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Modeling End-to-End Throughput of MultipleFlows in Wireless Mesh Networks

Xiaofei Wang , Ye Yan , Hua Cai , Taekyoung Kwon , Yanghee Choi , Seungwoo Seo and Sunghyun Choi

School of Computer Science and Engineering , School of Electrical Engineering

Seoul National [email protected], [email protected], [email protected], {tkkwon,yhchoi,sseo,schoi }@snu.ac.kr

Abstract Wireless Mesh Networks (WMNs) have gained a lotof attention recently. Due to the characteristics as an infrastruc-ture, many efforts are made in order to improve or guaranteethroughput in WMNs. In this paper, we propose a generalmodeling methodology to analyze the end-to-end throughputof multiple concurrent ows. We take into account the carriersensing behaviors, interference and the IEEE 802.11 DistributedCoordination Function mechanism. By probabilistically calculat-ing the average service time for each successful transmission ateach node, we analyze the bottleneck throughput of each ow, andhence obtain the achievable end-to-end throughput. We carry outsimulation experiments with various trafc patterns of multipleows in WMNs to validate our modeling.

Index Terms Multi-Flow, End-to-End Throughput, WirelessMesh Network

I. INTRODUCTION

Recently, Wireless Mesh Network (WMN) systems based onthe IEEE 802.11 WLAN technology [1] have been proliferatedrapidly. The WMNs are expected to provide high throughputchannels from aggregators through intermediate routers to thegateway(s). Aggregators are mesh nodes that directly collect

data from their clients. Routers are intermediate mesh nodesthat relay data to the gateway, which is connected to theInternet.

The performance of a WMN system is signicantly limitedby the broadcast nature of the wireless medium. A nodehas to compete with others within its carrier sensing (CS)range for data transmission. This operation is called channelcompetition. In IEEE 802.11a/b/g standards, devices are usingthe CSMA/CA mechanism to share the medium and to avoidcollisions with each other. However, there are still otherproblems, e.g. hidden node problem (HNP), exposed nodeproblem and so on. HNP is mainly caused by the ignorance of the transmissions outside the CS range. There are two kindsof he HNPs: (1) protocol level HNP and (2) physical levelHNP. If we use the RTS/CTS mechanism, we can solve theprotocol level HNP. However, the physical level HNP cannotbe solved by the RTS/CTS. The protocol level and physicallevel HNPs are detailed later.

Many research efforts are made to theoretically model thethroughput from the view of entire WMN system, or from aspecied one hop, or a typical path. But in realistic scenarios,analyzing throughput of multiple concurrently ongoing owsis viable to evaluate the topology design, routing strategy, and

resource allocation. Our contribution is to model the end-to-end throughput of multiple communication ows in WMNsystems.

The rest of this paper is organized as follows: In SectionII, we will briey introduce the constraints of throughput inWMNs. In Section III, we will explain preliminary denitionsand the proposed modeling procedure in detail. In Section IV,

we carry out comprehensive simulation experiments in orderto evaluate our modeling. In Section V, our work will beconcluded and future work will be briey mentioned.

I I . BACKGROUND

A. Fundamental Constraints of WMNs

WMN systems mainly suffer from three fundamental con-straints: channel competition by the CS mechanism, protocollevel HNP that RTS/CTS can solve, and physical level HNPthat cannot be handled by RTS/CTS.

1) Channel Competition: In WMN systems, a node hasto compete to occupy the channel to transmit a packet.In IEEE 802.11a/b/g, the Distributed Coordination Function

(DCF) based on CSMA/CA is used for nodes to share thecommon channel. Once a node is occupying one channel,all nodes within its CS range can detect and have to befrozen. This signicantly limits the performance of WMNs.Recently some techniques are used to reduce the limitationof channel competition, e.g. multi-channel and dynamicalchannel assignment strategy. However, those techniques comewith additional hardware or signaling cost/hazards.

2) Protocol Level Hidden Node Problem: The Hidden Nodeproblem is well-known in wireless networking. There are twokinds of HNPs, protocol level HNP and physical level HNP.Protocol level HNP is caused by the nodes that are in theCS range of a receiver but not in the CS range of a sender.People developed the RTS/CTS mechanism in order to solvethe protocol level HNP. In our analysis, we only evaluate thescenarios without RTS/CTS for two reasons: (1) it is easy tomodify our modeling to analyze scenarios with RTS/CTS, and(2) the overhead of RTS/CTS is not negligible and sometimesit becomes ineffective [8].

