DTIC ADA461743: Channel Access Scheduling in Ad Hoc Networks with Unidirectional Links

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by  Defense Technical Information Center

Channel Access Scheduling in Ad Hoc Networks
(cid:3)
with Unidirectional Links
Lichun Bao J.J. Garcia-Luna-Aceves
ComputerScienceDepartment ComputerEngineeringDepartment
UniversityofCalifornia UniversityofCalifornia
SantaCruz,CA95064 SantaCruz,CA95064
[email protected] [email protected]
ABSTRACT than simple neighbor information. Proper use of unidirec-
Anewfamilyofcollision-freechannelaccessprotocolsforad tional links demands a topology-dependent channel access
hoc networkswith unidirectional linksisintroduced. These scheme to ensure fast and impromptu data transmission,
protocols are based on a distributed contention resolution without incurring collisions.
algorithm that operates at each node based on the list of
direct contenders (one-hop neighbors or incident links) and Channel access control in ad hoc networks with unidirec-
indirectinterferences(two-hopneighborsandrelatedlinks). tional links can be either contention-based or scheduled.
Dependingontheactivationscheme(nodeactivationorlink Contention-based methods are not well suited to wireless
activation), a network nodeuses theidenti(cid:12)ersof its neigh- terrestrial networks with unidirectional links, because they
borsoneandtwohopsawaytoelectdeterministicallyoneor all need feedback from thereceiver, which requires medium
multiple winners for channel access in each contention con- access control (MAC) control packets to traverse multiple
text (e.g., a time slot or a frequency band). The protocols hops from receiver to sender. Even the ALOHA protocol
areshowntobefairandcapableofachievingmaximumuti- applied on terrestrial links requires an acknowledgment to
lization of the channel bandwidth. The delay and through- be sent to the sender of a packet in order for the sender to
putcharacteristicsofthechannelaccessprotocolsisstudied decide if there was a collision or not.
by simulations.
Scheduled access schemes prearrange or negotiate a set of
1. INTRODUCTION time tables for individual nodes or links before hand, such
thatthetransmissionsfromthesenodesorontheselinksare
Many routing protocols ([1] [2] [10] [12] [14] [15] [23]) have
collision-freeinthetimeslotsandfrequencybands. Previous
beenproposedintherecentpasttotakeadvantageoftheex-
MACprotocolsbasedonschedulingdonotworkinmultihop
istenceofunidirectionallinksandimprovenetworkthrough-
packet radio networks with unidirectional links, because of
putinadhocnetworks. However,therehasbeenverylittle
their dependence on collision-avoidance handshakes among
progress in the corresponding channel access mechanisms
nodes,which workcorrectly onlyoverbidirectionallinks[5]
thatprovidesafeande(cid:14)cientdatatransmission overunidi-
[16] [21] [24]. Only a few algorithms based on topology-
rectional links.
transparent transmission scheduling are viable for handling
unidirectional links in multihop networks [3] [4] [20]. How-
Usingunidirectional linksfordatacommunications isprob-
ever,intheseprotocols, thesenderisunabletoknowwhich
lematic. Although stable and usable unidirectional links
neighbor(s) can correctly receive its packet in a particular
can provideshorter pathsto reach certain destinations, up-
slot. This implies that the sender has to send its packet
streamnodesofunidirectionallinksmaycreatesevereinter-
in the various slots in a frame and that the frame length
ference at the downstream nodes unintentionally when the
(numberof slots) must be larger than the numberof nodes
linksaretemporaryorunnoticed. Inaddition,thecoordina-
inatwo-hopneighborhoodanddependsonthenetworksize,
tionbetweenthenodesatbothendsofaunidirectionallink
which is less scalable.
requires sending information over a multihop path, which
requires larger scale knowledge about thenetwork topology
Theproblemofderivinganoptimalchannelaccessschedule
(cid:3)
This work was supported by the Defense Advanced Research in multihop network is NP-hard [6] [7] [18]. Polynomial al-
ProjectsAgency(DARPA)underGrantNo. F30602-97-2-0338. gorithmsareknowntoachievesuboptimalsolutions. Auni-
(cid:12)edframeworkfor(T/F/C)DMAchannelassignment,called
UxDMA,wasdescribedbyRamanathan[17]tocomputeak-
coloringofadirectedgraphinpolynomialsteps. Theheuris-
tic consists of starting coloring nodes or edges randomly or
sequentiallyaccordingtovertexdegrees,andderivingamin-
imal number of colors such that a set of constraints on the
nodes or links are satis(cid:12)ed. The constraints on the color-
ingpatterncomprehendsuchcommonlyknowninterferences
as direct and hidden-terminal interferences [22]. Unfortu-
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4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Channel Access Scheduling in Ad Hoc Networks with Unidirectional
5b. GRANT NUMBER
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unclassified unclassified unclassified
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
nately, the need for global topology collection and sched- Ifnode uis an upstream neighbor of v,and bw(u;v) =0, we
ule dissemination poses a major challenge for applying this say that the head is an upstream-only neighbor of the tail,
scheduling approach in mobile ad-hoc networks. which means the head does not send data packets to the
tail, but may only interfere at thetail of thelink.
