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8/3/2019 Performance Model of Flooding in OLSR

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Performance Model of Flooding in OLSR

Andres MedinaDept. of Electrical and Computer Eng.

University of Delaware

[email protected]

Stephan BohacekDept. of Electrical and Computer Eng.

University of Delaware

[email protected]

ABSTRACT

OLSR is one of the most well developed routing protocolsfor MANETs. OLSR as a link state routing protocol relieson its ooding mechanism to disseminate topology informa-tion to all nodes in the network. However, the performanceof the ooding algorithm is poorly understood. In this pa-per models of key performance metrics of this algorithm arepresented. Specically, it describes a mo del for the controloverhead generated by the ooding algorithm and a model

of eciency in terms of network coverage. The models arevalidated against simulations. The results presented in thispaper have signicant implications for the standardizationprocess.

Categories and Subject Descriptors

C.2.2 [Computer-Communication Networks]: Network Pro-tocolsRouting protocols

General Terms

algorithms, design, performance

KeywordsMANETs, routing, ooding, OLSR, model, performance

The research reported in this document/presentation wasperformed in connection with contract DAAD19-01-C-0062with the U.S. Army Research Laboratory. The views andconclusions contained in this document/presentation arethose of the authors and should not be interpreted as pre-senting the ocial policies or position, either expressed orimplied, of the U.S. Army Research Laboratory of the U.S.Government unless so designated by other authorized docu-ments.Citation of manufacturers or trade names does not consti-tute an ocial endorsement or approval of the use thereof.The U.S. Government is authorized to reproduce and dis-tribute reprints for Government purposes notwithstanding

any copyright notation hereon.

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.PE-WASUN10, October 1718, 2010, Bodrum, Turkey.Copyright 2010 ACM 978-1-4503-0276-0/10/10 ...$5.00.

1. INTRODUCTIONThe Optimized Link State Routing protocol (OLSR) [1]

for mobile ad hoc networks has been widely implementedand studied. It has been chosen by the IETF MANETCharter as the proactive routing protocol that will continuethe standardization process. There are implementations ofOLSR for almost all platforms including Windows, MAC,Linux, Windows Mobile, Android, etc. A variation of OLSRhas also been chosen by the 802.11s IEEE TG [2] as the

proactive protocol of choice. However, its performance isnot completely understood.

OLSR stands for optimized link state routing protocol.The optimization refers to three methods present in theprotocol to decrease the control overhead generated by thetopology dissemination mechanism. All three methods relyon a subset of neighbors selected by each node known as theMultipoint Relay (MPR) set of a node, which are chosen fol-lowing the algorithm in [1]. Although dierent algorithmsmay be used, the MPR subset must ensure that all nodesreachable in two hops are still reachable through MPRs.

The rst optimization method shortens the length of topol-ogy control packets. Contrary to other link state protocolslike OSPF [3], where nodes advertise all of their neighborsto all nodes in the network, nodes in OLSR advertise only

the subset of neighbors that have selected them as MPRs.The eect of this optimization is that all nodes will maintainonly partial topology information. However, if the MPR setis up-to-date, then this partial topology information is su-cient to determine the shortest paths. The impact of partialtopology information in realistic scenario where the MPRsets are not up-to-date is unknown. However, this impact isnot the focus of this paper.

The second optimization supported by OLSR reduces con-trol overhead by limiting the number of nodes that generatetopology control packets. Only nodes that are MPRs of an-other node generate such packets. An exception to this ruleare nodes that were recently selected as MPRs, but are nolonger MPRs. These nodes continue to send empty topol-ogy control packets for the validity time of the last topology

information packet they sent as MPRs. Thus, in mobile sce-narios and lossy scenarios where the MPR set changes fre-quently, a signicant fraction of nodes either are or recentlywere MPRs, and the impact of the optimization method islimited. In this paper, a model for the fraction of nodes thatgenerate a Topology Control (TC) packet is presented andvalidated. The model accounts for dierent node densities,node mobility, neighbor discovery methods, and dierentphysical radios.

The third method reduces control overhead by oodingtopology control packets only over MPR links. In [1] it is


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stated that only if a node receives a packet for the rsttime from an MPR selector it will forward it. However,some popular implementations of OLSR like OLSRD [4] dif-fer from the standard. In [4], nodes forward the packet if ithas received the message from an MPR selector, regardlessof whether it had previously received the message from anon-MPR selector. In this paper, we present a model of thefraction of nodes that retransmit a packet for both oodingmethods. The paper also describes a model of the fraction

of nodes covered by a ood. This metric shows how ecientis the ooding method to reach all nodes in the network.It is shown in the paper that there is a tradeo betweenthe amount of overhead generated and the level of coverageachieved by a ooding method.