3) Physical Level Hidden Node Problem: Physical levelHNP is caused by the nodes that are out of the CS rangeof both sender and receiver, but their transmission signalcan still affect the signal-to-interference-noise-ratio (SINR)


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value of receiver, so that the receiver cannot demodulate thesenders packet. The physical level HNP cannot be solved bythe RTS/CTS mechanism. Capture Effect [6] is substantiallyintertwined with the physical level HNP. In this paper, wefollow a simple capture model, where the SINR value mustbe always higher than the capture threshold during the entiretransmission.

C

A

C

A

B B

(b) (c)(a)

C A

B

Fig. 1. Interference Relationship

We demonstrate interference and capture effect in our mod-eling as shown in Figure.1 , where our focus is on the packetfrom A to B, and C is the interferer. During the period in whichAs transmission is going on, the packet reception is vulnerableto Cs interference (both protocol level HNP and physical levelHNP). With the above the simple capture effect model, thisvulnerable period is twice as long as the transmission time of a packet. That is, when As transmission time overlaps withthat of C, the receiver (or B) cannot demodulate the packet.

B. Current Related Work

Realistic modeling of WMN systems is crucial for furtherWMN resource management, such as channel allocation, dy-namic routing, load balancing, adjustment of topology and soon. Bianchi [3] initially proposed the basic analysis on DCFfor saturated trafc case in infrastructure mode WLANs. KenDuffys Model [2] made an effort for analyzing accurately withthe non-saturated trafc by extending the Bianchis model.However, both consider only single hop WLAN cases. MukeshHiras Model [5] analyzed a single ow in wireless multi-hopnetworks by considering the probability of PHY/MAC layerbehaviors but neither multiple ows nor physical HNPs is notconsidered. Yan Gaos Model [4] presented the probabilisticanalysis of the link throughput. It considers multiple owsfrom the perspective of links, not of nodes. Our work extendsthe Mukeshs modeling methodology for scenarios with mul-tiple ows from the perspective of nodes considering channelcompetition and both protocol level and physical level HNPs.

III . M ODELING AND A NALYSIS

A. PreliminariesIn our analysis and modeling, a homogeneous WMN with

one channel is assumed. Static routing is used, since weconsider the throughput analysis of the predened paths. If there are concurrently multiple interferers, our model considersinterference signals one by one, not the cumulative interfer-ence.

The main idea of modeling is to locate the bottleneck of each ow. Bottleneck nodes in WMNs are the nodes thatwill be constrained by much more CS neighbors and both

kinds of HNPs than others. Even if the downstream nodesof a bottleneck node in the ow have less constraints andhence higher link capacity, the ows end-to-end achievablethroughput is limited by the bottleneck node already. If weadjust the input trafc load to be equal to the capacity of thebottleneck node, the maximum end-to-end throughput of thisow can be obtained.

In a WMN, there are total N concurrently ongoing ows,denoted by F i , i {1, 2, . . . , N }. As F i will go from an ag-gregator through zero or more intermediate routers to gateway,we can denote the ow F i s hop count by M i .

We denote all nodes belonging to the ow F i by n i,j , and jis the nodes hop count number counting from the aggregatorthrough the ow until gateway, j {0, 1, . . . , M i }. n i, 0 is therst node which should be the aggregator, and n i,M i is thedestination which should be a gateway.

Suppose the set of total nodes in a WMN is S , we candene several specic subsets based on relationships:

S CS (n i,j ) : the set of nodes within the CS range of n i,j

, excluding n i,j S CS (n i,j )+ : the set of nodes within the CS range of n i,j

, including n i,j S CS (i)+ = S S CS (i)+ : the set of nodes out of the

CS range of n i,j S I (i) : the set of nodes that are out of n i,j s CS range,

but within the interference range of n i,j S RT S (n i,j ) : the set of nodes within RTS range of n i,j S CT S (n i,j ) : the set of nodes within CTS range of n i,j

The above set information can be obtained by the idealpropagation model, or by some measurement methodologies(e.g RSS-based Prediction Method [7]).

We rst focus on the analysis and modeling of one singleow in the WMN. Suppose a ow F x spans over M x hops,and hence has M x + 1 nodes, (from n x, 0 to n x,M x ). For thepurpose of understanding, we skip the index x in the followingand describe our modeling from the standpoint of a single owchosen among multiple ows. As the chosen ow goes fromn 0 to n M , we can pick up two intermediate adjacent nodes n iand n i+1 for analysis, where n i+1 is the next hop of n i .

The key to nding the bottleneck is to calculate the expec-tation of the service time, E [T i ], for each node n i , which istaken to transfer one packet successfully. The bottleneck nodein the ow must have the largest E [T i ], because it will takethe longest time to successfully transmit one packet since it

will suffer from channel competitions and HNPs more severelythan any other nodes in the ow.