This paper presentsa distributed MACprotocol for ad hoc
networks with unidirectional links called PANAMA (Pair-
3. MODELING CONTENTION
wise linkActivation andNodeActivation MultipleAccess).
Inmultihopwirelessnetworks,contendingentitiesarenodes
PANAMAsupportscollision-free broadcasting and unicast-
or links between nodes. A contention between two entities
ing, without either repetitious schedule adjustments due to
isasituationinwhichsimultaneousactivation ofoneentity
network topology changes or global topology information.
would render the activation of another unsuccessful. Colli-
TheonlyinformationPANAMAneedstogeneratecollision-
sions happen in three cases, as illustrated in Figure 1 [19].
free schedules at a node is the two-hop neighbor informa-
tion of the node. Section 2 describes network concepts and This indicates that nodes within two hops cannot trans-
mit in the same time, code, or frequency division to ensure
topology notation used to describe ad hoc networks with
collision-freedom. To enforce this, a node needs to at least
unidirectional links. Section 3 describes our approach to
knowits neighbors and its neighbors’ neighbors for channel
modeling contention in networks with unidirectional links.
access scheduling.
Section 4 presents a new distributed contention resolution
algorithm onwhichPANAMAisbased. Section 5describes
PANAMA, which is based on an algorithm for collision-
freeunicasttransmissionsandanalgorithmforcollision-free
broadcast transmissions. Section 6 describes the neighbor
protocol neededtohandlemobility. Section7addressesthe
performance of PANAMA by simulation. Section 8 con-
cludes thepaper. (a) Hidden Terminal Problem
2. TOPOLOGYASSUMPTIONS
The topology of a network with unidirectional links can be
abstractedasadirectedgraphG=(V;A),whereV istheset
ofnodes,andAisthesetofdirectionallinksbetweennodes,
i.e.,A(cid:18)V (cid:2)V. Weassumethateachnodeinthemultihop
(b) Direct Interference (c) Self Interference
packetradionetworkhasauniqueidenti(cid:12)er,andismounted
withanomnidirectionalradiotransceiver. Alink(u;v)2A
Figure 1: Examples of Collision Types
meansthatnodev iswithintheradiotransmission rangeof
nodeuandthatapossibledatatransmission channelexists
fromnodeutonodev. Alink(u;v)2Adoesnotnecessarily Wemake thefollowing assumptions:
mean that (v;u)2A in unidirectional networks.
If a link (u;v) 2 A, node u and v are called the head and 1. A radio module of each node may either transmit or
tail of the link, respectively. Sometimes, node u is called receive data packet at a time, but not both.
upstream neighbor of node v, and node v is the downstream
neighborofnodeu. Similarly,link(u;v)iscalleddownstream 2. Every entity already knows the set of its contenders
link of node u, and the upstream link of node v. We denote by theneighbor protocol.
the set of upstream and downstream neighbors of a node i
as U and D , respectively. Two distinct nodes adjacent to 3. Atime,code,orfrequencydivisionunitisacontention
i i
the same node are called two-hop neighbors to each other. context, and each contention context is identi(cid:12)able.
A unidirectional link is always (cid:12)rst detected by the tail of
the link, and its existence is propagated back to the head In the description of our collision resolution algorithm, we
of the link. Hence, there is causal asymmetric knowledge consider the time slot number as the identi(cid:12)er of a con-
about theexistenceof aunidirectional linkat theheadand tention context. Code and frequency assignments are left
tail of the link. For instance, if (u;v) 2 A, then v 2 D out until individualMAC protocols are speci(cid:12)ed. Ina time
u
implies u2U , but not the opposite. The establishment of division multipleaccessscheme,eachtimeslot canbenum-
v
adownstream neighborat anoderequiresacycleincluding bered,becausenodesmustbesynchronizedatthegranular-
the link to exist in the network [2]. ity of a time slot.
Each nodeorlinkofthenetworkhasabandwidthproperty Thecontention-resolutionproblem(CRP)canthusbestated
that indicates the portion of the channel available to the as follows:
nodeorlink. Thebandwidthassignedtoanodeiisdenoted
by bw , which is a floating-point number that ranges over
i
[0;1). Likewise, the bandwidth of a link (u;v) is a floating- CRP: Givenasetofcontenders, Mi,againstan
point number bw(u;v) 2 [0;1). The bandwidth is requested entityiincontentioncontextt,howdoesidecide
by thenodeor thehead of thelink dynamically,depending if itself is the winner among the set Mi [ fig
on theneeds from network-level protocols. without conflicts with others?
4. CONTENTIONRESOLUTION Lemma 1. Accesstothecommonchanneliscollision-free
ALGORITHM at all times.
