Abstract — Carrier Sense Multiple Access with Collision Avoidance

1

Multiple access protocol misbehavior in WLANs

Lukas Kunz and Olav Queseth

Radio Communication Systems,S3,KTH,Stockholm,Sweden

Abstract—Carrier Sense Multiple Access with Collision Avoid-ance(CSMA/CA)is probably the most widespread multiple ac-cess protocol in use today,mainly due to the tremendous success of the IEEE802.11suite of standards.Until now most of the studies done about the protocol have focused on maximizing the performance.However as the bands become more crowded and the user terminals become easier to recon?gure,it is reasonable to assume that users will try to modify their equipment in order to achieve better performance,even if this may be in expense of the other users.The focus of this paper is from an overall network point of view,where two competing networks are considered. The competing network scenarios are modeled by the use of game theory,applying simple and repeated form games.The outcome of the games is described by the Nash Equilibrium(NE). We argue that by modifying the contention window,based on respective network parameters and by simple interaction between the contending networks,a superior performance than provided by the standard can be obtained.In the?rst part of the paper we compare the performance of a network following the standard to a network that is maximizing its throughput.The result is that by modifying the contention window size it is actually possible to achieve better performance than for a network that adheres to the standard.We then continue on analyzing the case where both networks try to achieve maximum performance in a sel?sh manner.

Index Terms—802.11,WLAN,access misbehavior,game the-ory

I.I NTRODUCTION

Wireless LAN operators are interested in obtaining suf?-cient resource access to provide their user’s demands.Nowa-days,different mechanisms are standardized to provide equi-table resource sharing among the users in unlicensed wireless networks.The focus of the paper is on a geographical area with two coexistent operators,who access the channel according to the IEEE802.11a standard.This possible scenario occurs frequently in the?eld of public access networks like airport terminals,train stations,etc.An operator is de?ned as a single cell consisting of an Access Point(AP)and its allocated STAtions(STA).Such a network deployment is de?ned as an Infrastructure Basic Service Set(IsBSS).Assuming that the competing IsBSS access the channel according to the stan-dardized CSMA/CA protocol,the medium is equitable shared. The systemwide goal of a misbehaving operator is to achieve higher throughput for the users.The enhanced performance is achieved by modifying the existing access protocol,i.e by adapting the Contention Window(CW)size to the traf?c conditions.Both of the operators are therefore considered to operate in saturated conditions,e.q each node within the network has always a packet to transmit.Throughout the paper, we de?ne a node as either an AP or a STA.Focusing on the CSMA protocol of the IEEE802.11a standard,the contending nodes imply a random backoff period to resolve contention in order to prevent packet collisions.The goal of an operator is now to constantly modify its backoff period to achieve higher channel access probability with reference to the opponent network.Considering the fact that both operators are able to modify the access probability of their assigned nodes,the scenario becomes more complex.To model such a competitive case deployment,we make use of Game Theory(GT)in form of Single Stage Games(SSG)as well as Multiple Stage Games (MSG).

The following section describes the existing IEEE802.11a CSMA protocol and the relevant parameters.Assumptions, simulation models as well as analytical models are described in the proximate section.The achieved results with reference to the game theoretical models are described in the latter sections of the paper.

II.T HE MAC LAYER OF IEEE802.11A STANDARD The IEEE802.11a de?nes the basic MAC protocol,which guarantees equitably shared medium allocation among the contending stations by using the CSMA/CA access mecha-nism.If a contending node detects the medium to be busy it defers and gets back into contention the next time the medium is idle.If the medium is idle longer than the Distributed Interframe Space(DIFS)[1],the station is backing off and starts its transmission when the backoff-counter reaches zero. Due to the random allocation of a backoff to each contending node,the possibility of a collision is small.The node having the smallest backoff allocated wins the contention,while the other need to wait for the next contention round,taking place after the packet transmission.The MAC protocol further implements a positive ACKnowledgment(ACK)transmission upon successful transmission of a data packet.Fig.1depicts the sequence of a successful data packet transmission.The size