We denote by i as the probability of having a non-emptyqueue at node n i . By the similar technique as the xed pointapproximation, we rst suppose the source node has alwayspackets to send, so 0 = 1 . For the downstream nodes alongthe path of the ow, they can only receive packets that aresuccessfully sent from the previous hop. Then an intermediatenode can only receive packets at a rate determined by themaximum average service time among the previous (upstream)


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nodes in the ow. Therefore,

0 = 1i = Min (1, i E [T i ])

= M in 1, E [T i ]Max j


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Then we will focus on total average amount of the collisionprobability. Suppose A i is a random variable which is theaverage amount of successful transmissions by other nodes inS CS (n i ) between two successive successful transmissions byn i . Then,

E [T U i ] = E A i

k=0

tk,i = E [A i ]E [tk,i ] (15)

Here, the independence between A i and t k,i is assumed, wheret k,i is the time used by the k th successful transmission of anode in S CS (n i ). Then,

E [A i ] =1 i

i=

1 i

1 =kS cs ( i )

k

i(16)

And

E [t k,i ] =j S cs (n i )

j

k S cs (n i ) k

T s (17)

we can get the nal E [T U i ]:

E [T U i ] = Pk S cs ( i ) k i j S cs (n i )

j

Pk S cs ( n i ) kT s

= 1 ij S cs (n i )

( j T s )(18)

4) E [T C i ]: E [T C i ] is the average time period spent incollisions regardless of whether node n i is involved or not.In other words, in order to transmit one packet successfully,we can estimate how many collisions will happen within n i sCS range on the average. There are two types of events thatcan induce E [T C i ]: A successful transmission by n i or acollision occurs involved in S CS (n i ). Then we denote by x i

the probability that a successful transmission is made by n igiven that at least one node in S CS (n i ) has transmitted. Then,

x i = i

1 (1 i )k S cs (n i )

(1 k )(19)

yi is the probability that a collision occurs in S CS (n i ) giventhat at least one node within n i s CS range has attempted atransmission already. Then,

yi = 1 kS cs (n i )

k + i

1 (1 i )k S cs (n i )

(1 k )(20)

The number of unsuccessful transmission attempts that canbe known by n i between its two successful transmissionsis a geometric distribution with parameter x ix i + y i . Then theaverage time spent in the collisions between two successivetransmissions by n i is given by,

E [T C i ] = y ix i T c

=1 i Pk S cs ( i ) k ! (1

i ) Qk S cs ( i ) (1

k )

i T c(21)

Here T C is the time wasted for each collision. It can becalculated by the parameters in the IEEE802.11 standard forbasic and RTS/CTS modes, respectively:

T Basicc = P HY + M AC + Payload + DIFS T RTS/CTSc = RT S + DIFS

(22)

After analysis, we get the same number of equations as thenumber of nodes in all the ows, and equations are numericalsolvable. This modeling can adapt to multi-channel WMNseasily. During the analysis of the sets of CS and HNPs, wecan just put related nodes within the range of the node in thesame channel into its related set, and then calculate in thesame manner.

5) Calculation for Multiple Flows: The calculation formultiple ows follows the same procedure as single ow. Whatwe need to do is accurately analyze the CS neighbor nodesand interference neighbor nodes of each node, including notonly the nodes in the same ow, but also the the nodes inother ows, if they are in related range. From the examplein the Figure.2, between two ows, the red line means CS

relationship, and the dash lines means nodes are interferencerelationship. Node n m, 1 in ow F m has S CS (n m, 1) set {n m, 0 ,n m, 2 , n n, 2}. Note that even node n n, 2 should be included inS CS (n m, 1), while S CS (n n, 2) is {n n, 1 , n n, 3 , n m, 1} as well.Also, interference relationship set S I (n m, 1) must contain n n, 1and n n, 3 . After we get the relationship sets, by the samemodeling procedure, and calculation of massive equations,throughput of each ow can be obtained nally.

Flow m

Flow n

n m,1

n m,3

n m,0n m,2

n n,0

n n,1n n,2 n n,3

Fig. 2. A Example of Calculation on Multiple Flows)

IV. S IMULATION AND EVALUATION

A. Simulation Parameters

We use QualNet 4.0 T M as our simulation platform. Becausethere is no signicant behavioral difference between IEEE802.11a and 802.11b, the calculations and simulations exactlyfollow the specication of IEEE802.11a standard. Also, sincethere will not be essential changes in the modeling procedurein the presence of multiple bit rates from 6Mbps to 54Mbps,we only consider the basic rate, 6Mbps. The transmissionrange is adjusted to 380 meters and it equals the CS range.All the adjacent nodes are 380 meters apart. The interferencerange, which means the range of physical HNP, is around500 meters, about 1.3 times of the CS distance. The UDPdatagrams following a Poisson arrival pattern is utilized tovalidate our probabilistic analysis. The basic DCF scheme


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without RTS/CTS is tested, as RTS/CTS wont matter themodeling and the performance signicantly.