Thechannelassignmentprobleminthetime,frequencyand
codedomains hastraditionally beentreated asa graphcol-
oringproblem. Ak-coloringonthenodesorlinksofthenet- Proof: Because it is assumed that contenders havemutual
worktopologygraphcorrespondstoksequentialactivations knowledge and t is synchronized, the order of contenders
to thenodes orlinksin thesame color without collisions at based on the priorities is consistent at every participant.
the intended receivers, thusobtaining temporal and spatial WhentheentityihasthehighestpriorityinthesetMi[fig,
reuse of the available bandwidth. The schedules derived each k2Mi yields to i, and allows i to access the common
from graph coloring are static, because the network topol- channel collision-free. 2
ogy has to remain unchanged; otherwise, a new schedule is
re-computed and broadcast after new topology information
iscollected. Inmobilenetworks,thisconsumesasigni(cid:12)cant Lemma 2. The contention resolution algorithm is live.
portion of the scarce wireless bandwidth. The e(cid:14)ciency of
staticcoloringalgorithmsmayalsosu(cid:11)erfromthefactthat
some of the colors could be so rarely used for coloring that Proof: Inmultihopwirelessnetworkswherewehavea(cid:12)nite
theactivationofnodesorlinksinthosecolorscannotengage numberof entities to consider, thealgorithm always results
su(cid:14)cient spatial reuseof thechannelinmultihopnetworks. inatleastoneormorewinnersineachcontentionsituation,
because CRA-FP gives a floating-point priority to each en-
Weadoptadi(cid:11)erentapproachtographcoloringtosolvethe tity,andmultiplelocallymaximalprioritiesmayexistinthe
CRP problem. First, node or link activation scheduling is network. The case without a winner elected where two pri-
dynamic,suchthatadi(cid:11)erentscheduleisestablishedineach orities are the same and also the global maximum is rare
contention context (e.g., each time slot). Second,thecolor- andnegligible. Therefore,CRA-FPallowsliveutilizationof
ing needs only two colors, r and b. An entity i gives itself thecommon channelin each contention context. 2
colorr ifitshasthehighestpriorityamongst itscontenders
in a contention context. Otherwise, i colors itself with b.
Nodes in color r are active in the corresponding contention Lemma 3. Each contending member has a fair share of
context. Third,thecolor r isusedin eachcontention situa- the common channel, the portion of which available to an
tiontothemaximaldegreewithoutanycollision possibility. entityisrelativetotheencounteredcontentionsbytheentity.
Fourth,themaximum topology information required in the That is:
coloring process consists of the one- and two-hop neighbor
bw
information of a node, instead of the complete topology of q = i : (3)
i bw
the network. k2Mi[fig k
To describe our solution to the CRP problem, we assume P
thatprimaryoperantsinmathematicalformulasareof(cid:12)xed
length,andthesign‘(cid:8)’lendstocarryingoutconcatenation Proof: CRA-FPbasically generates arandom permutation
operation on its operants. ofthecontendingmembers,theorderofwhichisdecidedby
thepriorities of all participants. Since thepriorities change
During the contention context t, the following algorithm from time to time, the permutation also varies randomly
solves theCRP problem: such that an entity i has certain probability to win in each
contention context.
CRA-FP (Floating Point):
Without loss of accuracy, we assume that the priorities of
di(cid:11)erent entities are always distinct. For convenience, we
1. Computeapriorityforeachmemberk insetMi[fig, temporarily introduce random variable Xk and Yk to de-
which is denoted by pt: notetheresultoffunction bwk Rand(k(cid:8)t)andRand(k(cid:8)t),
k
respectively. This gives usthe following relations:
ptk = bwk Rand(k(cid:8)t);k2Mi[fig (1) pp
X =pt = bwk Y ;k2M [fig:
2. i wins the contenption at t if: k k k i
8j2M ;pt >pt (2)
i i j Inaddition,PfY <yg=y sincetherandom variableY is
k k
Otherwise, i yields toother contenders. 2 uniformally distributed over the range [0;1). Thus the cu-
mulativedistributionfunction(CDF)ofthederivedrandom
where Rand(x) is a floating-point pseudo-random number variable Xk is:
p
generatorthatproducesauniformlydistributedrandomnum- F (x)=PfX <xg=Pfbwk Y <xg
ber over [0;1) using the random-seed x. bwk is the band- k =PfYk<xbwkg=xbwk k
width requested by entityk. If bw =0, pt =0. k
k k
which gives the probability density function (PDF) of ran-
The following lemmas demonstrate that CRA-FP provides dom variable X as:
k
collision-freechannelaccess,withoutcreatingdeadlocksand
in a fair manner. f (x)=F0(x)=bw (cid:1)xbwk−1
k k k
Speci(cid:12)cally,whenthepriorityofentityiisx,theprobability Codeassignment in anetworkbased onDSSScanbebased
that entityi wins thecontention is derived from Eq. (2): on transmitter-oriented (also known as TOCA), receiver-
oriented (ROCA) or a per-link-oriented code assignment
q (x)=PfX <x;k2M g= PfX <xg
i k i k (POCA)schemes[9][13]. Becauseanodecanonlytransmit
k2Mi or receive at one time on a single code, it is unnecessary to
= xbwk =xPk2MibwkY assign di(cid:11)erent codes to links incident to a single node as
k2Mi in a POCA scheme. Furthermore, as Figure 2 illustrates,
Y
simply using two-hop topology information at each node is
Since the value of x ranges in [0;1), we achieve the prob- insu(cid:14)cient to resolve collisions in a network with unidirec-
ability of entity i winning the contention by the following tionallinksusingaROCAscheme. InFigure2,thenumber
beside each node gives the current receive-code assigned to
integration:
thenode. Aunidirectionallink(b;c)partitionsthenetwork.