Fig.1.Successful frame transmission

of the backoff itself is a random integer drawn from a uniform distribution over the interval[0,CW].CW is the Contention Window size and has a standardized initial value of CW min. For an unsuccessful transmission,a retransmission is initiated and a new backoff window assigned.The backoff window is randomly selected,based on the updated CW size.The CW size itself is dependent on the retransmission attempt(T R n):

CW T R

n+1

=2·CW T R

n

+1(1) CW is increased every retransmission attempt until it reaches CW max and stays on this value for every further unsuccessful

2 retransmission.After a successful transmission the value is re-

set to CW min.Moreover,the standard de?nes a retransmission

limit[1].The packet is dropped when the limit is exceeded.

III.G AME T HEORY

Game Theory provides a powerful mathematical tool to pro-

vide con?ict resolutions in competitive scenarios.The models

are distinguished by the mapping of the actual interaction

process to the players.Considering the basic model,a game

contains the following components:

?Two or more players,i.e.the contending operators

?Each player has an action set to chose a speci?c action

from,i.e.the different CW sizes

?Each player’s action dependent outcome is de?ned by the

utility function,i.e.the resulting saturation throughput

A single interaction between players is modeled by a Single

Stage Game(SSG).Considering a repeated interaction over a

?nite or in?nite time space,Multi Stage Game(MSG)models

are applied.An important aspect of multi stage games is,

that a user can decide upon its behavior in each state and

base its decision upon current measurements,the history of

the game as well as the achieved results.By investigating

in?nite repeated games,we introduce a discounting factor in

order to model the uncertainty of the future.Since the players

act purely rational,we can assume that present payoffs are

worth more than future payoffs.We de?ne the discounting

factorδ∈[0,1],showing how much a payoff of1unit in the

current stage is worth in the next stage.The total achievable

throughput can be computed:

S i,0+δS i,1+δ2S i,2+...+δ∞S i,∞=

∞

t=0

δt S i,t(2)

whereδt is the discounting factor and S i,t is the saturation throughput of user i at stage t.The value of the factor basically depends on the traf?c characteristics.Since we assume equal distributed traf?c with identical arrival process,the discounting factor is de?ned to be constant throughout the game.

A.Prisoner’s dilemma

In order to describe the results of the investigations,we introduce the Prisoner’s Dilemma(PD)based on a basic example[2].The PD model describes a reciprocal con?ict scenario of two criminals,arrested for a crime.The criminals are kept in different cells:hence,they are not able to com-municate throughout the process.If both suspects cooperate (C),they back each other and therefore receive moderate sentences.If one implicates the other,i.e.he defects(D),he receives an acquittal,while the latter is sentenced for life.A general implication of the players,results in severe punishment for both.Table I re?ects the numerical interpretation of the described scenario,where player one is represented by the rows and player two by the columns.Moreover,each cell in the matrix contains two values:the left one is the row player’s sentence,the right one the column player’s sentence. With reference to table II,we denote the individual payoff if both players cooperate as’R’(Reward).If both players

cooperate defect

cooperate(5,5)(25,0)

defect(0,25)(15,15)

TABLE I

P RISONER’S DILEMMA

defect,they both earn the payoff’P’(Punishment).If one player cooperates and the other defects,former obtains payoff ’M’(Mysti?ed)and latter payoff’T’(Temptation).Moreover,

cooperate defect

cooperate R,R M,T

defect T,M P,P

TABLE II

P AYOFF RELATIONS WITHIN PRISONER’S DILEMMA

the PD is characterized by the following conditions:

T>R>P>M(3)

2R>T+M(4) where the second condition shows that in a repeated process, both player gain higher payoff if they cooperate than if they mutually defect and then share the total payoff.If there is no communication between the players,they both choose strategy D in order to maximize the achievable minimum payoff.This results in a payoff less than obtainable by a common choice for cooperation and therefore is known as the prisoner’s dilemma. Due to repetitive interaction between the players,known as the alternating continuous PD,we try to achieve a basic way of communication in order to achieve cooperation.

