Distributed Reaction Mechanisms to Prevent ... - Semantic Scholar
Distributed Reaction Mechanisms to Prevent Selfish Misbehavior in Wireless Ad Hoc Networks Neeraj Jaggi, Vamshikrishna Reddy Giri and Vinod Namboodiri Department of Electrical Engineering and Computer Science, Wichita State University, Wichita, KS 67260 Email:{neeraj.jaggi, vrgiri, vinod.namboodiri}@wichita.edu Abstract—We address the issue of misbehavior detection and reaction in IEEE 802.11 based Ad Hoc networks. Selfish misbehavior involves disobeying standard protocol mechanisms to gain unfair access to the channel at the expense of other users. We outline conditions on genuine (non-misbehaving) node’s throughput to guarantee the presence of misbehavior, and propose nonadaptive and strong reaction mechanism for such aggressive misbehaviors. For selfish misbehaviors which do not result in severe throughput degradation for genuine users, we design an adaptive reaction mechanism. Both mechanisms are distributed in nature, rely only upon local information available at genuine nodes, and are thus easily implementable in practice. Proposed reaction mechanisms provide the necessary disincentive towards selfish misbehavior, and are aimed at preventing misbehavior. Index Terms—Selfish misbehavior, Reaction mechanisms
I. I NTRODUCTION Contention for wireless spectrum has never been higher with rapid increase in wireless enabled devices. These devices compete for bandwidth in a wireless LAN leading to increased congestion (and increased contention in channel access). A user could employ the following two basic approaches to obtain better performance in the presence of increasing resource constraints in wireless channels: (i) rely on the cognitive radio paradigm to seek better spectrums to use, and move away from congested channels [1], or (ii) behave selfishly to gain unfair access to the channel at the expense of other users [2]. The first approach involves hardware and infrastructure upgrades, and is expensive. However, the latter approach can be achieved by modifying the radio to disobey standard protocol mechanisms, and is becoming easier to incorporate with increased programmability of network devices [2] and with software defined radios [3]. Today, selfish misbehavior is an easy way out for users to improve their performance, for instance in a 802.11 hotspot. Moreover, such misbehaviors are also a matter of concern in cognitive radio networks [4]. Selfish misbehavior employed by one or more users could starve other genuine nodes of throughput, depending upon the level or aggressiveness of such misbehavior [5], [6], [7]. A selfish user could employ mildly aggressive cheating with respect to backoff rules [8], [9], or the choice of contention window [10], DIFS or SIFS. Note that selfish misbehavior is mild (compared to malicious misbehavior, such as jamming or DoS attacks) and is employed to increase one’s own throughput share at the expense of other genuine users. Thwarting This work was supported in part by the Army Research Office under DEPSCoR ARO Grant W911NF-08-1-0256.
such misbehavior requires the network to both detect the misbehavior, and then react towards it [7]. Most prior work has focused only towards the detection problem, with many of them relying upon a centralized infrastructure or protocol modifications for detection [9], [11], [12], [13]. In this paper, we focus towards distributed reaction mechanisms to prevent selfish misbehaviors. Existing reaction mechanisms at genuine nodes attempt to penalize [8], [9] or isolate [5] the selfish user. Among these [8], [9] rely upon reliable collaborations with the receiver nodes in the network to be effective, and thus assume that the receiver is a genuine (non-misbehaving) node. [5] suggests that isolation of misbehaving nodes is not the best strategy to react, as it affects the performance at network and higher layers, as more and more nodes get isolated. This paper considers selfish misbehavior achieved via modifications to IEEE 802.11 Binary Exponential Backoff (BEB) algorithm employed in Distributed Coordination Function (DCF) mode, and proposes two reaction mechanisms that provide the much needed