distributed dynamic channel access scheduling for ad hoc networks

J. Parallel Distrib. Comput. 63 (2003) 3–14

Distributed dynamic channel access scheduling for ad hoc networks$

Lichun Bao and J.J. Garcia-Luna-Aceves

School of Engineering BE399, University of California, Santa Cruz, CA 95064, USA

Received 17 October 2002

Abstract

Three types of collision-free channel access protocols for ad hoc networks are presented. These protocols are derived from a novel

approach to contention resolution that allows contending entities to elect one or multiple winners for channel access in any given

contention context (e.g., a time slot) in a distributed fashion. The only required information for each entity is the identifiers of its

neighbors one and two hops away in the wireless network. The new protocols are shown to be fair and capable of achieving maximal

utilization of the channel bandwidth. The delay and throughput characteristics of the contention resolution algorithms are analyzed,

and the performance of the three types of channel access protocols is studied by simulations and compared with that of optimal

static scheduling algorithms.

r 2002 Published by Elsevier Science (USA).

Keywords: Ad hoc network; Channel access scheduling; Medium access control (MAC); Distributed computing

1. Introduction

Channel access schemes for ad hoc networks can becontention-based or scheduled. The advantage ofcontention-based schemes is that they are relatively easyto deploy; this has resulted in many contention-basedschemes for ad hoc networks being proposed based oncarrier sense multiple access with collision avoidance(CSMA/CA), and the success of the IEEE 801.11(b)standard for wireless local area networks [8]. Collision-avoidance schemes are attractive for ad hoc networks,because they attempt to eliminate collisions of datapackets, which degrade network performance. However,collision-avoidance schemes cannot fully prevent colli-sions due to near–far phenomena, fading, and captureeffects on the channel [12,14]. In addition, it is difficultto provide quality of service or fairness with thesechannel access schemes. This points to the need forchannel access methods based on scheduling.

Scheduled access schemes prearrange or negotiate aset of timetables for individual nodes or links, such that

the transmissions from these nodes or on these links arecollision-free within the effective range of the transmis-sions on the time and frequency axes. TDMA, FDMA,CDMA, SDMA, and their combinations are widelydeployed in cellular systems [1,11]. However, thesesolutions require a central base station, and the peer-to-peer scheduling needed in ad hoc networks is muchharder to solve.

The quest for optimal solutions to channel accessscheduling in ad hoc networks (i.e., multihop packetradio networks) often results in NP-hard problems ingraph theory (such as k-colorability on nodes or edges)[9,10,21]. In some cases, however, the problems can besolved by reducing them to simpler ones for whichpolynomial algorithms are known to achieve suboptimalsolutions using randomized approaches or heuristicsbased on such graph attributes as the degree of thenodes.

Many solutions have been proposed combining bothrandom and scheduled access approaches [5,6,24].Specifically, a few time slot assignment algorithms werepresented by Cidon and Sidi [7], and Pond and Li [19]using a dedicated control segment of the channel toresolve conflicts and broadcast channel reservations.However, the complex resolution of neighbor schedulesvia message exchanges in the channel consume aconsiderable portion of the scarce bandwidth and

$This work was supported by the Defense Advanced Research

Projects Agency (DARPA) under Grant No. F30602-97-2-0338 and by

the US Air Force/OSR under Grant No. F49620-00-1-0330.

E-mail addresses: [email protected] (L. Bao), [email protected]

(J.J. Garcia-Luna-Aceves).

0743-7315/03/$ - see front matter r 2002 Published by Elsevier Science (USA).

doi:10.1016/S0743-7315(02)00039-4

introduce long delays to obtain the correct schedule.Several channel scheduling and reservation protocolshave been proposed based on in-band signaling (phaseddialogs or RTS/CTS handshakes) before transmissions[25,27] to secure a temporary schedule for channelaccess. Because of the in-band signaling required, theseprotocols suffer from unused time slots when signalscollide because of their randomness.

Topology-transparent scheduling methods have beenproposed by Chlamtac and others [4,17] to avoid theneed for the in-band signaling of the above ‘‘topology-dependent’’ schemes. The basic idea of the topology-transparent scheduling approach is for a node totransmit in a number of time slots in each time frame.The times (slots) when node i transmits in a framecorresponds to a unique code, such that for any givenneighbor k of i; node i has at least one transmission slotduring which k and none of k’s own neighbors aretransmitting. 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-indepen-dent scheduling approaches described to date is that thesender is unable to know which neighbor(s) cancorrectly receive the packet it sends in a particular slot.This implies that the sender has to send its packet in thevarious slots in a frame, making the frame length(number of slots) much larger than the number of nodesin a two-hop neighborhood and dependent on thenetwork size, which is less scalable.