Input Load

End-to-End Throughput

0 x

y

y=x

SustainableThroughput

Input Load

End-to-End Output

0 x

y

y=x

SustainableThroughput

Experimental Curve of End-to-endThroughput Generalized from Simulations

Analytical Curve Generalized by OurModeling of End-to-end Throughput

Fig. 3. Average Throughput of All Flows (Simulation on the left andModeling on the right)

As shown in Figure.3, the throughput before the threshold(called sustainable throughput) is the same as input trafcload. After the input load exceeds the threshold, the owwill have a high packet loss rate. In the analytical curve, theupper boundary is calculated by our model, then end-to-endthroughput is approximated by the line shown in right gure.In the following we will show the comparison between the

simulation results with our analytical results.

B. Scenarios with a single ow

The simplest scenario is with one single straight ow. Thetopology is shown as Figure.4(a), and the hop count variesfrom 3 hops to 20 hops. Also, we tested one zigzag ow whichwill experience more intra-ow channel competition and HNPsthan straight ows, as shown in Figure.4(b).

(a)

(b)0.00

250.00k

500.00k

750.00k

1.00M

1.25M

1.50M

1.75M

S u s

t a i n a

b l e T h r o u g

h p u

t ( b p s

)

Analytical ValueExperimental Result

3hops 4hops 5hops 7hops 10hops 20hops zigzag

Fig. 4. Topology and Single ow results.

The histogram demonstrates the boundaries that we cal-culated by theoretical modeling t the values of the turningpoints of the simulation results.

C. Scenarios with two owsDiverse trafc patterns of two ows are evaluated in this

part. Firstly there are two ows going concurrently and weadjust the distances between intermediate nodes of the twoows, in order to make one or two pairs of nodes be locatedin each others interference range and CS range, respectively.Figures.5(a), 5(b), 5(c), and 5(d) show those topologies. Notethat in each topology, a dot line indicates interference, and around circle is the transmission range as well as the CS range.As we can see from the comparison the modeling method can

(a) (b)

(c) (d)

0.00

250.00k

500.00k

750.00k

1.00M

( a ) ( b ) ( c ) ( d )

S u s

t a i n a

b l e T h r o u g

h p u

t ( b p s

)


Fig. 5. Topology and Two ow results.

provide very accurate analytical value compared with practicalsimulation results in these scenarios.

Trafc patterns of parallel ows is likely to be commonin WMNs. Four different topologies with parallel ows inFigure.6 are evaluated. Firstly, the distance between twoparallel ows is adjusted to be equal to the interference range.And the ows in same and opposite directions are tested.Then the distance between the two ows is adjusted to be the

same as the CS range, which means nodes will suffer channelcompetition instead of interference.Finally we found that the parallel trafc ows achieve poor

throughput in WMNs, since there are many hidden nodes. Andthe situation becomes worse if two ows are going in oppositedirection. The reason is that the last node of one ow suffersfrom the rst node of the other ow, which is always tryingto make transmissions. We should avoid this kind of topologyin trafc engineering.

(a) (b)

(c) (d)

0.00

250.00k

500.00k

750.00k

S u s t a

i n a

b l e T h r o u g

h p u

t ( b p s )


( a ) ( b ) ( c ) ( d )

Fig. 6. Topology and simulation results.

The crossing ows can frequently happen in reality. Wetest 3 crossing trafc patterns, as shown in Figure.7. Topol-ogy in Figure.7(a) shows that two ows rendezvous at thegateway, and Figure.7(b) and 7(c) show two ows merge atan intermediate router and have common sub-path to the samegateway. The nodes near the rendezvous point in Figure.7(b)are hidden to each other, and the ones near the rendezvouspoint in Figure.7(c) are within the CS range each other.

From Figure.7, (b) performs much better than (c). Sincethe joining nodes are in each others CS range, the joiningcommunication can be organically made. If joining nodes ineach ow are hidden to each other, the performance at the joint will be seriously bad. Therefore, in topology and routingdesign, we should avoid joint, however, if we have to make joint path for ows, wed better make the nodes near to the joint nodes in each others CS range.


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