Several eorts have been made to evaluate the perfor-mance of OLSR. In [5], a model for control overhead ispresented. However only orders of magnitude are given toestimate the overhead and no validation of the model is in-cluded. In [6] authors propose a simple model to estimatethe amount of control overhead used by OLSR and compareit to that of reactive protocols such as DSR. In [7] providesa very simple model of control overhead. In [8] MPR ood-ing is studied. They provide results of simple simulationsof the fraction of nodes that retransmit a packet and the

fraction of nodes covered by a ood. In [9] authors proposea model of control overhead in OLSR as a function of nodemobility, whoever this impact is restricted to the optionalfeature of OLSR to react to topology changes and also dis-regards neighbor discovery dynamics. All of these modelsneglect the dynamics of the neighbor discovery mechanismand thus disregards the impact of incorrect local topologyinformation has on ooding, which requires up-to-date lo-cal topology information. One complicating factor is that,as mentioned, several used implementations of OLSR (e.g.,OLSRD and QualNet) include signicant bugs. Thus, it issometimes unclear which version of OLSR is being modeled.Because of the accuracy of the models presented here, cross-validation detected the bugs, which are described in [10].

The rest of this paper is organized as follows. In section2, the neighbor discovery model is briey described withreferences to more detailed descriptions. Section 3 describesthe base overhead model. The components of this modelare developed in subsequent sections. Section 4 describes themodel of the fraction of nodes that generate topology controlpacket, and Section 5 the fraction of nodes that retransmittopology control packets. Section 5 also describes a modelfor the fraction of nodes covered in the propagation of a TCmessage. Section 6 compares the model to other models.Finally, Section 7 concludes the paper.

Because of page limitations, some parts of the model areonly briey described. However, complete details, includingMatlab functions and precomputed data are available online[11].

2. NEIGHBOR DISCOVERY MODELProactive routing protocols rely on a Neighbor Discovery

(ND) mechanism to estimate for which neighbors bidirec-tional communication is possible. ND utilizes past observa-tions from passive and active probing of neighbors. Thus,when nodes move fast as compared to the reaction speed ofND, the estimation of link states can become stale. Thisdegradation of the estimate of link state impacts the qual-ity of information in link state announcements as well asooding algorithms that rely on local topology information.

OLSR employs an ecient algorithm for ooding topologycontrol (TC) messages. OLSRs algorithm utilizes link statein two ways. First, a node will only accept TC messages thathave been transmitted over a link that ND has marked as asymmetric link. Second, the symmetric links of a node andthe symmetric links of the neighbors, are used to select aset of multipoint relays. As explained in more detail below,nodes will only forward TC messages that were transmittedby nodes that are MPR-selectors1 . Hence, if NDs estimate

of the set of symmetric neighbors is incorrect, the ooding ofTC messages can be signicantly impacted. Modeling thisimpact is a key contribution of this paper.

There are various methods to detect neighbor nodes. RFC3626 [1] species two neighbor discovery method that aredescribed next. The model described here is detailed in [12]and can be used to model a wide range of neighbor discoverymethods besides those dened in RFC 3626.

The rst method described in [12] is a generalization ofthe method presented in RFC 3626 is referred to as EventCounting (EC) ND. In this method, a link is declared to beup if U Hello messages are received over the link. Once thelink is up, the link remains up until D consecutive Hellos arelost. Nodes advertise which links are up in Hello messages.By utilizing this information, a node can determine whether

a link is bidirectional. A bidirectional link is declared to besymmetric. The algorithm described in RFC 3626 is equiv-alent to a specic case of this method where U = 1 andD = 3.

The second method described in RFC 3626 uses an ex-ponential moving average of a measure of link quality lq toestablish whether the link is up. We refer to this algorithmas Exponential Moving Average (EMA) ND. In this algo-rithm, a link is declared to be up when lq rst exceeds athreshold LQup. Once the link is up, the link status willchange to down only when lq drops below LQdown, where,of course, LQdown LQup. If a link quality measure is notdirectly available from the MAC layer, then RFC 3626 pro-poses a method based on the reception of Hello messagesvia

lq =

lq w + (1 w) , if received Hello

lq w; if Hello is missed;

where w is the weight of the exponential moving average. InRFC 3626, the values suggested are LQup = 0:8, LQdown =0:3, w = 0:5.

The dynamics of both ND algorithms can be representedby Markov chains that depend on the link loss probability.For example, in EC, the state of a link between node Aand nodes B is given by the tuple (uA, dA, sA, uB; dB; sB),where uA is the number of consecutive Hellos received bynode A. Once uA = U, it remains xed until dA = D, wheredA counts the number of Hellos missed. sA = 1 if nodeA believes that the link is symmetric. uB, dB, and sB aredened similarly, but for node B. Note that node As andnode Bs estimate of whether the link is symmetric are notsynchronized. Hence, it is possible that sA 6= sB.

The probability of moving from state (k; 0; 0; j; 0; 0) tostate (k + 1; 0; 0; j; 0; 0) is the probability of a successfultransmission of a Hello over the link. By ordering all the

1 A nodes MPRs are a set of nodes such that if the nodeand its MPRs broadcast a message, then all nodes withinthe 2-hop neighborhood will receive the message. If a nodehas been selected to be an MPR, then its MPR selectors isthe nodes that selected it to be an MPR. See RFC 3626 fordetails [1].