A unified framework for static channel assignment intime, frequency, and code division multiple access calledUxDMA was described by Ramanathan [20] to computea k-coloring of an arbitrary graph within polynomialsteps. The heuristic consists of first coloring nodes oredges randomly or sequentially according to vertexdegrees, and then conclude with a minimum number ofcolors, such that a set of constraints on the nodes orlinks are satisfied. The constraints on the coloringpattern include commonly known interferences, such asdirect and hidden-terminal interferences [26]. A limita-tion of this and similar schemes based on k-colorings ofgraphs is that, inherently, topology information needs tobe collected and frequent schedule broadcasts have to becarried out in dynamic networks, which would consumea significant portion of the scarce wireless bandwidth.

To avoid the repetitious schedule adjustments orredundant multiple transmissions of data packets due tothe volatility of wireless network topologies, we propose

that local topology be an integral ingredient of thechannel-access scheduling for each node of an ad hocnetwork.

Section 2 shows that the scheduling problems of node-activation and link-activation channel access can beapproached as a 2-coloring problem on graphs. A newcontention resolution algorithm called neighborhood-aware contention resolution (NCR) is introduced, whichworks by each node maintaining the identifiers of itsone- and two-hop neighbors, and making a new node orlink activation decision during each contention context(e.g., each time slot). Section 3 addresses the perfor-mance of NCR, its fairness, and its proper operation.Section 4 describes three channel access protocols basedon node-activation and link activation-schemes, derivedfrom NCR. Section 5 addresses the performance of theseprotocols by means of simulation experiments. Section 6concludes the paper.

2. Neighborhood-aware contention resolution

In multihop wireless networks, a single radio channelis spatially reused in different parts of the network, andcontending entities are nodes or links (edges) betweennodes. Collisions happen in three cases, as illustrated inFig. 1 [23]. Nodes can avoid such collisions usingtopology information within two hops.

We assume that every entity knows the set of itscontenders through some appropriate means, such as aseparate neighbor protocol, which is beyond the scopeof this paper. We also assume that each contentioncontext is identifiable, which is reasonable in networksbased on time-division multiple access or frequencyhopping.

We formulate the problem of contention resolutionwith neighborhood information as follows:

Given a set of contenders, Mi; against an entity i incontention context t; how should the precedence of i

be arbitrated in the set Mi,fig; such that everycontender yields to i whenever i decides that it is thewinner for the common channel?

To describe our solution to the problem, we assumethat the primary operands in mathematical formulas areof fixed length, and the sign ‘"’ represents theconcatenation operation on its operands. We alsodenote by MDðxÞ the message digest function that

(a) Hidden Terminal Problem (c) Self Interference(b) Direct Interference

Fig. 1. Examples of collision types.

L. Bao, J.J. Garcia-Luna-Aceves / J. Parallel Distrib. Comput. 63 (2003) 3–144

produces a uniformly distributed random number usingbyte-string x as the seed [22]. Based on function MDðxÞ;we define the priority of node i in a contention context t

as:

pti ¼ MDði"tÞ"i: ð1ÞThe algorithm for neighbor-aware contention resolu-

tion (NCR) is the following:NCR (entity i; contention context t):

1. Compute a priority ptk for each member k in set

Mi,fig:pt

k ¼ MDðk"tÞ"k; kAMi,fig: ð2Þ

2. Exit if Eq. (3) is not true.

8jAMi; pti4pt

j : ð3Þ

3. Have entity i access the common channel during thecontention context t:

Note that, while the MD function can generate thesame number on different inputs, each priority numberis unique, because pt

k; kAMi,fig is appended with k to

the corresponding message digest.Describing NCR in terms of a two-coloring problem,

an entity i gives itself color r if its has the highest priorityamongst its contenders in a contention context; other-wise, i colors itself with b: Nodes in color r are active inthe corresponding contention context. The color r isextensively used in each contention situation to themaximal degree without collisions.

The description of NCR provided thus far assumesthat each node requires the same amount of bandwidth.In practice, traffic and bandwidth demands fromdifferent nodes can vary. NCR can be easily improvedto accommodate variable bandwidth requirements byassigning multiple pseudo-identities to each entity.