qi = 01qi(x)(cid:1)fi(x)dx= 01xPk2Mibwk (cid:1)bwi(cid:1)xbwi−1dx Ntoopdoelobgyisinufonramwaatrieonofpnerocdeeivecd. bSyinec,enaodiesebiesynoenvdertwceor-thaoinp
=Z bwi Z about the collision threat from b when it sends data to c.
bw
k2Mi[fig k Accordingly,thealgorithmsusedinPANAMAarebasedon
2 a TOCA scheme.
P
5. PANAMA Unidirectional Link
15
b Bidirectional Link
PANAMA is a distributed multiple access control proto-
col that combinestwo channelaccess schedulingalgorithms a Part 1
based on time-slotted code-division multiple access scheme 10 c10
usingdirectsequencespreadspectrum(DSSS)transmission
techniques. The(cid:12)rstschedulingalgorithmusedinPANAMA e 15
d
is NAMA-UN (Node Activation Multiple Access for Uni- 5 Part 2
directional Networks), which is a node-activation oriented
channel access algorithm suitable for broadcasting in wire-
Figure 2: Irresolvable Situation in ROCA
lessnetworkswithunidirectionallinks. Thesecondschedul-
ingalgorithminPANAMAisPAMA-UN(Pair-wiselinkAc-
tivationMultipleAccessforUnidirectionalNetworks),which We assume that a pool of quasi-orthogonal pseudo-noise
isalink-activationorientedchannelaccesscontrolalgorithm codes, Cpn = fckg, are available for each node to choose
suitable for unicasting in wireless networks with unidirec- from, and the pseudo-noise codes inside Cpn are sorted as
tional links. c0 < c1 < ::: < cjCpnj−1. The code for each node is com-
puted in each time slot so that the contention situation is
InbothNAMA-UNandPAMA-UN,anodeisinthereceiv- di(cid:11)erentfromtimeslottotimeslot. Apseudo-noisecodeci
ing mode when it does not win the contention. It listens from Cpn is assigned to a node i in time slot t according to
to the tra(cid:14)c in the channel by tuning its reception code thefollowing algorithm:
to the potential transmitter. In NAMA-UN, the potential
c =ck;k=iRand(i(cid:8)t) mod jC j: (4)
transmitter is an upstream neighbor that has the highest i pn
node-priority amongtheupstream neighborset. InPAMA- whereiRand(x)isanintegerpseudo-randomnumbergener-
UN, the potential transmitter is the head of an upstream ator that produces a random integer using input x as the
link with thehighest link-priority among theupstream link
randomizing seed.
set.
To describe the algorithms used in PANAMA, we assume
PANAMAcombinesNAMA-UNandPAMA-UNtosupport
thateachnodehasalreadyacquiredtheknowledgeaboutits
unicast and broadcast tra(cid:14)c e(cid:14)ciently. Deciding on what
one-andtwo-hopneighborsandtheirbandwidthallocations.
portion of the channel to assign to each protocol is a very Thegoalofnodeactivationsandlinkactivationsatanodei
pragmaticdecisionthatdependsonexpectedtra(cid:14)cpatterns
istosenddatapacketstoasubsetofdownstreamneighbors,
in the network. In this paper a (cid:12)xed channel allocation is
which is de(cid:12)ned as:
assumed for NAMA-UN and PAMA-UN,with each section
daneddicTated totimNeAMsloAts-,UrNesapnedctiPvAelMy.AA-UccNorldaisntginlyg,fborroaTdncaamsat Ri=fkjk2Di;bw(i;k) >0g (5)
pama
tra(cid:14)calwayswaitsfortheNAMA-UNsection,whileunicast
tra(cid:14)c is sent during the PAMA-UNsection, or NAMA-UN R iscalledthereceiver setofnodeithathasapositivelink
i
section if broadcast tra(cid:14)c is not present. bandwidthflowingoutofi. Downstreamlinksofnodeithat
are assigned 0 bandwidth are either unknown to i because
We do not address synchronization issues for time division ofunidirectionaldrawbacksorunusablebecauseoftopology
channelaccess,butsuggestachievingitbyeither: (a)listen- control mechanisms.
ingtodatatra(cid:14)cinthenetwork,andaligning timeslotsto
the latest starting point of a complete packet transmission Becausewehavealimitednumberofpseudo-noisecodesfor
byone-hopneighbors;or(b)suchothermeansasusingGPS assignment,itispossiblethatmultiplenodessharethesame
(globalpositioning systems)timingsignalsandthenetwork code. The methods of resolving transmissions on the same
time protocol (NTP). code are described below.