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C

BA

Figure 1: Trajectories of nodes B and C relative to A. NodeB was outside communication range (packet delivery prob.below 1%) when last change in trajectory took place. How-ever, this is not the case for node C.

possible values of (uA, dA, sA, uA; dA; sA), we can dene avector Xwhere Xi is the probability of b eing in the ith state.We can then determine the transmission probability matrixA (p), which depends on the transmission probability p. Let-ting Xi (t) be the probability of being in state i at time t,we have X(t + TH) = X(t) A (p (t)), where TH is the Helloperiod and p (t) is the transmission probability at time t.Thus, given a trajectory of transmission probabilities, p (t),one can compute the probability of the ND declaring the linkto be symmetric. [12] provides signicantly more details oncomputing link state probabilities.

Note that the probability of the link state estimate de-pends on the trajectory of the transmission probabilities.While this trajectory depends on the full trajectory of thenodes, in random waypoint mobility, it can be estimatedfrom the nodes locations and velocities. That is, given twonodes position and velocity at time t, the distance betweenthe nodes can be determined for time t 0 to t, whereneither of the nodes changed direction or speed during theinterval (t o; t). Assuming that the nodes were well outof communication range at time t 0, the probability ofthe link state can be accurately computed. However, if thenodes are within communication range at time t o, thenthe estimate of the link state is less accurate (See Figure 1).In the case of random waypoint mobility over a large region,

nodes change direction infrequent. However, over small re-gions, the nodes frequently change directions, resulting insome errors. However, for moderate sized regions, the es-timate of model quality is goo d. See [12] for details. Notethat the performance of ad hoc network is of little interestwhen the region is very small, e.g., when most nodes arewithin one hop.

3. OVERHEAD MODELOLSR allows the option of generating TC messages when

the topology has changed. In this case, the rate that TCmessages are generated depends on the node speed. How-ever, here we do not consider this option and assume thatTC messages are generated as a rate of TC. TC messages

announce topology information, and thus, the size of thesemessages depends on the number of detected neighbors.

With this notation, the overhead in packets generated byeach node is given by

OHpkts = TC fGenTC fRET N; (1)

where N is the number of nodes in the network, fGenTC isthe fraction of nodes that generate a TC packet, and fRETis the fraction of nodes that forwards a packet. Models offGenTC and fRET are key contributions of this paper andare given in Sections 4 and 5, respectively.

4. FRACTION OF NODES THAT GENER-

ATE TC MESSAGESIn OLSR, nodes that are MPRs of at least one neighbor

generate topology control packets. When a node receivesa Hello packet of its last MPR selector indicating it is nolonger an MPR, it will continue to send empty TC packetsto invalidate previously distributed topology information. Itcontinuous to generate empty TC messages for the validitytime of its last disseminated topology control packet, wherethe validity time is a user dened parameter. Thus, thefraction of nodes that generate topology control packets isgiven by

fGenTC = fMPR + fEmptyTC;

where fMPR is the fraction of nodes in the network that areMPRs and fEmptyTC is the fraction of nodes that generateempty TC packets. In this section, models for these twoquantities are presented. First, an idealized model is de-scribed. Then, a sub-model to account for imperfect neigh-bor discovery mechanism and channel losses is added.

4.1 Idealized Model

The two quantities fMPR and fEmptyTC are modeled us-ing an on/o process, where nodes goes from the state "se-lected as MPR by at least one node (MP R)" to the state"not selected as MPR (NoMPR)". Denote by FNoMPR (tjs; ; Lthe CDF of the time a node remains in state NoMPR whenthe average node speed is s, average number of neighbors is, and the length of one side of the simulated region is L(i.e., the simulated region is LL). Let tNoMPR (TE; s; ; L)and tMPR (TE; s; ; L) be the expected duration that a nodeis in the states NoMPR and MP R, respectively, where TEis the duration that a node continues to generate TC mes-sages when it is no longer an MPR. The expected time thata node sends empty TC packets is given by

tEmptyTC (TE; s; ; L) = (1 FNoMPR (TEjs; ; L)) TE+

FNoMPR (TEjs; ; L)ZTE0

1 FNoMPR

(tjs; ; L)

FNoMPR (TEjs; ; L) dt.

To see this, note that the rst term on the right accountsfor the duration of TE when a node is in state NoMPR forlonger than TE. The second term on the right accounts forthe duration in state NoMPR when the node is in the stateNoMPR for less than TE, where 1

FNoMPR(tjs;;L)FNoMPR(TEjs;;L)

is

the probability of being in state NoMPR for no more thant, conditioned on the duration being no more than TE.