IV.S YSTEM MODEL

As previously mentioned,the investigations are focused on a coexistence of two competing operators.An operator is mod-eled by an AP and and a variable number of associated nodes. To investigate the consequences of access misbehavior we derived an analytical model.In order to justify the analytical model,we further implemented a simulation model,where all the MAC parameters are taken from[1].

A.Analytical model

The investigations of the analytical model are based on Bianchi’s[3]saturation model of the802.11a protocol.In this model,Bianchi focused on a scenario where all the involved nodes exhibit identical access behavior.Since in this paper the focus lies on competitive access between two or more networks,the existing model needs to be extended.To estimate the throughput of IEEE802.11a with no misbehaving nodes,Bianchi applied a two-dimensional Markov Chain of m backoff stages,where each stage represents the time of the backoff counter of each node.A transition between the states takes place upon a successful,respectively collided transmission[3].The access probabilityτof a node can be derived upon the stationary distribution of the chain,

τ=

2(1?2p)

(1?2p)(W+1)+pW(1?(2p)m)

(5)

3 where p is the conditional collision probability,W is the initial

contention window size CW min and m is the maximum back-

off stage.For the applications referring to the standard within

this paper,we set m equal to6.If we consider misbehaving

nodes using a?xed CW,regardless of their retransmission state

(m=0),5can be simpli?ed to the following expression.

τ=

2

W+1

(6)

The throughput calculations are based on the normalized throughput S,which is de?ned as the fraction of time where the channel is successfully used to transmit data.Based on the access probability of each node,we can compute the proba-bility that there is at least one transmission in a speci?c time slot.Focusing on a scenario with M competitive operators, possessing n k nodes applying different contention windows cw k this probability is given by:

P tr=1?

M

k=1

(1?τk)n k(7)

The probability P si,that a transmission initiated by network i is successful is given by the probability that exactly one node of network i is transmitting,whereas the nodes of the competing networks(n k)remain inactive.

P si=n iτi(1?τi)(n i?1)

M

k=1,k=i

(1?τk)n k(8)

Let us now de?ne the probability of a successful data trans-mission P s regarding all the competing networks.To obtain P s,we need to compute the probability of the union of the in-dividual probabilities of successful data transmission(P si)[4, p.34].Let us therefore de?ne A i as the event of a successful individual transmission of network i(P si=P[A i]).

P M

i=1

A i

=

M

j=1

P[A j]?

j

P[A j∩A i]+ (9)

+(?1)M+1P[A1∩···∩A M](10)

Regarding the fact,that the probability of more than one network successfully transmitting in the same time slot is equal to zero,the expression is simpli?ed to:

P M

i=1

A i

=

M

i=1

P[A i](11) P s=

M

i=1

P si(12)

Focusing on two competing operators possessing n1respec-tively n2number of nodes,applying CW1,CW2the expres-sions7,8and12can be rewritten as:

P tr=1?(1?τ1)n1(1?τ2)n2(13)

P s1=n1τ1(1?τ1)(n1?1)(1?τ2)n2(14)

P s2=n2τ2(1?τ2)(n2?1)(1?τ1)n1(15)

P s=P s1+P s2(16)The normalized throughput S can now be express as the ratio S=

E[payload information transmitted in a slot time]

E[length of a slot time]

(17) The average amount of payload information within network i transmitted in a slot time is P si L,since a successful transmission occurs in a slot time with probability P si.Further on a?xed packet size of L is assumed within each transmission attempt.The average length of a slot time is based on the fact that with probability1?P tr the slot is empty,with probability P s it contains a successful transmission,and with probability 1?P s a collision can occur.The throughput for network i can be written as

S i=

P si L

(1?P tr)σ+P s T s+(1?P s)T c

(18) where,T s is time time needed for a successful transmission, T c the time a channel is busy due to a collision,andσis the duration of an empty time slot.As previously mentioned,L represents the data packet size which is assumed to be?xed 256bytes for each transmission.