5.1 NAMA-UN 5.2 PAMA-UN
InNAMA-UN,everynodeisassociatedwithsomeamountof Unlike NAMA-UN,a link in PAMA-UNmay be assigned 0
bandwidth. NAMA-UNdecideswhetheranodeicantrans- bandwidth dependingon following two situations:
mit in a time slot t, such that its receiver set receives the
data packet without collisions. Therefore, the contenders
for nodei are of thefollowing three kinds: 1. When a link is initially detected by its tail, the band-
width of thelink is set to 0 bythe tail.
1. The receiver set of node i, R ;
i 2. If a link is able to propagate back to the head, the
2. All of i’s upstream neighbors, U ; bandwidth of the link can be set to any value in the
i rage [0;1). A node may choose to set the bandwidth
3. Allupstreamneighborsofnodesini’sreceiverset,i.e., request of thelink to 0 because of data flow controls.
U
k2Ri k
AccorSdingly, theset of contendersfor nodei is: With synchronized information about local topologies and
bandwidth allocations, PAMA-UN decides whether a di-
rected link (u;v) with positive bandwidth can be activated
M =U [R [ U (6) by node u in time slot t. Herein, the set of contenders to
i i i k
0k2Ri 1 link (u;v) are the incident links of u and v with positive
[ bandwidths, excluding(u;v) itself. That is:
which contains all nodes that m@ay sentAinformation to or
receive information from i and those that may incur inter- M(u;v) =f(x;y) j(x;y)2E and bw(x;y)>0 and
ference at i’s receiver when itransmits. (x2fu;vg or y2fu;vg) g−f(u;v)g:
NAMA-UN decides the activation of node i at time slot t
according to following algorithm:
PAMA-UN:
NAMA-UN:
1. Compute the priority pt of every link (x;y) in set
(x;y)
1. Compute the priority pt of every node k 2 M [fig M(u;v)[f(u;v)g usingthe following equation:
k i
using Eq. (1). pt(x;y)= bw(x;y) Rand(x(cid:8)y(cid:8)t) (8)
2. Exit if Eq. (2) does not hold.
p
2. Exit if thefollowing equation does not hold:
3. Exit if any upstream-only neighbor of i’s downstream
neighborspossesses thesametransmission codeasi’s, 8(x;y)2M(u;v);pt(u;v)>pt(x;y) (9)
i.e.,
9v2R and u2U and 3. Computetheprioritiesofupstreamneighborsofnodes
i bw(u;v) =v0 and ci =cu (7) in u’s receiver set:
where ci and cu are obtained from Eq. (4). ptk =iRand(k(cid:8)t);k2Uj;8j 2Ru: (10)
4. Broadcast in current time slot t. 2 where function iRand(x) is given in Eq. (4).
4. Exit if either of thefollowing two conditions holds:
Step3avoidspossiblehiddenterminalconflictsfromv’sup-
stream neighbor u when node u is assigned the same code (cid:15) One of the upstream-only neighbor of a u’s re-
as i’sand doesnot knowabout link(u;v)duetotheasym- ceiverpossesses thesametransmission codeasu.
That is:
metric properties of unidirectional links.
9k2U ; where j 2R and
0.u23 0.j05 j bw(k;j) =0 anud cu =ck (11)
0.39 Code assignments, c and c , are obtained from
k u k
i 0.02 Eq. (4).
k v
(cid:15) One of the upstream links of a u’s receiver is as-
signed positive bandwidth, and the head of the
Figure 3: Collision Resolution in NAMA-UN link possesses the same transmission code as u,
and the priority of the head is greater than that
Figure 3 illustrates an example of collision avoidance in
of u. That is:
NAMA-UN.The numbersbeside each node are thecurrent
prioritiesofthenodes,andkisthecodeassignedtouandi. 9k2Uj; where j 2Ru and bw(k;j) >0 (12)
Thoughbothianducantransmitoncodekbythe(cid:12)rsttwo and c =c and pt <pt:
u k u k
steps in NAMA-UN, but i will be deactivated in the third
step which avoid collision at node v. 5. Activatelink (u;v). 2
PAMA-UN encounters similar hidden-terminalproblems as u/d Meaning
NAMA-UN. Using the sample network in Figure 3 as an 00 Updateabout theneighbor.
example with the same transmission code assignments, col- 01 Updateof thedownstream link to theneighbor.
lisionhappensatnodeviflink(i;v)and(u;j)areactivated 10 Updateof theupstream link from the neighbor.
simultaneouslyoncodek. PAMA-UNdeactivateslink(i;v) 11 Updateof thelink with the neighborin both
for thecurrent time slot as described bystep 4. directions.
where the value 00 indicates neighbor updates for NAMA-
6. NEIGHBORPROTOCOL UN and all others are for PAMA-UN.
In both NAMA-UN and PAMA-UN, topology information
withintwohopsofanode,includingbandwidthallocationto Using signals, a node may send topology changes or band-
nodes and links, playsa critical role. Unfortunately,in mo- widthadjustments. Whenanewmobilenodeisbroughtup,
bile networks, network topologies change frequently, which sending out signal is the (cid:12)rst activity to notify its one-hop
a(cid:11)ects the transmission schedules of the mobile nodes. In neighbors of its existence.
