA and LAMA seem to
(cid:12)twellwiththetheoreticanalysis,butPAMAshowshigher
If we examine the number of active links when a node may delaysinthesamesituations. Thisisbecausethecontention
transmitpacketinthecurrenttimeslot,NAMAcanactivate sources are di(cid:11)erent in PAMA from NAMA and LAMA.In
all of its incident links, and LAMA can activate a subset of PAMA,contending entities are links, and contention comes
itsincidentlinks,whilePAMAcanactivateasingleincident fromadjacentlinksofeverylink. Theqi valueforPAMAin
link at all times. In the case of unicasting, PAMA sustains thefully connected scenario is:
highest throughputto the network because of a better spa-
jVj−2
1 1
tial reuse of the channel,as shown in thesimulations. qi = 4(cid:1)jVj−2 (cid:1) 1− 2jCpnj (21)
6.2 SimulationResults (cid:18) (cid:19)
where thesecond factor is duetoelimination of hiddenter-
WesimulatetheperformanceofNAMA,LAMAandPAMA minal interference. Hidden terminal problem can be im-
instatictopologies. Theperformanceofthethreeprotocols proved if more spreading codes are available.
are studied in two scenarios: fully connected networks with
di(cid:11)erentnumbersofnodes,andmultihopnetworkswithdif- Taking the 10-node network as an example, the qi value
ferent radio transmission ranges. The packet arrival and for each link is 1 (cid:1) 59 10−2 =0.023 in PAMA, which
4(cid:2)10−2 60
departure events are modeled as M/G/1 queuing systems
would result in a delay of at least 46 time slots by Eq. (8).
with vacations. The delay of packets at each node and the
In cases of NAMA and (cid:0)LAM(cid:1) A, nodes are the contending
throughput of thenetwork are collected in each simulation. entities, and the qi values for each node are both around
1 = 1 =0.1, which leads to delays of at least 12.5 time
Thesimulationsareguidedbythefollowingparametersand jVj 10
slots.
behaviors:
Figure 10 shows the throughput of the three protocols. As
(cid:15) Signalpropagationinthechannelfollowsthefree-space predictedinEq. (9),allprotocolsshowlinearsystemthrough-
modelandthee(cid:11)ectiverangeofradioisdeterminedby putunderthedi(cid:11)erentsustainableloadsandflatthroughput
thepower level of theradio. All radios havethesame when network load exceeds the available channel capacity,
transmission range. which is advantageous over any other randomized multiple
q=0.5, 2 Nodes q=0.2, 5 Nodes 6.2.2 MultihopNetworkScenario:
i i
200 200
NAMA Figure11and12showthedelayandthroughputfeaturesof
LAMA thethreeprotocolsinmultihopnetworks. Thenetworksare
Delay T (Time Slot)i11055000 PThAeMoAry Delay T (Time Slot)i11055000 htg1he0ane0s0ecsr(cid:2)qoa1nute0sadt0rae0bnyatsqrnreuaoansdredeeaompmmleaelydtceeprtmsloa.egcneiTttnhogdeers1n,i0ms0wiutnhyla,oictdtheheseivnwio(cid:12)spuintpaihtloielnsyiptatelnuasnrainedrseetashthaooetff
squareareaintoatorus. Bysettingthetransmissionranges
0 0
0 0.1 0.2 0.3 0.4 0.5 0 0.05 0.1 0.15 0.2 0.25 of the transceiver on each node to 100, 200, 300, 400 me-
Arrival Rate l (Packet/Slot) Arrival Rate l (Packet/Slot)
i i ters,respectively,wealsovirtuallychangethetopology and
q=0.1, 10 Nodes q=0.05, 20 Nodes
300 i 300 i contention levels in each case.
250 250
me Slot)200 me Slot)200 300 Transmission Range=100 500 Transmission Range=200
Delay T (Tii110500 Delay T (Tii110500 me Slot)220500 me Slot)340000
50 50 Ti150 Ti
00 A0r.r0iv5al Rate 0l.i 1(Packet0/S.1lo5t) 0.2 00 0A.0r2rival R0.a0t4e li (P0a.0c6ket/S0lo.0t)8 0.1 Delay T (i10500 Delay T (i120000
0 0
Figure 9: Average Packet Delays In Fully- 0 0.05 0.1 0.15 0.2 0 0.05 0.1
Arrival Rate l (Packet/Slot) Arrival Rate l (Packet/Slot)
i i
Connected Networks
Transmission Range=300 Transmission Range=400
1000 1400
1200
apcucteswshpernottohceonlsettwhoartkelxopaedrigenoecsebgereyaotndlocsseritnainthpeotihnrto.uNgho-- me Slot) 680000 me Slot)1800000
tice that PAMA allows higher sustainable load in the sys- Ti Ti
treemusetheavnenNwAhMenAtahnedtLopAoMloAgybiescafuulslyePcoAnMneActaeldlo.wschannel Delay T (i240000 Delay T (i246000000 NLAAMMAA
PAMA
0 0
1.5 qi=0.5, 2 Nodes 1.5 qi=0.2, 5 Nodes 0 Arriv0a.l0 R2ate li (Pac0k.e0t4/Slot) 0.06 0 A0r.r0iv1al Rate0 l.0i (2Packet0/S.0lo3t) 0.04
Packet/Slot) 1 NLPTAhAAeMMMoAAAry Packet/Slot) 1 Fwiogrukrse 11: AveragePacketDelaysInMultihopNet-
S ( S (
Throughput 0.050 Arri0v.a2l Rate li (0P.a4cket/Slot)0.6 Throughput 0.050 Ar0ri.v1al Rate l0i .(2Packet/Sl0o.t3) Packet/Slot)223050 Transmission Range=100 Packet/Slot)1250 Transmission Range=200
Throughput S (Packet/Slot)012...01235550 Arriva0ql. i=1R0a.t1e, l1i0 ( PNaocd0kee.2st/Slot) 0.3 Throughput S (Packet/Slot)012340 0A.0r5rivqail= R00a..01te5 ,l 2i 0(P 0Na.1oc5dkeets/Sl0o.t2) 0.25 Throughput S (Packet/Slot)11105005680 0A.T1rrriavnasl mR0ias.2tsei olni (RP0aa.nc3gkee=t/S30l0o0.t4) 0.5 Throughput S (Packet/Slot)1005680 0A.0Tr5rriavnasl mR0ias.1tsei olni (RP0aa.1nc5gkee=t/S40l0o0.t2) 0.25
S ( S (4
FNiegtuwroerk10s: Packet Throughput Of Fully-Connected Throughput 24 Throughput 2 NLPAAAMMMAAA
0 0
0 0.05 0.1 0.15 0 0.02 0.04 0.06 0.08 0.1
Arrival Rate l (Packet/Slot) Arrival Rate l (Packet/Slot)
i i
Figure 12: Packet Throughput Of Multihop Net-
works
Figure11demonstratestheadvantageofLAMAoverNAMA
because of improvements on channel reuse within two hops
ofeachnodebyapplyingcodedivisionmultiplexinginLAMA.
PAMA still gives higher starting point to delays than the
othertwoevenwhennetworkload islowduetosimilarrea-