Countering Selfish Misbehavior in Multi-channel MAC Protocols

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C M B DtimeATIM(PCLM)ACK(fj)ATIM(PCLM)ACK(fi)Fig. 4. M performs incomplete channel negotiation with B and C.However, nodes in the communication range of the receiverconsider the channel contained in the ATIM-ACK packet asreserved, since they could be hidden terminals to the sender.Multiple incomplete negotiations lead to the distortion of thePCL at all nodes around the receiver. We emphasize thatincomplete negotiations can occur under benign conditionsif the sender and the receiver do not agree on the channelselection. This could be due to other existing reservations thatare only known to one of the two parties.An example of an incomplete negotiation is shown in Fig.4. Node M initiates negotiations with B and C, but does notrespond to the ACKs received by each node. As a result, thepriorities of channels f i and f j are lowered at the PCL of anynode that overhears the ACKs from B and C.C. Optimal Misbehavior StrategiesIn this section, we analytically derive the optimal MRAstrategy for guaranteeing exclusive access of the misbehavingnode M to a desired subset of channels. In our analysis,we consider M contending with well-behaved pairs that wantto place l reservations during one control phase. For thesimplification of our analysis, we model the control phase as aseries of reservation rounds. A reservation round consists of thethree-way handshake process (exchange of ATIM, ATIM-ACKand ATIM-RES packets) detailed by the MMAC protocol.Number of reservations: The number of reservations dneeded by M during the control phase to guarantee the exclusiveuse of n M out of n available channels during the dataphase is given by the following proposition.Proposition 1: A misbehaving node M can gain exclusiveuse of n M out of n available channels when it successfullylplaces d = ⌈n−n M⌉n M consecutive reservations before anywell-behaved node can place a reservation. Parameter l definesthe number of reservations to be placed by the contending wellbehavednodes within the same collision domain.Proof: Without loss of generality, assume that M wantsto isolate channels {f 1 , f 2 , . . . , f nM }. To prevent well-behavednodes from placing a reservation on {f 1 , f 2 , . . . , f nM }, thepriority of each of those channels in the PCLs of the wellbehavednodes must be lower than the priorities of all remaining(n−n M ) channels at any time. Let M lower the priority of eachof the n M channels by x, by placing d = n M x consecutivereservations, evenly distributed on the n M channels. It takes(n − n M )x reservations until the priorities of the remaining(n − n M ) channels become equal to x. Equating (n − n M )xto the l reservations to be placed by well-behaved nodes andsolving for d yields the desired result (d is an integer). It isstraightforward to show via example, that placing d reservationsTleaf vertexlevel 0R(u 2,5)u 1,1 u 1,2 u 1,3 u 1,4{∅} {A} {B} {A,B}level 1u 2,1 u 2,2 u 2,3 u 2,4 u 2,5 u 2,6 u 2,7 u 2,8.{∅} {A} {∅} {B}..{∅}Fig. 5.{A}{B}{A,B}Representation of the MMAC control phase as a rooted tree.is a sufficient but not necessary condition for isolating n Mchannels.Proposition 1 suggests that the best strategy for M is to placed consecutive reservations before any contending pair obtainsthe opportunity to reserve a channel. This can be achievedby attempting a reservation in every reservation round untild reservations are successfully placed and the priority of eachtargeted channel is lowered by ⌈n−n M⌉.Number of reservation rounds: We now evaluate thenumber of reservation rounds required until M successfullyplaces d consecutive reservations. This number is computedunder the assumption that M follows the optimal strategy ofattempting a reservation on every reservation round by selectinga zero backoff value.Let S denote the random variable representing the number ofreservation rounds until d reservations are successfully placedby M. To find the probability mass function (pmf) of S, wemodel the MMAC control phase contention process after arooted tree T with a vertex set V. For a vertex u i,j ∈ Vlocated at the i th level of T , let p(u i,j ) denote the parent ofu i,j . Let also R(u i,j ) denote the path traversed from the rootof T to u i,j . The i th tree level represents the i th reservationround. At each reservation round, a well-behaved pair couldbe in either transmit state or backoff state, depending on thebackoff value selected by the sender of the pair. A vertex u i,j atlevel i represents a unique combination of the possible statesof the senders of well-behaved pairs contending for the setof channels. We denote the probability of occurrence of thatcombination as Pr[u i,j ]. The set of leaf vertices at level i,denoted by L i , corresponds to all possible state combinationsfor which well-behaved senders do not transmit at reservationround i, thus allowing M to seize the control channel.The first two levels of the tree model for three contendingpairs (one misbehaving and two well-behaved ones) is shown inFig. 5. The senders of the two well-behaved pairs are denotedby A and B. For each vertex, the corresponding set of nodes intransmit state is indicated within brackets. For instance, vertexu 1,4 at level 1 with set {A, B}, represents the state where bothA and B transmit in reservation round 1 (due to selecting abackoff value equal to zero). Based on the tree model of Fig.5, the pmf of S is given by the following proposition.l