Thus,

fEmptyTC (TE;s; ; L)

=tEmptyTC (TE; s; ; L)

tNoMPR (TE; s; ; L) + tMPR (s; ; L)

and

fMPR (TE; s; ; L)

=tMPR (s; ; L)

tNoMPR (TE; s; ; L) + tMPR (s; ; L):

Note that by scaling time, we can eliminate the depen-dence on speed s. Specically, if s = sref, then

fEmptyTC (TE;s; ; L) = fEmptyTC (TE=;sref; ; L)

fMPR (TE;s; ; L) = fMPR (TE=;sref; ; L) :


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=6, 4 x 4

=6, 7 x 7

=6, 10 x 10

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=18, 7 x 7

=18, 10 x 10

(c)

Figure 2: (a) CDF of time a node is not an MPR of some other node. (b) Expected time as MPR. (c) OLSR Optimization of reducingthe fraction of nodes that generate TC is degraded with speed.

Thus, fEmptyTC and fMPR are functions of three variables,TE, , and L.

To obtain fEmptyTC and fMPR, idealized simulations overthese three parameters was performed. By idealized simu-lations, we mean where the radio is modeled as on/o withtransmission range r = 1. Nodes move at a speed sref = 1tx:range=s and follow the random waypoint mobility [13].Moreover, for these simulations, a perfect neighbor discov-

ery mechanism is assumed. That is, once two nodes arein range, nodes instantly detect each other as symmetricneighbors and update their MPR sets accordingly. Figure2(a) shows FNoMPR for dierent values of , and L. Fig-ure 2(b) shows tMPR as a function of density. As can beobserved in both Figures 2(a) and 2(b), both FNoMPR andtMPR converge for large L. Hence, FNoMPR and tMPR donot need to be determined for all L, but only for small L,e.g., for L 10.

Figure 2(c) shows fGenTC, the fraction of time that a nodegenerates a TC message, when TE is three TC intervals. Itcan be seen that the OLSR optimization of reducing thenumber of nodes that generate at TC packet is ineectiveas speed increases. For example, as seen in Fig. 2(c), at 0:2tx:range=hello interval almost all nodes generate topology

packets. This indicates the importance of accounting for theoverhead generation by empty TC messages.Data and a Matlab function for estimating fGenTC for

4 20 are available for download [11].

4.2 Realistic ModelThe idealized scenario discussed above is unrealistic in

two ways; it neglects transmission errors, and it neglectsthe impact of ND. When transmission errors are considered,even when nodes are not moving, ND might determine thatlinks break. Thus, to estimate tEmptyTC in a more realisticsetting, we use a tEmptyTC from an idealized scenario. Thekey question is, which idealized scenario should be used tomodel the realistic scenario? We use the idealized scenariowhere

1. the average number of symmetric neighbors is the sameas the realistic scenario,

2. L is such that the number of nodes in the network isthe same as the realistic scenario, and

3. the average link lifetime is the same as the realisticscenario.

The model of the ND in [12] provides an estimate of theaverage number of symmetric neighbors in the realistic sce-nario, while the average number of symmetric neighbors inthe idealized scenario is simply the number of nodes withincommunication range.

Note that when ND is such that only strong links areconsidered symmetric, the number of symmetric neighborsis reduced. Essentially, such a ND increases the size of thenetwork, in that a message will need to cross more sym-metric links to reach a destination. Hence, L, the lengthof one side of the simulated region is impacted by ND andthe radio. In order to solve for L, we need to determineNidealized (L; ), the number of nodes as a function of L

and when the on/o radio model is used. This functionis easily determined from simulation. Given this function,we solve for L in N = Nidealized (L; sym), where sym isthe average number of symmetric neighbors found in step 1and N is the number of nodes in the network.

Matching the average link lifetime is done as follows. Inthe realistic case, the link lifetime depends on the nodespeed, on the ND method, and on the radio. Again, themodel of ND presented in [12] provides an estimate of thelink lifetime. In the idealized case, the link lifetime can bedetermined from the simulations described in the previoussubsection. Note that these simulations need to be only per-formed for one speed, denoted by sref. The link formationrate at some other speed, s, can be found by scaling, i.e.,

LT(s) =srefLTref

s, where LTref is the link lifetime found

from simulations, and LT(s) is the link lifetime at speed s.In summary, using the model in [12] for a particular nodedensity, node speed, radio, and ND method, one can com-pute LTND be the average link lifetime and sym be the av-erage number of symmetric neighbors. Then, the fraction ofnodes that generate TC messages is fGenTC(s; ; L), where

s = srefLTrefLTND

, = sym, and L solves N = Nidealized (L; sym)

4.3 Model ValidationTo validate the model of the fraction of nodes that gener-

ate TC messages, extensive QualNet [14] simulations wereperformed. The values derived from QualNet simulationsthroughout this paper were found by averaging over 120 sim-ulation trials where the simulation time is 180 seconds, butdata is only saved from the last 60 seconds (the rst 120 sec-onds allow the protocols to stabilize). Here, the nodes wereconstrained to be within a 1125m1125m region. 802.11gs54Mbps bit-rate was used. With this bit-rate, the packetloss probability for 80Bytes packets probability is 1% whenthe transmitter and receiver are 196m apart, and is 99%when they are spaced 237m apart. Thus, 1125m is approx-imately four "transmission ranges." For some experiments,background trac as included. To this end, nodes broad-casted 80Bytes packets at Poisson distributed times suchthe average rate that a node generates background trac is0Bps, 1250Bps, 2500Bps or 5000Bps. Fig. 3(a) show ex-


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CDFErrorProb.