B.Simulation model

This section describes the models,deduced from the IEEE 802.11a standard,we implemented in the simulator.

1)Traf?c model:Both of the operators are assumed to operate in saturated conditions.Hence,each node always has a packet to transmit upon successful transmition.The investigations are therefore solely focused on the achievable saturation throughput from the systems point of view.No delay constraints are considered.

2)User distribution:The distribution of the nodes is con-sidered to be uniform over the area.The user allocation is deemed to be static and unchanged throughout the investi-gations.Further on the size of the area was chosen that no hidden terminals occur.Hence,a collision can only appear due to identical backoff-values of the contending nodes.

3)PHY layer:We assume perfect channel conditions and ?xed modulation level for all the transmissions.Therefore the length of a successful packet transmition remains constant for all the contending nodes.Each transmitted packet is chosen to be256byte.The relevant parameters for implementing the transmission sequences(Fig.1)are taken from[1].

V.P ERFORMANCE R ESULTS

The results are focused on two different approaches of the misbehaving operators.In the?rst approach,we analyze the superior performance an operator can gain due to the adaptive channel access in expense of its rival.The second approach investigates the scenario,where both of the operators have the ability to misbehave,i.e they both can adapt the CW size.

A.Standard access vs adaptive access

Fig.2shows the individual saturation throughput S of both networks versus the CW size of the misbehaving network. We therefore denote the network operating according to the standard as N1and the misbehaving network as N2.Two

4

different network sizes are considered(7STAs+1AP and10 STAs+1AP for each network).Focusing on the characteristics of S(N2),it is straight forward that the operating point N2is seeking for is given by the maximum of the concave curves. Moreover,the graphs clearly show that this operating point

Fig.2.Throughput of N1and N2

depends on the overall number of contending nodes of both networks.The numerical values of the two operating points show,that N2gains superior performance due to the adaptive modi?cation of the CW size.Fig.2further indicates that the results from the analytical model?t very accurately with the empirical results deduced from the simulation model.

B.Adaptive access vs.adaptive access

Fig.3depicts the saturation throughput dependent on the CW size.The solid line equals to the sum of the individual throughputs(S(N1)+S(N2)),considering that both networks apply an identical but variable CW size.The line achieves a maximum of0.79at a CW size of90(CW(N1)=CW(N2)=90). This point is de?ned as the maximum achievable S,where the resource is equitably shared.The saturation throughput of the individual network is represented by the dotted line. Networks act cooperatively seek to operate in this maximum which results in a superior performance,compared to the stan-dardized CSMA/CA DCF operation.Speci?cally for scenarios with higher density of contenting STAs(>20)the effect becomes more signi?cant.

A further interesting point is to investigate possible gain due to unilateral deviation from the operating point by one of the networks.The dashed line plots S(N1)as a function of CW(N1),whereas N2is working at the operating point and therefore is obliged to set its CW to CW(N2)=90.S(N1) shows that by choosing CW(N1)CW(N2)we can ascertain an increase of S(N2)in expense of S(N1).This behavior stems from the fact that we decrease the access probability of N1by increasing CW(N1).

S

a

t

u

r

a

t

i

o

n

T

h

r

o

u

g

h

p

u

t

S

Fig.3.Saturation throughput analysis

VI.G AME T HEORETICAL A PPROACH

A.Single stage game analysis

Considering a scenario with no feedback,i.e.the networks can only modify their contention window once,both networks act in a sel?sh manner and choose the contention window size maximizing their throughput.This type of interaction can be formulated as a single stage game.Due to the competitive medium access this strategy results in a throughput lower than provided by the standard.This type of network behavior stems from the uncertainty upon the rivals action and can be formulated as the prisoner’s dilemma[2].With reference to the previous section,the scenario of two networks,adaptively modifying the CW size,is modeled in a single stage game. Table III shows the resulting throughput for all possible N1↓N2→C S

C(0,396/0,396)(0,147/0,567)

S(0,567/0,147)(0,293/0,293)