An entity i may claim piiZ0 pseudo-identities, andeach pseudo-identity of i is defined as the concatenationof i with a number chosen from f1; y; piig: Therefore,the lth pseudo-identity is denoted as i"l: To accountfor stability of bandwidth requests, an upper bound canbe placed on the number of pseudo-identities availableto each entity, so as to allow reasonable granularity ofbandwidth allocation. Especially if pii ¼ 0; the entity i

cannot access the channel.Consequently, NCR can be modified as follows to

support multiple identities for each node:NCR-MI (entity i; contention context t):

1. Compute the priority numbers on the pseudo-identities of each member kAMi,fig; the lthpriority number of which is denoted as pt

k"l :

ptk"l ¼ MDðk"l"tÞ"k"l;

kAMi,fig; 1rlrpikð4Þ


8jAMi; (m; pti"m4pt

j"n;

1omopii; 1onopij:ð5Þ

3. Have entity i access the common channel during thecontention context t:

The portion of the common channel available to anentity i is

qi ¼piiP

kAMi,fig pik: ð6Þ

Note that NCR is the special case of NCR-MI withthe restriction 8kAMi,fig; pik ¼ 1: For simplicity, therest of this paper addresses only NCR.

3. Behavior of NCR

3.1. Correctness

Once the nodes in an ad hoc network have consistentknowledge of their two-hop neighborhood, NCRachieves the following three goals:

1. Avoid unintentional collisions from simultaneoustransmissions.

2. Fair sharing of network bandwidth for each node,so as to avoid the resource starvation problempresent in contention-based schemes.

3. Permit constant bandwidth utilization, even underheavy traffic load, so as to keep network datatransmission live at all times.

Because it is assumed that contenders have mutualknowledge and t is synchronized, the order of con-tenders based on the priority numbers is consistent atevery participant. When entity i has the highest priorityin the set Mi,fig; each kAMi respects the right of i; andallows i to access the common channel collision-free.

NCR basically generates a permutation of thecontending members, the order of which is decided bythe priorities of all participants. Since the priority is apseudo-random number generated from a seed thatchanges from time to time, the permutation alsobecomes random such that i has certain probability towin in each contention context, commensurate to itscontention level:

qi ¼1

jMi,figj: ð7Þ

An ad hoc network has a finite number of entities;therefore, NCR always produces one or multiplewinners for each contention context because NCR givesa unique priority number to each entity and multiple

L. Bao, J.J. Garcia-Luna-Aceves / J. Parallel Distrib. Comput. 63 (2003) 3–14 5

locally maximal priorities exist in the network. Accord-ingly, NCR allows live utilization of the commonchannel.

3.2. Delay and throughput analysis

When the arrival rate of the queuing system in achannel access scheduling system is below the servicerate, we can analyze the delay properties of the queuingsystem using a steady-state M/G/1 queue with servervacations, where the single server is an entity (node orlink).

We assume that data packets arrive at an entity i

according to a Poisson process with rate li and areserved by first-come-first-serve (FIFO) strategy. Server i

takes a vacation that lasts for V of length one time slotwhen there is no data packet in the queue; otherwise, i

looks for the next available time slot to transmit the firstpacket waiting in the queue. Because of the randomnessin NCR and NCR-MI, the number of time slots thatan entity must wait before activation is a geometricdistribution with parameter qi; which is the probabilityof the entity i winning a contention context (Eqs. (7) and(6)). Therefore, the probability of the service time Xi for

a data packet follows PfXi ¼ kg ¼ ð1� qiÞk�1qi:

The mean and second moments of random variable Xi

are:

Xi ¼1

q; X 2

i ¼ 2� q

q2:

And the mean and second moments of random

variable V (a constant) are %V ¼ V2 ¼ 1:So that the extended Pollaczek-Kinchin formula [3]

for M/G/1 system with vacations readily yields theaverage waiting time in the queue at entity i:

Wi ¼lX 2

i

2ð1� lXiÞþ V2

2 %V

Adding the average service time to the queuing delay,we obtain the overall delay in the system:

Ti ¼ Wi þ Xi ¼2þ qi � 2l2ðqi � lÞ : ð8Þ

When li ¼ 0; the expected latency of the systemprocess is at least:

Ti ¼ 1=qi þ 0:5: ð9Þ

Depending on whether the entity is a node or a link,the probabilities of the entity winning a contentioncontext are different, so are the delays of data packetsgoing through that entity. Fig. 2 shows the averagedelay of a packet in the queuing system at an entity i

with different channel access probability qi and arrivalrate li: To keep the queuing system in a steady state, it isnecessary that lioqi:

Because of the collision freedom of NCR, thecommon channel can serve certain load up to themaximum channel capacity. That is, the throughputover the common channel is the summation of arrivalrates at all competing entities as long as the queuingsystem at each entity remains in equilibrium on thearrival and departure events. Accordingly, the systemthroughput S from each and every entity k thatcompetes for the common channel is:

S ¼X

k

minðlk; qkÞ; ð10Þ

where qk is the probability that k may be activated, andlk is the data packet arrival rate at k:

4. Channel access protocols

4.1. Topology assumptions

For simplicity, we model the topology of a packetradio network as an undirected graph G ¼ ðV ;EÞ;where V is the set of nodes, each mounted with anomni-directional radio transceiver and assigned aunique identifier (ID), and EDV V is the set of linksbetween nodes. Unless specified otherwise, a linkðu; vÞAE indicates node u and v are within thetransmission range for each other, so that they canexchange packets via the common channel, in whichcase the two nodes are called one-hop neighbors. Twodistinct nodes that are not one-hop neighbors but sharea common one-hop neighbor are called two-hop

neighbors to each other. The set of one-hop and two-

hop neighbors of node i is denoted by N1i and N2

i ;respectively.

Contentions at a node i should be resolved on thesubgraph covered within two hops from the node i; i.e.,

N1i ,N2

i ; depending on node or link activation schemes

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

60

q=0.05

q=0.10

q=0.20q=0.50

Arrival Rate λ (Packet/Time Slot)

Del

ay T

(T

ime

Slo

ts)

Average Packet Delays in the System

Fig. 2. Average system delay of packets.


and signal coding methods used in the specific channelaccess protocols.

The following channel access protocols are describedassuming that nodes already know their neighborhood,i.e., that they have exchanged the necessary informationabout their two-hop neighborhood. In addition, theseprotocols are based on a distributed time divisionmultiplexing scheme, which makes channel accessdecisions based on the time slot boundaries. However,we do not address the time synchronization issue.

4.2. Node activation protocol

We first describe a node-activation multiple access(NAMA) protocol, in which the contender set of node i

is the set of one-hop and two-hop neighbors, i.e., Mi ¼N1

i ,N2i : For each time slot t; NAMA decides the

activation of node i based on following algorithm:NAMA (node i, time slot t):

1. Compute the priority ptk of every node k in the set

Mi,fig using Eq. (2).2. Exit if Eq. (3) does not hold for node i:3. Have node i access the common channel during

time slot t:

NAMA is suitable for broadcast and multicastservices in ad hoc networks, where the receivers of apacket transmission include all or some of the transmit-ter one-hop neighbors. This is because each activatednode has the highest priority among the two-hopneighborhood of the node, and is able to deliver apacket to all its one-hop neighbors without interferencefrom its two-hop neighbor.

4.3. Link activation protocol

The link activation multiple access (LAMA) protocolis a time-slotted code division medium access schemeusing direct sequence spread spectrum (DSSS), togetherwith NCR.

In DSSS, code assignment can be based on atransmitter-oriented, a receiver-oriented or a per-linkoriented coding scheme [13,16,18]. In LAMA, we opt fora receiver-oriented code assignment, which is suitablefor unicasting using a link-activation scheme. Althoughmany collision resolution protocols have relied on codeassignment algorithms to eliminate packet collisions[2,15]. In contrast, the code assignment for LAMA israndom and does not consider contention resolution.Instead, the contentions for transmission on the code ofthe intended receiver are resolved by additional compu-tations using NCR.

We assume that a pool of well-chosen quasi-ortho-gonal pseudo-noise codes, the set of which is denoted as

Cpn ¼ fckg; are available for each node to choose from,

where k ¼ 0; y; jCpnj � 1: A receiver i is assigned a

pseudo-noise code ci from Cpn by the following hashing

function, which utilizes the message digest function usedin Eq. (1):

ci ¼ ck; k ¼ MDði"tÞmodjCpnj: ð11Þ

Because we have only a limited number of pseudo-noise codes to assign, it is possible for multiple nodes toshare the same code. If we denote the set of i’s one-hop

neighbors assigned with code c as n1i;c; our goal in

LAMA is to decide whether node i can activate a link on

a code c and send a packet to one of the receivers in n1i;c

during time slot t: Therefore, the set of contenders tonode i includes the one-hop neighbors of i and the one-

hop neighbors of nodes in the set n1i;c excluding node i

itself, as shown in the following equation:

Mi ¼ N1i ,

[kAn1

i;c

N1k

0@

1A� fig: ð12Þ

The resulting link activation algorithm is the follow-ing:

LAMA (node i, time slot t, code c):

1. Compute the priority ptk of every node kAMi,fig

using Eq. (2).2. If Eq. (3) holds, have node i activate link ði; jÞ; jAn1

i;c

during time slot t:

LAMA ensures that the transmissions on a given codein any time slot are always collision-free at the receivers.Because multiple receivers may be waiting on the code,the transmitter can choose to deliver multiple packets ormulticast packets to the receiving neighbors.