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kt

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Model (No P. Speed)

(b)

Figure 3: (a)Validation of Model of the fraction of nodes thatgenerate TC packets. (solid) Model (dashed) Qualnet. (b) CDF

of model error when full model is used (solid) and real speed is

match to that of the idialized case (dashed).

amples of the quality of t provided by this model. Figure3(b) shows the CDF of the relative error over all scenariosconsidered. Each scenario is characterized by the numberof nodes, N, the node speed, s, the ND method and its pa-rameters, and the intensity of the background trac. Herewe considered N = 52, 66, 73, 84, or 91 and s = 0, 5, ...,

25 (meters/sec), and interference 0Bps, 1250Bps, 2500Bpsand 5000Bps. The two ND methods from RFC 3626 wereconsidered, namely the EC ND and the EMA ND. In thecase of EC, (U; D) = (1; 3) and (U; D) = (4; 3). For theEMA method, LQup = 0:8, LQdown = 0:3, w = 0:5.

For reference, Fig. 3(b) shows the CDF of the relativeerror when step 3 is replaced as follows

30. the speed s in the idealized case is the same as thespeed in the realistic case.

Note that step 30 is a reasonable approach. However, thisapproach results in signicant error. On the other hand,matching link lifetimes results in a much smaller error.

5. FRACTION OF NODES THAT RETRANS-MIT A PACKET AND COVERAGE

In this section we present models of the fraction of nodesthat retransmit a packet, ret, and the fraction of nodes thatreceive the ooded message, or coverage, cover. Two model-ing approaches are followed. First, a detailed rst-principlessimulation-based model is developed in the next subsection.This approach relies on an analytic model of neighbor dis-covery but makes use of simulations of node locations. Thesesimulations can be quickly performed in Matlab and allowsret and cover to be estimated for a wide range of topologyand protocol parameters. Based on these simulations, black-box models are developed in Section 5.2. These black-boxmodels give analytic formulas for ret and cover.

5.1 First Principles Simulation-based ModelA large number of methods have been proposed for ood-

ing messages in MANETs. RFC 3626 details one method[1], while the popular implementation of OLSR available at[4] utilizes a slightly dierent approach. According to RFC3626, when a node receives a TC message from a symmet-ric neighbor, two conditions are checked: 1. that the TCmessage has never been received from a symmetric neighborbefore, 2. that the symmetric neighbor is also an MPR se-lector. If both of these conditions are met, then the nodeforwards the message. On the other hand, according to the

OLSRD implementation, a TC message is forwarded if themessage has not been forwarded before and the second con-dition is met. Thus, according to RFC 3626, if the messageis rst received from a symmetric neighbor that is not anMPR selector, then the message is never forwarded. On theother hand, in the OLSRD method, a node may have re-ceived the message rst from a symmetric neighbor, and yetstill forward the message when it is receives from a MPR se-lector. Intuitively, the OLSRDs implementation generates

more overhead, but reaches more nodes than the methoddescribed in RFC 3626. Since both ooding methods arewidely deployed, we develop models for both of them andvalidate this intuition.

It turns out that simulations of ooding can be performedvery eciently. For example, simulating ooding over a 100node network takes about 50 msec on a standard desktop2 .Hence, Monte Carlo evaluation of ooding is reasonable.On the other hand, determining which nodes are symmetricneighbors and hence which nodes are MPRs is more com-plicated to simulate. However, the model of ND presentedin [12] can be employed to determine the probability thatnodes are symmetric neighbors. Thus, the following stepscan be used to compute the fraction of nodes that relaythe message, ret; and the fraction of nodes that receive the

message, cover.1. For each node i, select its location, (xi; yi), and its

velocity, (vi; wi), according to the random waypointstable node distribution [13].

2. Use the ND model to determine the probability thatnodes i and j are symmetric neighbors. Specically,let symi;j denote the event that node i has markednode j as a symmetric neighbor and let symi;j bethe event that node i does not declare node j as asymmetric neighbor. The ND model estimates theof probabilities P(symi;j;symj;i), P

symi;j;symj;i

,

P

symi;j;symj;i

, P

symi;j;symj;i

.

3. Select a realization of symmetric neighbors, i.e., based

on the probabilities computed in Step 2, select whichnodes have been declared symmetric neighbors.

4. Given the set of symmetric neighbors, compute theMPRs.

5. Estimate which nodes believe they are MPR selectors

6. Flood a message

Several comments are in order. Regarding Step 5, a nodewill inform a neighbor that it has been selected as an MPRvia Hello messages. However, these Hello messages are subject to transmission error. Consequently, a node might notbe aware that it has been selected as a MPR. Of course,the next Hello might also inform the neighbor that it is aMPR. Eventually, either the node becomes aware that it

has been selected as an MPR, or the neighbor stops beinga symmetric neighbor. Unfortunately, a complete model ofthis behavior is complicated. Thus, we seek a simple modelthat captures the essential behavior as follows. We makethe approximation that there are two cases.