TABLE III

G AME SCENARIO

combinations of actions.If both networks cooperate and access the channel applying the same CW,they gain an individual relative throughput of0,396.In the case where both networks implement the802.11a protocol,a relative saturation through-put of0,365could only be provided.If one of the networks acts sel?shly,it obtains a throughput of0,567whereas the throughput of the cooperative network decreases to0,147.If both network act sel?shly,the individual throughput equals 0,293.The unique Nash Equilibrium indicates,that both oper-ators should act sel?shly(S,S).However,there exists a better solution where both network cooperate(C,C).To end up in this solution,a minimum of cooperation or trust is necessary, which is not conceivable in a single stage game,though. Further on,such a solution is not very stable due to the fact that a player can gain major bene?t if he misbehaves.The solution concept of the game is given as the minimax strategy[5,p.83]. Applying the minimax concept,a player chooses the strategy that maximizes it’s minimal payoff.Therefore the stable point

5 of the game is where both players act sel?sh.The model

shows us that the achievable throughput decreases,if both

network apply misbehavioral access strategies,given that there

is no cooperation or primitive way of mutual communication.

To model mutual communication,the prisoner’s dilemma is

reformulated in a repeated single stage game,known as a multi

stage game.

B.Multi stage game analysis

Since none of the networks is interested in the operating

point described in the previous section,they both have an

incentive to cooperate in order to achieve higher throughput.

To achieve cooperation,some simple interaction between the

players is necessary.In the last part of the paper we address

this problem by modeling the networks competitive scenario

as a sequence of single stage games,known as in?nite multi

stage games[5].Now one network has the possibility of

punishing the other network if that network misbehaves.The

investigations show that cooperation is in fact the better

strategy for most cases if we consider in?nite multi stage

games.

The single stage game analysis has shown that we end up in

a prisoner’s dilemma,where a sel?sh action for both players

appears to be the NE strategy.With the repeated prisoner’s

dilemma we try to achieve some cooperation in order to obtain

a higher saturation throughput.Therefore we make use of the

TFT[2]and the GRIM[6]trigger strategies.In the following

sections,we investigate the GRIM and TFT strategies in order

to evaluate whether they are a NE.

1)TFT Strategy:The TFT strategy,is a NE strategy,if

none of the players can pro?tably,unilaterally deviate by

choosing another strategy.Since the TFT strategy is based on

cooperation,it is interesting to investigate whether a player

can pro?t while acting sel?shly throughout the whole game

(ALLS).The result for a constant sel?sh action is:

S i(ALLS|TFT)>S i(TFT|TFT)(19)

S SC+

δ

1?δ

S SS>

1

1?δ

S CC(20)

0.624>δ(21)

The notations as well as the numerical values are taken from table III.The result shows that a player will continuously act sel?sh beginning from the?rst stage if his discounting factor is smaller than0.624.Another possible scenario is to act sel?sh in a single stage L of the game(SEFL).

S i(SEFL|TFT)>S i(TFT|TFT)(22) S SCδL+S CSδL+1>S CCδL+S CCδL+1(23)

0.687>δ(24) Focusing on the two results,we can show that for a discounting factorδ>0.687we can sustain TFT against a single sel?sh action(SEFL)as well as continuous sel?sh actions(ALLS). Therefore,TFT is a NE if the discounting factor isδ>0.687.

2)GRIM Strategy:To investigate the GRIM strategy, we make use of the same sel?sh action types like in the previous section.In the case of constant sel?sh action S i(ALLS|TFT)>S i(TFT|TFT),we obtain identical results to the TFT case(0.624>δ).The second strategy of sel?sh actions is de?ned by a continues sel?sh action,triggered at stage L(SEFL).The payoffs therefore only differ from stage L on:

S i(SEFL|GRIM)>S i(GRIM|GRIM)(25)

S SCδL+S SS

δL+1

1?δ

>S CC

δL

1?δ

(26)

0.624>δ(27) The results show,that for a discounting factorδ>0.624 the GRIM strategy can sustain against single and continuous sel?sh actions(ALLS).The GRIM strategy is a NE ifδ> 0.624.