Fig. 3 exemplifies a contention situation at node i

during time slot t: The topology is an undirected graph.The number beside each node represents the currentpriority of the node. Node j and k happen to have thesame code x: To determine if node i can activate linkson code x; we compare the priorities of the nodesaccording to LAMA. Node i has the highest priority

e

f

g

i

a

b

c

d

23

5

8

1

21

19

11

14

6

20

j

kx

x

Non-contending LinkContending LinkActive Link

Fig. 3. An Example of Contending Resolution.


within one-hop neighbors, and higher priority than j

and k as well as their one-hop neighbors. Therefore, i

can activate either ði; jÞ or ði; kÞ in the current time slot t;depending on back-logged data flows at i: In addition,node e may activate link ðe; dÞ if d is assigned a codeother than code x:

4.4. Pairwise link activation protocol

The pairwise-link activation multiple access (PAMA)protocol is based on link activation, using a time-slottedcode-division multiplexing scheme with DSSS. Thedifference between PAMA and LAMA is that a codeis assigned for a given transmitter–receiver pair, andcomputed every time slot. Unlike NAMA and LAMA,in which the contending entities are nodes, links are theentities competing for channel access in PAMA. Linksare directed in PAMA to signify transmission directions.Each undirected physical link is represented by twodirected links in the opposite directions.

PAMA assumes a pool of quasi-orthogonal pseudo-

noise codes, Cpn ¼ fckg: A pseudo-noise code cu from

Cpn is assigned to a directional link ðu; vÞ at time slot t

according to the following hashing function:

cðu;vÞ ¼ ck; k ¼ MDðu"tÞmodjCpnj: ð13Þ

Note that Eq. (13) does not involve v in the codeassignment. This is because of two reasons: (a) a nodecan activate only one link at a time, and (b) other nodesdo not have to know both u and v to decide the codeassignment of link ðu; vÞ:

PAMA decides whether a directed link ðu; vÞ can beactivated for unicast packet transmission by node u intime slot t using the two-hop neighbor information. Theset of contenders to link ðu; vÞ are the incident links of u

and v excluding ðu; vÞ itself, i.e.,Mðu;vÞ ¼ fðx; yÞjðx; yÞAE;xAfu; vgg,

fðx; yÞjðx; yÞAE; yAfu; vgg � fðu; vÞg:

The resulting link activation algorithm is the follow-ing:

PAMA (link ðu; vÞ; time slot t):

1. Compute the priority ptðx;yÞ of every link ðx; yÞ

belonging to Mðu;vÞ,fðu; vÞg using (14):

ptðx;yÞ ¼ MDðx"y"tÞ: ð14Þ


8ðx; yÞAMðu;vÞ; ptðu;vÞ4pt

ðx;yÞ: ð15Þ

3. Compute the priorities of every incident (incomingand outgoing) link of u’s one-hop neighbors using(14). Introduce set Lu to be the subset of incominglinks of u’s one-hop neighbors, each element of

which has the highest priority among the incidentlinks of the corresponding one-hop neighbor.That is

Lu ¼fðx; yÞjyAN1u ; yav; andxAN1

y ; xau;

and8zAN1y ; pt

ðx;yÞ4ptðz;yÞandpt

ðx;yÞ4ptðy;zÞg: ð16Þ

4. For each link ðx; yÞALu; compute the code assign-ment cx as well as cu using (13). If condition cu ¼ cx

holds for link ðx; yÞ; then exit if(a) xAN1

u and link ðx; yÞ has the highest priority

among the incident links of node x;(b) xeN1

u :5. Have node u activate link ðu; vÞ during time slot t:

The first two steps in PAMA determine the eligibilityof link ðu; vÞ for activation, while steps 3 and 4 avoidpossible hidden terminal conflicts on u’s one-hopneighbors. Step 3 chooses the candidate incoming linkof each one-hop neighbor for activation, and then step 4tries to avoid interference to u’s one-hop neighbors iflink ðu; vÞ is ever activated. The transmitter is the onethat tries to avoid collisions on its one-hop neighbors.Two conditions are considered in step 4. Case 4a occurswhen the end points of the active incoming link are bothone-hop neighbors of u; such that u has completeknowledge about their contention situation. Case 4boccurs when u knows only a partial contention situationof the active incoming link, such that u gives up ðu; vÞactivation if only the active incoming link has the samecode assignment.