PANAMA,theabilitytodetectandnotifysuchchangesre-
lies on theneighbor protocol described in this section. Thenumberoftimesegmentsinthesignalsection,TsignalSs,
andtheintervalbetweensignalsections,LintermsofNAMA-
UN and PAMA-UN sections, depend on the average num-
berofone-hopneighborsforeachnodeandthefrequencyof
6.1 Signal Sections topologychanges. Ingeneral,thevalueofLissetsmalland
Both NAMA-UN and PAMA-UN adopt dynamic code as- thevalueofT S issetlargeforhighlymobilenetworks
signal s
signment for channel access. Therefore, it is impossible for so as to quicklyadjust to topology variations.
a node to follow a new one-hop neighbor that transmits a
datapacketinvarioustimeslotsonvariouscodes. Wehave Besides signals, one-hop neighbor updates are also propa-
to use an additional time section, called the signal section gated using broadcast data packets in the NAMA-UN sec-
thatlasts forT timeslots aftereveryLalternations of tion so thattheupdateinformation of anodegetstoall its
signal
NAMA-UN and PAMA-UN for mobility management pur- neighbors e(cid:14)ciently. One-hop neighbor updates are piggy-
poses. Nodes exclusively depend on the signals to detect backintheoption(cid:12)eldofadataframewhenevernecessary.
new upstream neighbor. Figure 5 illustrates the data packet format, which includes
similar neighbor update(cid:12)elds as in Figure 4.
ChannelaccessinPANAMAisbasedoncodedivisionscheme
but solely dependent on the current time slot number t as DATA PACKET
given in Eq. (13), similar to Eq. (4). Option Field
frameType src ID dst ID #nbrUpd nbrUpds payload
c =ck;k=iRand(t) mod jC j: (13)
t pn
nbrID opCodeu/d bw . . . . . .
Neighbor Update
In addition, a time slot within the signal section is further
dividedintoS timesegments,whichimpliesT S time
s signal s Figure 5: Data Frame Format
segmentsinthesignalsection. Eachtimesegmentlastslong
enough to send out a signal, illustrated in Figure 4.
6.2 Neighbor StateMaintenance
In a mobile network, topology changes happen in the fol-
SIGNAL lowing scenarios asfar as theoperations of NAMA-UNand
PAMA-UNis concerned:
frameTypesrcID #nbrUpd nbrUpds
nbrID opCodeu/d bw . . . . . . (cid:15) Theestablishmentofanewlink,suchasnewupstream
link detected bya node;
Neighbor Update
(cid:15) Thedisappearanceofanexistinglink,suchasone-hop
Figure 4: Signal Frame Format neighbors departing from each other;
(cid:15) Link state changes, such as bandwidth reassignment
In Figure 4, the (cid:12)eld nbrUpds contains #nbrUpds neighbor to a nodeor a link.
updates, each including the updated neighbor ID (nbrID),
thetypeoftheneighbor(upstream/downstreamasindicated
inthe(cid:12)eldu/d)andcorrespondingbandwidth(bw)assigned To ascertain the liveliness of outgoing links, it is required
tothatneighbor. Thevalueinthe(cid:12)eldopCodeinstructsthe thatanodesendsoutasignalpacketaftereverycertainpe-
operation code, which may suggest addition or deletion of riodoftime. Thetimeperiodisderivedsuchthatitishighly
the neighbor from the transmitter’s one-hop neighborhood. probablethateverytwo-hopneighborofanodecantransmit
The(cid:12)eldu/d takesoneoffourvaluesusingtwobitsasgiven at least one signal packetduring theperiod. Therefore, the
in thefollowing table: signal transmitted bythenodeisleast likely tocollide with
others. We consider two-hop instead of one-hop neighbors Network Network Network
becausethecontendersofanodeforbroadcastingsignalsin (a,b) ((ba,,ba))Signal(a,b) ((ab,,ba)) ((ba,,ba))
the channelare two-hop neighbors of the node. a b a b a b
Signal Signal
Thelengthoftheperiodduringwhicheverytwo-hopneigh-
bor of a node may transmit can be formulated as an occu-
pancyproblemincombinatorialmathematics[8][11],which (1) (2) (3)
pursues the probability of having m empty cells after ran-
domly placing r balls into n cells, where r corresponds to Figure 7: Link State Propagation
length of the period, and n corresponds to the number of
two-hop neighbors of the node. We directly use the result
on the probability of leaving exactly m cells empty, which b at each node. The eventsare described as follow:
is:
n−m 1. Nodeawaitsforacertainperiodtotransmitasignal;
pm(r;n)=n−r mn (−1)v n-vm (n−m−v)r (14) Ifbreceivesthesignalfromaforthe(cid:12)rsttime,ittrig-
(cid:18) (cid:19) v=0 (cid:18) (cid:19) gers b to send a second signal after a random number
X
oftimesegmentstonotifyitsone-hopneighborsofthe
Wechoosearvalueforthenetworksuchthattheprobability new upstream link (a;b).
of every two-hop neighbor having transmitted at least one
signal is greater than 0:99, i.e. p0(r;n) > 0:99. Figure 6 2. If a receives the second signal, a acknowledges b as a
demonstrates the interval values in terms of time segments newupstreamneighbor,andnoti(cid:12)eslink(b;a)aswell
for successive signal transmissions versus di(cid:11)erent numbers as (a;b) to its upper layer control protocols, which in
of two-hop neighbors. turn assign bandwidth property to link (a;b). New
link information about (a;b) and (b;a) is propagated
back to b.