Prefect MPR Knowledge: In this case, we assume thatnodes that have been selected as MPRs are aware that theyare MPRs.2 Simulation times in this paper are obtained from programsand scrpits running on an Intel Core i7 CPU running 64bitOS and 12GB RAM.


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(c)

Figure 4: Fraction of nodes reached by a TC message ood as predicted by the model (soild curves) and QualNet simulation (dashed)for OLSRDs ooding method (a), and ooding method specied by RFC 3626 (b). (c) The CDF of the relative error between the

fraction of nodes that a TC message ood reaches as predicted by the model and QualNet simulations.

Imperfect MPR Knowledge: In this case, we assume that aneighbor is aware that it is a nodes MPR only if it receivesa Hello message from the node. Thus, after a node hasselected a subset of its neighbors to be MPRs, we assumethat the probability that each of these MPRs is aware that itis an MPR is equal to the probability of the MPR receivinga Hello message from the node, which depends on the radio,the distance to the MPR, and the interference.

The Perfect MPR Knowledge case is valid when nodesremain are MPRs for an extended period of time. In thiscase, a MPR has several chances to receive Hello messagesand learn that it has been selected as an MPR. The Imper-fect MPR Knowledge case is valid when a nodes MPR fre-quently change. While there are scenarios that are betweenthese cases, but as an approximation, we only consider thesetwo cases. We use the Perfect MPR Knowledge model whennodes are stationary and use the Imperfect MPR Knowl-edge model when nodes are mobile. The utility of Step 5 isexplored in Section 5.1.1.

When simulating ooding a message (i.e., Step 6), eitherthe method described by RFC 3626 or the method imple-mented in OLSRD is used. In both cases, packet trans-missions are subject to transmission errors, which depend

on the radio, distance between nodes, and interference. Asmentioned, in both ooding methods, a node will only con-sider messages that are received from symmetric neighbors.It is important to note that the nodes do not have synchro-nized estimates of which links are symmetric (i.e., each end-node of a link might have dierent estimates as to whetherthe link is symmetric). We have found signicant errorsresult when it is assumed that nodes estimates are synchro-nized. Similarly, signicant errors result when it is assumedthat the end-nodes estimates are independent, i.e., signi-cant errors result if one assumes that P(symi;j;symj;i) =P(symi;j) P(symj;i).

5.1.1 Model Quality

Figure 4 (a) and (b) shows the average fraction of nodesthat receive a TC message ood. As can be observed, themodel accurately predicts the values and the trends in cover-age. Figure 4 (c) shows the CDF of the relative error of thecoverage predicted by the model and QualNet simulations.Here the CDF is over all scenarios discussed in Section 4.3where the coverage exceeds 70%. When the coverage is lessthan 70%, then ooding protocol is performing poorly andlikely impacts the utility of the network. In such cases, weare not interested in the degree of poor performance, butrather whether the performance is po or or not.

As can be observed in Figure 4 (c), the model and QualNetresults yield similar results over a wide range of scenarios.The median error is less than 1% and the 90th percentileerror is less than 5%.

Figure 4 (c) also shows the CDF of the relative error whenStep 5 from Section 5.1 is not used and instead we assumePerfect MPR Knowledge, that is, we assume that nodes arealways aware when they have been selected as MPRs. Note

that this assumption causes signicant increase in the error.Figure 5 is similar to Figure 4, except that Figure 5 consid-

ers the fraction of nodes that forward a TC message, whichis fRET in (1). As is the case of the coverage, the model ac-curately predicts the values and the trends observed in Qual-Net results. Similarly, Figure 5 (b) indicates that uniformlyassuming Perfect MPR Knowledge results in signicantlylarger error, especially in the tail of the error distribution.

Figure 5(c) show some samples of the time to compute theooding performance with the simulation-based model de-scribed above and with QualNet simulations. Recall that thesimulation-based model, does require some Monte Carlo sim-ulations. Specically, for each scenario, 120 sample topolo-gies were used. For each topology, 10 TC messages wereooded from each node. Similarly, the QualNet simulations

use 120 trials where each trial is run long enough for theprotocols to stabilize and then for enough time for eachnode to generate 10 TC message oods. 5(c) shows thatthe simulation-based model computes the performance ofthe ooding between one and three orders of magnitudefaster than QualNet. For example, the estimated time tocompute the ooding performance over a 500 node networkwith QualNet takes 123 days on a single processor, while thesimulation-based model requires only about 4800 sec. Con-sequently, accurate performance estimates of ooding overlarge networks via packet simulation is currently computa-tionally intractable. However, the simulation-based mod-eling approach described here allows accurate performanceestimates even for large networks, which is not possible withpacket simulation.