Proposition 2: The pmf of S is given by,∑Pr[S = d + l] = P r[R(u l+1,j )], l ≥ 0, (1)u l+1,j ∈L l+1where L l+1 is the set of leaf vertices at level l + 1 of T ,Pr[R(u l+1,j )] is the probability of events expressed by thevertices along path R(u l+1,j ) of T given by,∏Pr[R(u l+1,j )] =Pr[u w,k ], 1 ≤ w ≤ l + 1, (2)u w,k ∈R(u l+1,j )and Pr[u w,k ] is given by,() nu1Pr[u w,k ] =min{cw w−1 , cw max }() np−n1u· 1 −, (3)min{cw w−1 , cw max }where n u and n p are the number of nodes in transmit state foru w,k and p(u w,k ) respectively, and cw i = 2 i−1 cw 0 , i ≥ 1.Proof: We first show that if M adopts the optimal strategyof attempting a reservation at every reservation round (i.e.always selecting a zero backoff value), then after M’s firstsuccessful reservation, M will successfully place the remaining(d − 1) reservations in the next (d − 1) reservation rounds,without contending. In order for M to have a successfulreservation on a given reservation round, all senders of the wellbehavedpairs must have a backoff counter greater than zero.Because M chooses a zero backoff value on all consecutiverounds, well-behaved nodes do not get the opportunity todecrement their backoff counter, once they have selected abackoff value greater than zero. Thus, M successfully placesthe remaining (d − 1) reservations in the following (d − 1)rounds. For the (l + 1) th (l ≥ 0) reservation round, the eventthat none of the well-behaved nodes is in transmit state isrepresented by the leaf vertices at level (l + 1). Summing overall probabilities of arriving at the leaf vertices of level (l + 1),yields the probability of having M’s first successful reservationat the (l + 1) th reservation round. Or equivalently, this eventyields the probability of finishing d reservations at reservationround (l + 1) + (d − 1) = d + l. Eq. (1) follows by noting thatall events at a given level are mutually exclusive.The probability of arriving at any vertex u i,j is equal to theprobability product of all vertices along the path R(u i,j ). Thispath corresponds to a unique combination of events (transmitstates) at reservation rounds 1 to (i − 1) that lead to theunique combination of transmit/backoff states expressed byu i,j . Because backoff values are independently selected ateach round, Pr[R(u i,j )] is equal to the product of the vertexprobabilities, which yields eq. (2).Finally, we compute the probability Pr[u w,k ] of the uniquecombination of transmit/backoff states expressed by vertexu w,k ∈ V. Let n u denote the number of transmitting nodesin u w,k , and n p the number of transmitting nodes in the parentnode p(u w,k ). The CW of a transmitting node at level wis equal to min{cw w−1 , cw max } since that node must havecollided (w − 1) times with M in order to be transmittingat reservation round w. Moreover, the probability of a nodetransmitting at reservation round w is equal to the probabilityof selecting a zero backoff value at that round, which is equal to1min{cw w−1,cw max}. Eq. (3) follows by noting that it expressesthe probability of exactly n u nodes being in transmit state atstage w when n p nodes were in transmit state in stage (w −1).This is equivalent to a particular subset of size n u choosinga zero backoff value, while the complementary subset of size(n p − n u ) chooses any other value. All nodes choose theirbackoff values independently of each other, independently ofprevious rounds, and in a random fashion. Therefore, a node is11in transmit state with probabilitycw w−1, orcw maxif the CW hasreached its maximum value. We note that the event expressedby eq. (3), corresponds to one unique combination of transmitand backoff states for the participating senders, and not anycombination that yields n u transmitting nodes. Therefore, it isnot given by a binomial distribution.Adaptive reservation strategy: In realistic scenarios, thenumber of reservations l to be placed by contending nodes ata given control phase is not known a priori. To account for anunknown l, we propose an adaptive strategy for capturing n Mchannels which is as follows.Step 1: Misbehaving node M lowers the priority of the n Mtargeted channels by one unit, by selecting a zero backoff valueand placing n M reservations before any other node can placea reservation. It then defers from further reservations.Step 2: M repeats Step 1 every time (n − n M ) reservationsare placed on the remaining (n − n M ) channels.It is straightforward to show that the n M targeted channelsalways have a lower priority than the remaining (n−n M ) ones.Therefore, based on the PCL rules, a well-behaved node willalways select one of the (n − n M ) channels, giving exclusiveuse of the n M channels to M. Moreover, this adaptive strategyis optimal in the number of reservations needed for capturingn M channels. If the number of reservations placed during Step1 is less than n M , some of the targeted channels will haveequal priority as the remaining (n − n M ) ones and therefore,be equally likely preferred by well-behaved nodes. The adaptivereservation strategy shows that the condition of Proposition 1is a sufficient but not necessary condition for the exclusive useof n M channels by M.V. MITIGATING MMAC MISBEHAVIORA. Mitigation of the Backoff Manipulation AttackWe first consider the manipulation of the backoff mechanismwhich is adopted during both the control and data phases.As explained in Section II, mechanisms proposed for singlechannelnetworks (e.g., [10], [16]) are not adequate for multichannelnetworks, because they are not designed to consistentlymonitor parallel transmissions on multiple channels. To addressthis limitation, we propose a BMA detection scheme that utilizesa priori publicized backoff sequences to detect deviationsfrom a random backoff strategy during both the control and thedata phase. Our scheme consists of the backoff generation andthe backoff monitoring modules.
Page 2 and 3: al. proposed a system called DOMINO
Page 6 and 7: Backoff generation module: The back
Page 8 and 9: T (Kbps)# of reservations3002502001

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