200
3. If b receives the third signal, b also knows its down-
stream link (b;a). Link (b;a) is reported to b’s upper
150
Balls lparyoepracgoantterdolbpacrokttoocoals. forbandwidthassignment,and
of
er 100
b
m If the companion link (b;a) does not exist for link (a;b) in
u
N 50 Figure 7, a needs more complex steps by the upper layer
control protocols for propagation of link (a;b) and other
coordinations between a and b.
0
0 5 10 15 20 25
Number of Cells 7. PERFORMANCE
ThedelayandthroughputattributesofPANAMAarestud-
Figure 6: Signal Intervals vs. Number of Two-hop
ied by simulations in static network topologies with unidi-
Neighbors Such That p0(r;n)>0:99 rectionallink. Manycon(cid:12)gurableparametersintheprotocol
are simpli(cid:12)ed, such as thedurations of di(cid:11)erent sections.
When r timesegments pass byat a node, thenode chooses
a random time segment of the next signal section to send Thesimulationsareguidedbythefollowingparametersand
a signal so that signal transmissions are evenly distributed behaviors, and most numbers are more of empirical prefer-
and encountervery few collisions.
ences rather than theoretical conjectures:
When the connection between two nodes is unidirectional,
we have to rely on more complex control protocols in the (cid:15) The networks are generated by randomly placing 100
upperlayertocoordinatetheneighborinformationbetween nodeswithinan areaof1000(cid:2)1000 squaremeters. To
adjacentnodesbecauseitrequiresmultihoppropagationsof simulate in(cid:12)nite plane that has constant node place-
thelink states. A neighborprotocol was proposed in [2] for mentdensity,theoppositesidesofthesquareareseamed
this purpose. PANAMAprovides a set of control interfaces together, which visually turns the square area into a
(APIs)for(a)reportingnewupstreamlinksorincidentlink torus.
statechanges,and(b)receivingcontrolmessagesfromother (cid:15) Signalpropagationinthechannelfollowsthefree-space
controlprotocolsforneighbormaintenance,suchasaddition
modelandthee(cid:11)ectiverangeofradioisdeterminedby
of a new neighbor, deletion of an existing neighbor, and
thepower leveloftheradio. Thepowerrange ofa ra-
propagatingthesecontrolmessagesusingeitherNAMA-UN dio is randomly chosen from the range [150m;300m],
broadcast packetsor signals.
which creates unidirectional links.
Figure 7 depicts the operations for establishing a new bidi- (cid:15) Tosimulatedeactivatedorunusableunidirectionallinks
rectional connection using signals only between two nodes, in the network, we assume that 10% of the network
aandb. Thelinksmarkedbesideeachnodeshowtheforma- links are assigned 0 bandwidth, while all other links
tion of the knowledge about the connection between a and and all nodes are assigned bandwidth 1.0.
(cid:15) Bandwidth of the radio channelis 2 Mbps. The constraint E1 in UxDMA eliminates hidden terminal
tr
problemasillustratedinFigure1(a). Furthermore,tomake
(cid:15) A time unit in the simulation equals one time slot.
afaircomparisonbetweenUxDMAandPANAMA,nodesin
A time slot last 8 milliseconds, including guard time,
UxDMA are assigned transmission codes so that constraint
long enough to transmit a 2KB packet. E1 isallowedwhentransmittershavedi(cid:11)erenttransmission
tr
(cid:15) L=1, T =25, T =95, T =5, thus the codes.
nama pama signal
period for one alternation of NAMA-UN, PAMA-UN
and signal section is 1 second. Because the coloring on nodes and links is closely coupled
withcodeassignments,thecodeassignmentsarecarriedout
(cid:15) In NAMA-UNand PAMA-UN,30 pseudo-noise codes only once at the beginning of each simulation, and remain
are available for code assignments, i.e., jCpnj=30. staticthroughoutthesimulation aswellasthecolorassign-
(cid:15) All nodes have the same packet arrival rate (cid:21), pct ments. Nodesareassigned codesrandomlychosen from the
b code base C .
percent of which is broadcast tra(cid:14)c and the rest is pn
unicasttra(cid:14)c. Thedestinationsoftheunicastpackets
In addition, inactive links in the network topology are not
inPAMA-UNaredistributedonalloutgoinglinkswith
coloredbuttakenintoaccountwhencoloringlinksandnodes,
positivebandwidth,proportionaltotheprobability of
so that these linksincur interference at other nodes.
activating the link.