5.2 Black-Box ModelWhile the model described in Section 5.1 provides accu-

rate predictions of performance, the computations are rea-sonably involved. Thus, to enable fast computation, a black-box approach is utilized. A two stage approach is utilizedfor developing black-box models. First, graph theoretic met-rics are selected. Second, curve tting is used to model therelationship between the ooding performance metric andthe graph theoretic metric. A well selected graph theoreticmetric improves the model quality of t. No methodology


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Figure 5: (a) Frraction of nodes that forward a TC message ood as predicted by the model (soild curves) and QualNet simulation(dashed) for OLSRDs ooding method (the upper part of (a)), and the ooding method specied by RFC 3626 (lower part of (a)). (b)

CDF of relative error between the fraction of nodes that forward a TC message ood as predicted by the model and QualNet simulations.

(c) Computation time for estimating performance of ooding via simulation-based model and full packet-level simulations with QualNet.

is presented for selecting the graph theoretic metric; we usea trial and error approach. Similarly, the form the curvesused to t the relationship between the graph theoretic met-ric and the ooding performance metric was selected by trialand error, while the curve parameters were selected to min-imize the mean square error.

A range of graph theoretic metrics are relevant to ooding.We consider the following metrics. is the average numberof neighbors that receive a broadcasted message, hence

= E

0@ X

v6=w, w2N

ptrans (!vw)

1A ;

whereN is the set of nodes in the network, ptrans (!vw) is the

probability of successfully transmitting from v to w and theexpectation is over arbitrarily select nodes v in an arbitrarilytopology.

is the average number of nodes reached by a one-hopood. We dene 2 to be the number of nodes reached

in a two hop ood. and 2 are dened similarly, butover the MPR-subgraph. Specically, given a node u, letG0 (u) = (V0 (u) ; E0 (u)) be the subgraph where v 2 V0 (u)if v is a MPR of u or if there exists a node w where w is aMPR of u and v is an MPR of w. Similarly, !vw 2 E0 (u) ifw is a MPR of v. is the number of nodes reached by aone-hop ood that is originated at u, i.e.,

:= E

0@ X

v6=w,v;w2V0(v)

ptrans (!vw) Pr (w is MPR of v)

1A :

And 2 is the average number of nodes reached by a two-hopood over G0 (u) originated at u, where the average is over

all nodes u and topologies. Finally, we dene similarly to and , but only symmetric links are considered, i.e.,

= E

0@ X

v6=w ,v;w2N

ptrans (!vw) P(symw;v)

1A

Through trial and error, the following models of the cover-age (cover) and fraction of nodes that retransmit (ret) werefound as a function of the metric vector X = (; 2; ; 2; ),

coverRFC (X) = 1 exp

6:50296

2

1:81899!

retRFC (X) = 1:02654

0:0023 coverRFC (X)

coverOLSRD (X) = 1 exp0:142082:8161

retOLSRD (X) = (0:006228(2 ) + 0:522713)

coverOLSRD (X) :

Here the parameters were selected by minimizing the squareerror between the black-box model and the simulation-basedmodel developed in Section 5.1.

Figure 6 shows the quality of t this black-box modelachieves. Specically, Figure 6 shows the CDF of the relativeerror between the black-box model and the results derivedfrom QualNet simulations. For reference, these gures in-clude the CDF of the relative error between the simulation-based model developed in Section 5.1 and the QualNet re-sults. As can be observed, the quality of t of the two mod-

els is similar, with the simulation-based model resulting inslightly better quality of t.

6. COMPARISON TO OTHER MODELSWhile there has been extensive simulation-based perfor-

mance evaluation of OLSR, to the best of our knowledge,there has been no research on modeling the coverage andonly limited research on modeling the fraction of nodes thatforward TC messages. In [9] a model of OLSR was devel-oped. This model is designed to model overhead when TCmessages are generated in response to link failures. Whileour model is focused on periodic TC message generation,the models have similar goals. Specically, in [9], the frac-tion of nodes that forward a TC message is modeled as No.MPRs/No. Neighbors. In [9], the number of neighbors was

dened to be the number of nodes within "communicationrange." Note that we have found that the dynamics of neigh-bor discovery play a signicant role in a nodes estimate ofthe number of neighbors, and hence, the concept of com-munication range is insucient to determine the number ofneighbors. Nonetheless, we can dene the No. Neighbors tobe the number of nodes that are close enough that the prob-ability of successfully receiving a 80Bytes packet is above0:5. We have found that a good estimate of the number

of MPRs is No. MPRs = 1:47 + 2:77 (No. Neighbors)1=3,which agrees with the order estimate given in [15]. With


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Figure 6: CDF relative error between black-box model prediction and QualNet simulations of coverage achieved by the o oding algorithmdescribed in RFC 3626 (a), the coverage achieved by OLSRDs implementation (b), fraction of nodes that forward a TC message underthe algorithm described in RFC 3626 (c), and fraction of nodes that forward a TC message under the algorithm implemented in OLSRD

(d). For reference, the CDF of the relative error between the model described in Section 5.1 and QualNet simulations is included.