disincentive to misbehaving node(s), in order to prevent selfish misbehaviors. The first mechanism is an analytical, non-adaptive and aggressive reaction strategy, and is applicable to aggressive misbehaviors. The second mechanism is an adaptive and distributed algorithm, which allows genuine nodes to adjust their reaction over time in response to the level of misbehavior detected in the network. Different types of MAC layer misbehaviors are possible using modifications to the BEB algorithm [6]. In addition, the misbehaving user may alter its behavior (either become more aggressive or leave the network), and the number of misbehaving users could change over time. Thus, there is a need for a uniform, adaptive, and distributed reaction mechanism, wherein the genuine users are able to adjust their reaction over time. Many mild misbehaviors do not yield additional throughput to the misbehaving node, and do not cause significant throughput degradation at genuine users (particularly in lightly loaded network scenarios) [6]. The reaction should thus focus towards misbehaviors which are effectively measured or detected using a genuine node’s throughput degradation. Therefore, the proposed mechanisms are based upon the node’s own throughput, do not require any coordination among the genuine nodes, and are thus easy to implement and deploy. The proposed reaction mechanisms strive to achieve the following objectives – (a) guarantee that the misbehaving user’s throughput reduces below what it would have been if the user had not misbehaved, and
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bi,k = bi,0 ∀i ∈ (0, m), ∀k ∈ (0, Wi − 1). (4) m Wi −1 b0,0 is determined using: i=0 k=0 bi,k = 1, which simplifies to (assuming 2p < 1),
Worst Case Access Probability.
(b) provide fairness amongst the post-reaction throughputs achieved by genuine nodes.
m W i −1
In the presence of aggressive misbehaviors, the genuine nodes’ throughput degrades severely. We outline conditions to detect such extreme scenarios, and propose a reaction mechanism which could be employed in these scenarios. Detection Scheme: Consider an IEEE 802.11 wireless LAN with N nodes, where all nodes are genuine, i.e. they correctly follow BEB. We derive a lower bound on the channel access probability of a node (and thus its throughput). Every time a node chooses a backoff value uniformly at random from 1 . [0 . . . CW − 1], it could choose CW − 1 with probability CW Let node A choose backoff values in this way every time. The channel access probability (τ ) and conditional collision probability (p) are obtained using equations (7) and (9) in [14]. The access probability of node A, denoted τA , is minimum (= τmin ) since the node chooses the largest backoff value in the allowed interval every time. Using Markov Chain analysis, we characterize the steady state probability τmin . The Discrete-time Markov Chain model for the backoff window size is given in [14]. Let Wi denote the contention window size during stage i. The state of the system is characterized as (s, b), where s ∈ (0, m) is the backoff stage of the node and b is the current backoff value of the node. Figure 1 depicts the state evolution for the DTMC for the node A. The transition probabilities for node A are given by:
m
bi,k = bi,0 Wi i=0 k=0 i=0 m−1 pm b0,0 2m W0 pi b0,0 2i W0 + 1 − p i=0 m−1 (2p)m i W0 b0,0 (2p) + 1−p i=0
m m
1 =
II. N ON - ADAPTIVE R EACTION M ECHANISM = =
1 − (2p) (2p) + 1 − 2p 1−p 1 − p(1 + (2p)m ) . = W0 b0,0 (1 − 2p)(1 − p) = W0 b0,0
(5)
This implies, b0,0 =
(1 − 2p)(1 − p) . W0 [1 − p(1 + (2p)m )]
(6)
Now, we can express the transmission probability of node A, denoted τA , as τA =
m i=0
bi,0 =
1 − 2p b0,0 = . 1−p W0 [1 − p(1 + (2p)m )]
(7)
Note that τA is less than the steady-state transmission probability τ of a general node in the network, given by (from equation (7) in [14]), τ=
2(1 − 2p) , (1 − 2p)(W0 + 1) + pW0 (1 − (2p)m )
(8)
The conditional collision probability is given by [14],
P {i, k|i, k + 1} = 1, i ∈ (0, m), k ∈ (0, Wi − 2) P {0, W0 − 1|i, 0} = 1 − p, i ∈ (0, m) P {i, Wi − 1|i − 1, 0} = p, P {m, Wm − 1|m, 0} = p.
bi,0 = pi b0,0 0 < i < m pm b0,0 . bm,0 = (2) 1−p
p = 1 − (1 − τ )N −1 .