Fig. 4 shows a sample network, where the numbernext to each link is the priority of that link, and thenumber beside each node is the code assignment of thatnode. Link ða; bÞ and ðu; vÞ (indicated by solid lines) areboth candidates for activation on code 5 according tostep 2. However, step 4 deactivates u to avoid a collisionat b by u and a:

5. Performance Evaluation

5.1. Expected performance differences

In NAMA, contending members are nodes within twohops. Therefore, the average number of contending

a

bv

u

5

5

129

12

5

3 9 91

38

Fig. 4. Collision avoidance in PAMA.


nodes in each time slot is

jN1i ,N2

i j

In LAMA, contentions happen on each code. When anode i tries to transmit on a code to one of its neighbors,contention occurs from both i’s one-hop neighbors andthe one-hop neighbors of the receivers possessing thecode. Hence, the average number of contenders to i on acode c is

N1i ,

[jAn1

i;c

N1j

0@

1A

��

�� 1

according to Eq. (12).PAMA is more sensitive to neighbor connections than

the other two protocols because two-hop neighbors aswell as links between two-hop neighbors become thecontention sources. The contenders of a link in PAMAare about twice as many as that of LAMA, because ofthe directional treatment of links in PAMA.

Above all, the density of packet radios placed in an adhoc network and the transmission range of the radiosdetermine contention levels in these protocols. Supposethat the network nodes are uniformly distributed on aninfinite plane with density r; and all nodes have the sameeffective transmission range r: A node in NAMA has

approximately 4rpr2 � 1 contending nodes with regardto two-hop neighbors. In LAMA, a node would have

around 2rpr2 � 1 contending nodes for activating a link,considering the two endpoints of the link, and assumingone-hop neighbors of the endpoints are always assigneddistinctive codes. While in PAMA, the number of

contending links of each link activation is 4rpr2 � 2;because of the directional treatment of links.

If we examine the number of active links when a nodemay transmit packet in the current time slot, NAMAcan activate all of its incident links, and LAMA canactivate a subset of its incident links, while PAMA canactivate a single incident link at all times. In the case ofunicasting, PAMA sustains the highest throughput,because of a better spatial reuse of the channel, asshown by the results of simulation experiments de-scribed subsequently.

To better understand the performance of dynamicscheduling protocols, we compare them with the optimalstatic scheduling algorithm UxDMA that uses globaltopology information [20].

The unified framework UxDMA defines a parametricalgorithm to derive a coloring on a graph according tothe network topology and the type of entities. Thenumber of colors used on the graph indicates theefficiency of the algorithm. In a time division multipleaccess scheme, the number of colors utilized determinesthe length of a time frame, during which every entity isactivated once in a time slots of the time frame.

A set of atomic constraints, which serves as input tothe UxDMA algorithm, enumerates all kinds of nodeand link relations that may result in collisions if therelated entities are assigned the same color and activatedat the same time during channel access. Accordingly, weselect an appropriate subset of the constraints for eachof our scheduling protocols, as shown in Table 1,corresponding to UxDMA for NAMA, LAMA andPAMA, respectively.

Fig. 5 illustrates the prohibited schemes of node andlink activations as referenced by UxDMA for NAMA,PAMA and LAMA, where solid dots and thick linesmean simultaneous node and link activations, respec-tively, thin lines indicate interferences. However, be-cause both LAMA and PAMA use code-division

channel access, constraint E1tr is allowed when the

transmission codes are different for node a and c inPAMA and reception codes are different for node b andd in LAMA.

An optimal ordering, progressive minimum neighborsfirst (PMNF) heuristic, has been applied in each computa-tion of the colorings on the graphs in UxDMA, so that thecolorings ‘‘perform quite close to optimum’’ [20].

5.2. Simulation results

We simulate NAMA, LAMA, PAMA and thecorresponding UxDMA algorithms in static topologies.The performance of the protocols are studied in twoscenarios: fully connected networks with differentnumbers of nodes, and multihop networks with differentradio transmission ranges. The packet arrival anddeparture events are modeled as M/G/1 queuing systemswith vacations. The delay of packets at each node andthe throughput of the network are collected in eachsimulation.

a

cb

aa

b

c

ab

ca

b

c

a

c

b

d

b

Fig. 5. Constraints used by UxDMA for NAMA, LAMA and PAMA.

Table 1

Constraint Sets Corresponding to NAMA, LAMA and PAMA

Protocol Type of Entities Constraint Set

UxDMA-NAMA Node fV 0tr;V1

ttgUxDMA-LAMA Link fE0

rr;E0tr;E1

trgUxDMA-PAMA Link fE0

rr;E0tt;E0

tr;E1trg


The simulations are guided by the following para-meters and behaviors:

* The signal propagation in the channel follows thefree-space model and the effective range of radio isdetermined by the power level of the radio. All radioshave the same transmission range.