(cid:15) PacketsareservedinFirst-InFirst-Out(FIFO)order. ThenumberofcolorsusedbyUxDMAdeterminesthetime
frame during which every entity is able to access the chan-
(cid:15) Thedurationofthesimulationis800seconds(equalto
nel once. A time frame, un(cid:12)nished in either NAMA-UN or
100000timeslots),longenoughtocomputethemetrics
PAMA-UNsection,continuesintheupcomingsectionofthe
of interests.
same type.
Four main factors influence the system delay and through- 2000 1000
putattributesofPANAMA,namely: thedatatra(cid:14)cloadon PANAMA−Unicast
eachnode(denotedby(cid:21)),theportionofbroadcasttra(cid:14)cin Slot)1500 PUUAxxDDNMMAMAA−−AUB−rnBoircaoadascdta c s at st Slot) 800
the overall tra(cid:14)c (pctb), the portion of inactive directional me me 600
lteihlnsekasrtatdheiaaotcthornannloysdmienits(esrri)ofe.nreTrawonigtmhesaonttihhfeaestrtatt(cid:11)rhaenecstemt(cid:11)hiesecsticosonnostfe(tnphctiteousne)aldenivfd-- Delay T (Ti1500000 Delay T (Ti 240000
ferent parameters on the system delay and throughput, we
0 0
(cid:12)x three of the four factors and variate the remaining pa- 0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1
Arrival Rate l (Packet/Slot) Portion of Broadcast Traffic
rameter to simulate theoperations of PANAMA.The (cid:12)xed
x 104
values of each simulation put lenient stress on the network 5 800
delays and throughput. Thus, we obtain four scenarios:
Slot)4 Slot)600
Scenario Valuesof Fixed Parameters Variable me 3 me
123 p(cid:21)(cid:21)c==tb00=..00066.,,05pp,ccttpuc==tu00=..0105,.,r1p=,cr1t=0=01000.1 r(cid:21)pctb Delay T (Ti12 Delay T (Ti240000
b u
4 (cid:21)=0.06, pct =0.05, r=100 pct
b u 0 0
50 100 150 200 250 0 0.05 0.1 0.15 0.2
Minimum Radio Transmission Range (m) Portion of Unusable Links
Table 1: Four Scenarios and Their Parameters Figure 8: Average Packet Delays In Multihop Net-
works
Secondly, we also simulate the static scheduling algorithm,
UxDMA,speci(cid:12)edin[17],forcomparisonwithPANAMAin
Figure 8 and 9 show the delay and throughput attributes
thesame simulation scenarios with as many similar param-
ofPANAMAandUxDMAinmultihopnetworksofthefour
eters as possible, such as percentage of inactive links and
scenarios.
channel divisions into NAMA-UN, PAMA-UN and signal
sections,whereUxDMAusesadi(cid:11)erentcoloringschemefor
In all scenarios except scenario 3, unicast tra(cid:14)c has lower
each section. The criteria for coloring nodes in the broad-
delays in PANAMA than in UxDMA; however, PANAMA
castsectionandlinksintheunicastsectionaregivenbythe
performs worse than UxDMA for broadcast tra(cid:14)c. Like-
following table:
wise, the network throughput is almost the same in both
PANAMA and UxDMA when the network load remains at
Section Colored Object Constraint Set sustainable levels. In scenario 3, however,both unicast and
Broadcast Node fV0;V1g broadcast tra(cid:14)cs endure much longer delay and worse net-
tr tt
Unicast Link fE0 ;E0;E0;E1g work throughput when the transmission ranges increase in
rr tt tr tr
PANAMA, because of higher contention levels from longer
radio transmission ranges that increase the probability of
Themeaningofeachsymbolisreferredtotheoriginalpaper code assignment conflicts between two-hop neighbors, and
in [17]. lead to many aborted transmission due to collision avoid-
10 6 Hong Kong, China, 16-17 Dec. 1999.
Slot) 8 Slot)5
Packet/ 6 Packet/4 [2] Lro.uBtianogainndnJet.Jw.oGrkasrcwiait-hLuunnaid-Airceecvteiosn.aLlinlikn-ksst.atIen
Throughput S ( 24 Throughput S (123 PC35ro8om{ce6pe3ud,tienBrgosCstEooming,mhMtuInAnict,eaUrtniSoaAntis,o1an1na-dl1C3NoOentcwfeto.rre1kn9sc9,e9p.oanges
0 0
0 0.A0r2rival R0.a0t4e l (P0a.0c6ket/Sl0o.t0)8 0.1 0 0.P0o2rtion0 o.0f 4Broad0c.a0s6t Tra0ff.i0c8 0.1 [3] I. Chlamtac and S.Kutten.A spatial-reuse
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Throughput S (123 Throughput S (123 PPUUAAxxDDNNMMAAMMAA−−AAUB−−rnUBoircnaoaidcascadta sc st a t st mIJEuaElxyEim19Ta8rl7al.ninskacaticotnivsatoinonCionmmmuultniihcoaptiornads,io35n(e7t)w:7o3r9k{s.46,
0 0
50 100 150 200 250 0 0.05 0.1 0.15 0.2 [5] I. Cidon and M. Sidi. Distributed assignment
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