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Figure 7: The CDF of the relative error between the fraction ofnodes that forward a TC message ood as predicted by dierent

models and QualNet simulations. The model presented in thispaper is refered to as Model, the model presented in the paper by

Wu et al. is Model. The 0-Speed Model is based on a modeling

approach found in several papers.these denitions, we can apply the model developed in [9],which we refer to as the Model, following the notation in[9].

In several other papers, the fraction of nodes that forwardTC messages is assumed to be independent of speed. How-ever, no model is given for the fraction of nodes that forwarda TC message at zero speed. Instead, it is suggested thatpacket simulation can be used. Recall that the dynamics ofND cause the ooding to be impacted by node speed, as canbe observed in Figures 4 and 5. Nonetheless, we can applysuch a modeling approach by using the fraction of nodesthat forward TC messages at zero speed as an approxima-tion of the fraction of nodes that forward TC messages atany speed. We call this model the 0-Speed Model.

Since we have only recently discovered the bug in the OL-SRD implementation (which was also a bug in QualNet), itis sometimes unclear which version of OLSR is being mod-eled in other papers. Thus, Figure 7(a) shows the CDF ofthe relative error between these models and a RFC compli-ant version of OLSR, while Figure 7(b) shows the CDF ofthe relative error between these models and the OLSRD ver-sion. As can be observed, the model presented in this paperprovides a much more accurate model. The 0-Speed Modelis the second best model. However, this model requires run-ning full packet level simulations, which is computationallydicult for large networks (see Section 5.1.1).

7. CONCLUSIONSIn this paper we present a detailed model of the over-

head generated by the topology information disseminationmechanism of OLSR. We study how each of the three opti-mizations present in OLSR vary with network parameters,such as speed, density, channel usage and neighbor discov-ery mechanism. The model shows that OLSR optimizationsare dramatically diminished in mobile and lossy scenarios.Also, dierent implementations of OLSR generate signi-cantly dierent overhead rates. The implications of thesemodels is currently under investigation.

Disclaimer

The views and conclusions contained in this document arethose of the authors and should not be interpreted as rep-resenting the ocial policies, either expressed or implied, ofthe Army Research Laboratory or the U. S. Government.

8. REFERENCES[1] T. Clausen and P. Jacquet, RFC 3626: Optimized link

state routing protocol (OLSR), October 2003.[2] (2010, May) IEEE p802.11 TGs. IEEE. [Online]. Available:

http://www.ieee802.org/ 11/Reports/tgs_update.htm

[3] J. Moy, RFC 2328: OSPF version 2, April 1998.[4] A. Tnnesen, T. Lopatic, H. Gredler, B. Petrovitsch,

A. Kaplan, S.-O. Tcke, and Others. (2010, May) An adhocwireless mesh routing daemon OLSRD. [Online]. Available:http://www.olsr.org/

[5] Z. Ye and A. A. Abouzeid, A unied model for jointthroughput-overhead analysis of mobile ad hoc networks,in MSWiM 08. ACM, 2008.

[6] L. Viennot, P. Jacquet, and T. H. Clausen, Analyzingcontrol trac overhead versus mobility and data tracactivity in mobile ad-hoc network protocols, Wirel. Netw.,vol. 10, no. 4, July 2004.

[7] Y. Huang, S. Bhatti, and S. A. Sorensen, Analysing theimpact of topology update strategies on the performance ofa proactive manet routing protocol, in ICDCSW 07, 2007.

[8] A. Qayyum, L. Viennot, and A. Laouiti, Multipointrelaying: An ecient technique for ooding in mobile

wireless networks, INRIA, Tech. Rep. RR-3898, February2000. [Online]. Available: ftp://ftp.inria.fr/INRIA/publication/publi- pdf/RR/RR-3898.pdf

[9] X. Wu, H. Sadjadpour, and J. Gracia, Modeling oftopology evolutions and implication on proactive routingoverhead in manets, Comp. Comm., vol. 31, no. 4, March2008.

[10] A. Medina and S. Bohacek, Technical report 02: Bugsfound in popular implementations of olsr. University ofDelaware, Tech. Rep., June 2010. [Online]. Available:http://cbr.eecis.udel.edu/ publications

[11] S. Bohacek, A. Medina, and C. Aponte. (2010, June)Component based routing. [Online]. Available:http://cbr.eecis.udel.edu/

[12] A. Medina and S. Bohacek, Technical report 01: Aperformance model of neighbor discovery in proactiverouting protocols. University of Delaware, Tech. Rep.,

June 2010. [Online]. Available: http://cbr.eecis.udel.edu/publications[13] W. Navidi and T. Camp, Stationary distributions for the

random waypoint mobility model, IEEE Trans. on MobileComputing, vol. 3, no. 1, 2004.

[14] (2006, October) Qualnet simulator 4.5. [Online]. Available:http://www.scalable-networks.com/ products/qualnet/

[15] P. Jacquet, A. Laouiti, P. Minet, and L. Viennot,Performance analysis of olsr multipoint relay ooding intwo ad hoc wireless network models, INRIA, Tech. Rep.,September 2001. [Online]. Available: ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4260.pdf

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