* The bandwidth available for a radio transmission is2Mbps.

* A time unit in the simulation equals one time slot. Atime slot lasts 4.5ms including the guard time, whichis enough to transmit a 1124-byte packet.

* Each node has an unlimited buffer for data packets.* In LAMA and PAMA, thirty pseudo-noise codes are

available for code assignments, i.e., jCpnj ¼ 30:* All nodes have the same packet arrival rate li in each

simulation. Unless otherwise specified, the destina-tions of the generated packets are evenly distributedon all outgoing links.

* Packets are served in first-in first-out (FIFO) order.* The duration of the simulation is 100,000 time slots

(equal to 450 se), long enough to compute the metricsof interests.

5.2.1. Fully connected scenario

In the fully connected scenario, simulations werecarried out in four configurations (2-, 5-, 10-, 20-nodenetworks) to manifest the effects of different contention

levels. Fig. 6 shows the logarithmic delay values underdifferent loads in the four network configurations aswell as two analytical curves derived from Eq. (8) withthe values of q1 for NAMA and LAMA, and the valuesof q2 for PAMA. All protocols appear to fit well with theanalytical curves. PAMA shows higher delays in thesame situations. This is because the contention sourcesare different in PAMA than in NAMA and LAMA. InPAMA, contending entities are links, which are muchmore than the number of nodes. The value of qi forPAMA in the fully connected scenario is:

qi ¼1

4 � jV j � 6: ð17Þ

For NAMA and LAMA, qi in the same scenarioequals:

qi ¼1

jV j: ð18Þ

Taking the 10-node network as an example, the value

of qi for each link is 1410�6

¼ 0:029 in PAMA, which

would result in a delay of at least 36.5 time slots byEq. (9). For NAMA and LAMA, nodes are thecontending entities, and the values of qi for each node

are both around 1jV j ¼ 1

10=0.1, which leads to delays of at

least 10.5 time slots.In every simulation setting, UxDMA performs better

than its counter protocol, NAMA, LAMA, and

0 0.1 0.2 0.3 0.4 0.5

101

Arrival Rate λ i (Packet/Slot)

Del

ay T

i (T

ime

Slo

t)

q1=0.5, q

2=0.5, 2 Nodes

NAMALAMAPAMAUxDMA-NAMAUxDMA-LAMAUxDMA-PAMAAnalysis 1Analysis 2

0 0.1 0.2 0.3

101


Del

ay T

i (T

ime

Slo

t)

q1=0.2, q

2=0.07, 5 Nodes

0 0.1 0.2 0.3

101

102

Arrival Rate λi (Packet/Slot)

Del

ay T

i (T

ime

Slo

t)

q1=0.1, q2=0.03, 10 Nodes

0 0.1 0.2 0.3 0.410

1

102

Arrival Rate λi (Packet/Slot)

Del

ay T

i (T

ime

Slo

t)

q1=0.05, q2=0.0135, 20 Nodes

Fig. 6. Average packet delays in fully-connected networks.


especially PAMA. This is because UxDMA can alwaysproduce a more compact schedule where a dynamicscheduling protocol may give up due to local prioritycomparisons. However, considering that UxDMA is acentralized algorithm with global topology information,NAMA, LAMA and PAMA trade off a little perfor-mance for much more efficiency.

Fig. 7 shows the linear throughput of the threeprotocols under different loads for each node. Aspredicted in Eq. (10), all protocols show linear systemthroughput under the different sustainable loads and flatthroughput when the network load exceeds the availablechannel capacity, which is advantageous over any otherrandomized multiple access protocols that experiencegreat losses in throughput when the network load goesbeyond a certain threshold. The analytical curves ineach subplot fit well the simulation results, obtained forrespective protocols.

5.2.2. Multihop network scenario:

Figs. 8 and 9 show the logarithmic delays and linearthroughput of the three protocols in multihop net-works, corresponding to different loads. The networksare generated by randomly placing 100 nodes within

an area of 1000 1000 m2: To simulate an infinite planethat has constant node placement density, the opposite

sides of the square are seamed together, which visuallyturns the square area into a torus. By setting thetransmission ranges of the transceiver on each node to100, 200, 300 and 400m, respectively, we also change thetopology and contention levels in each case.