We can deduce that for the speci?c scenario,the GRIM strategy is more”robust”against attempts of sel?sh actions. The more tempting it is to act sel?sh,the higher a player needs to value the future in order to sustain cooperation.

VII.C ONCLUSIONS

The results have shown that the achievable saturation throughput of the standardized IEEE802.11a protocol depends on the number of contending stations.Due to the adaptive modi?cation of the CW,a network can permanently provide a maximal achievable saturation throughput of≈0.8,indepen-dent of the network size.

Considering the scenario of two networks,where N1ac-cesses the channel according to the standardized DCF and N2 adapts the CW in order to achieve maximal saturation,N2 considerably outperforms N1.

If both networks have the ability to adapt their CW to the traf?c conditions,the scenarios becomes different.The resulting interaction can be modeled by a prisoner’s dilemma, resulting in lower performance than provided by the stan-dard.This performance loss is a result of lacking informa-tion between the contending networks.Due to the repeated interaction,modeled by a repeated prisoner’s dilemma,the networks create a basic way of communication which results in increased performance.Under some speci?c assumptions and trigger strategies,the overall throughput outperforms the standard.

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[2]T.Shishido and H.Shishido,“Alternating continuous prisoner’s dilemma,”

in IEEE International Conference Systems and Cybernetics,vol.2,oct 2001,pp.1276–1281.

[3]G.Bianchi,“Performance analysis of the ieee802.11distributed coor-

dination function,”in IEEE Selected Areas in Communications,vol.18, march2000,pp.535–547.

[4] A.Leon-Garcia,Probability and Random Processes for Electrical Engi-

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[5]T.Basar and G.Olsder,Dynamic Noncooperative Game Theory,Second

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研究生英语学术论文写作(考试大概)

Ⅰ. Gone up → increased set up → established Put up with → tolerate looking into → investigating Figure out → determine put into practice → implement Come up with → developed make up → constitute Get rid of → eliminate keep up → maintain Gone down → decrease thinking → considering Ⅱ. Structure of Data Commentary Data commentaries usually has these elements in the following order. 1.location elements and/or summary statements 2.highlighting statements 3.discussions of implications,problems,exceptions,recommendations,or other interesting aspects of the data 可能涉及到排序题，有例如下： ①A computer virus is a program that is specifically and maliciously designed to attack a computer system,destroying data.②As business have become inceasingly dependent on computers,e-mail,and the Internet,concern over the potential destructiveness of such viruses has also grown.③Table X shows the most common sources of infection for U.S. businesses.④As can be seen, in a great majority of cases,the entry point of the virus infection can be detected,with e-mail attachments being responsible for nearly 9 out of 10 viruses.⑤This very high percentage is increasingly alarming,especially since with a certain amount of caution such infections are largely preventable.⑥In consequence,e-mail users should be wary of all attachments,even thoes from a trusted colleague or a known sender.⑦In addition,all computers used for e-mail need to have a current version of a good antivirus progarm whose virus definitions are updated regularly.⑧While it may be possible to lessen the likelihood of downloading an infected file,businesses are still vulnerable to computer virus problems because of human error and the threat of new,quickly spreading viruses that cannot be identified by antivvirus software. ①②→Theory and common beliefs. ③→The start ④⑤⑥⑦⑧→Implications Ⅲ.信息性摘要 An informative abstract,as its name implies,summarizes the key points in the RP.It is an overview that briefly state the purpose,methods,results and conclutions with quantitative information. 信息性摘要主要报道论文的研究目的、研究方法、研究结果与结论。它是论文全文的高度浓缩，相当于论文的简介或概要，但它又不是简单对原文篇幅进行按比例的缩减，而是要进行深入加工。 比较流行的信息性摘要架构有： ①Objective→Methodology→Results→Conclusions ②Background→Purpose and aim→Methods→Results→Conclusions ③Background+purpose→Methodology→Result→Conclusion

学术英语写作总结分析解析

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