Fig. 8 shows that LAMA provides better channelreuse within two hops of each node that NAMA byapplying code division multiplexing. PAMA produceshigher delays than the other two protocols whennetwork load is low. This is because of the same reasonsdiscussed for the fully connected scenario. However,PAMA appears to have slower increases in delay whenthe network load increases, which is a consequence ofthe higher channel reuse of the common channel by purelink-oriented scheduling.

Because of the dramatic differences among thethroughput of NAMA, LAMA and PAMA, Fig. 9 onlyshows the maximum throughput available in eachindividual protocol, instead of showing the gradualthroughput variations in accordance with the loadchanges. Next to the bar of each dynamic schedulingprotocol, the throughput of the corresponding UxDMAalgorithm is also provided. Except for the firstsimulation when the transmission range is 100m,UxDMA performs better than NCR. This is becausenetwork connection densities show more variety atlower transmission ranges. While UxDMA schedules the

0 0.2 0.4 0.60

0.2

0.4

0.6

0.8

1


Thr

ough

put S

(P

acke

t/Slo

t)

q1=0.5, q2=0.5, 2 Nodes

NAMALAMAPAMAUxDMA-NAMAUxDMA-LAMAUxDMA-PAMAAnalysis 1Analysis 2

0 0.1 0.2 0.3 0.40

0.5

1

1.5

2


Thr

ough

put S

(P

acke

t/Slo

t)

q1=0.2, q2=0.07, 5 Nodes

0 0.1 0.2 0.3 0.40

1

2

3

4


Thr

ough

put S

(P

acke

t/Slo

t)

q1=0.1, q2=0.03, 10 Nodes

0 0.1 0.2 0.3 0.40

2

4

6

8


Thr

ough

put S

(P

acke

t/Slo

t)

q1=0.05, q2=0.0135, 20 Nodes

Fig. 7. Packet throughput of fully-connected networks.


network channel access according to the worst densepart of the network, NCR computes the channel accessschedule according to local topology only.

Although not shown in the figure, the throughput ofthese protocols still demonstrates linear increases alongwith load increases, and levels off when the load values

0 0.05 0.1

101

102


Del

ay T

i (T

ime

Slo

t)

Transmission Range=100

NAMALAMAPAMAUxDMA-NAMAUxDMA-LAMAUxDMA-PAMA

0 0.05 0.1 0.1510

1

102


Del

ay T

i (T

ime

Slo

t)


0 0.05 0.1 0.15

102


Del

ay T

i (T

ime

Slo

t)


0 0.02 0.04 0.06 0.08 0.1

102


Del

ay T

i (T

ime

Slo

t)


Fig. 8. Average packet delays in multihop networks.

1 2 30

10

20

30

40

NA

MA

UxD

MA

LAM

A

UxD

MA

PA

MA

UxD

MA

Thr

ough

put S

(P

acke

t/Slo

t)


1 2 30

10

20

30

40

NA

MA

UxD

MA

LAM

A

UxD

MA

PA

MA

UxD

MA

Thr

ough

put S

(P

acke

t/Slo

t)


1 2 30

10

20

30

40

NA

MA

UxD

MA

LAM

A

UxD

MA

PA

MA U

xDM

A

Thr

ough

put S

(P

acke

t/Slo

t)


1 2 30

10

20

30

40

NA

MA

UxD

MA

LAM

AU

xDM

A

PA

MA

UxD

MA

Thr

ough

put S

(P

acke

t/Slo

t)


Fig. 9. Packet throughput of multihop networks.


approximate or exceed the probabilities that a node andlink may be activated, at which point delays increasedrastically, as shown in Fig. 8. System throughput is anindication of the average channel reuse ratio in multihopwireless networks. PAMA achieves higher loads thanthe other two protocols.

6. Conclusion

We have introduced a new approach to contentionresolution that eliminates much of the complexity ofprior collision-free scheduling approaches by usingonly two-hop neighborhood information to dynamicallydetermine which node is allowed to transmit ineach collision-resolution context. Based on this ap-proach, protocols were introduced for both node-activation and link-activation channel access schedulingin packet radio networks. The advantages of theprotocols are that (a) they do not need the contentionphases or schedule broadcasts adopted by manyother channel access scheduling algorithms; and (b)they only need the local topology information withintwo hops, which can be obtained by the propagation ofone-hop neighbor information from each node to itsneighbors. This contrasts with other schedule broad-casting algorithms that require complete networktopology for collision-free channel access scheduling.NAMA is suitable for broadcasting and multicasting,while LAMA and PAMA are suitable for unicastingusing spread spectrum techniques. .

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and its Applications, Prentice–Hall, Englewood Cliffs, NJ,

1985.


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