i ∈ (1, m) (1)
Let bi,k denote the steady-state probability of state (i, k) for node A. We have,
(9)
Note that τA < τ since (2p)m < 1. It is interesting to observe that when m = 0, i.e. no exponential backoff is considered, τA = W10 < τ = W02+1 for W0 > 1. Here W0 = CWmin . As m increases, the difference between τA and τ increases. Since τA is the minimum transmission probability
possible for a node in the presence of all genuine nodes (i.e. in the absence of misbehavior), we also denote τA as τmin . 1 Lemma 1: For all m ≥ 0 and W0 ≥ 1, the worst case transmission probability τmin of a node in the network satisfies the following bound: τmin > τ2 . Proof: From equations (7) and (8), we have, τmin 1 (1 − 2p) = + . τ 2 2W0 [(1 − p) − p(2p)m ] Now using the assumption that 2p < 1, τmin > 12 . τ Let us compute the worst case throughput of node A in the network in the presence of all genuine nodes. Node A achieves the least throughput when the N −1 nodes in the network have access probability τ (given by (8)), and the node A has access probability τA (given by (7)). Using the arguments in [14], the throughput achieved in the network is given by, T =
Ps Ptr E[P ] . (1 − Ptr )σ + Ptr Ps Ts + Ptr (1 − Ps )Tc
(10)
where, Ptr is the probability that there is at least one transmission in the considered time slot, and equals 1 − (1 − τ )N , and Ps is the probability that a transmission is successful, and )N −1 equals nτ (1−τ . Here, E[P ] denotes the average packet Ptr length, and σ, Ts and Tc denote empty slot time, average time taken for a successful transmission and average time taken for an unsuccessful transmission respectively. The denominator in (10) denotes the average length of a time slot. Assuming each node gets a fair share of the LAN throughput, the throughput achieved by a node (other than A), denoted T0 , is given by, T0 =
T . N
(11)
With node A having access probability τA < τ , let the A and PsA (PsA denotes corresponding parameters be denoted Ptr the probability that node A’s transmission is successful), given by, A Ptr = 1 − (1 − τA )(1 − τ )N −1 ,
PsA =
τA (1 − τ )N −1 . A Ptr
Lemma 2: The worst case throughput achieved by a node in the network, denoted Tmin , satisfies the following bound: Tmin ≥
τmin 1 T0 > T0 τ 2
. Proof: Assuming, σ, Ts and Tc remain the same, the throughput achieved by node A, denoted Tmin , is given by, Tmin =
A E[P ] PsA Ptr . A A A (1 − P A )T A (1 − Ptr )σ + Ptr Ps Ts + Ptr c s
1 Note that this analysis is applicable if the number of nodes N is sufficiently large, and thus p is still approximately given by (9).
τA A A We have, Ptr Ps = τA (1 − τ )N −1 = N τ Ptr Ps . The expected length of a time slot would reduce when node A has transmission probability τA < τ , compared to the case where all nodes have same transmission probability τ . Therefore, denominator in the above expression is less than denominator in (10). Thus, τA τA 1 Tmin ≥ N τ T = τ T0 > 2 T0 , from Lemma 1. τmin is the minimum access probability a genuine node could possibly have in the absence of any misbehavior. Therefore, if a node’s throughput falls below T20 , it implies misbehavior almost surely, and hence the node declares detection of a misbehavior. Note that this detection rule can be used to detect the presence of any misbehavior type, as long as the throughput degradation caused is severe. For mild misbehaviors, we design a distributed algorithm in Section III. Reaction Mechanism: Once a misbehavior has been detected using the above policy (and hence an aggressive misbehavior is assumed), following reaction mechanism is employed to penalize the misbehaving user(s). All the N − 1 genuine nodes, upon detection of misbehavior, choose a constant contention window size = W , and do not vary the window size. From [15], each node transmits in a slot with probability τ = W 2+1 . The probability that none of the N − 1 genuine N −1 . Let B nodes transmits in a time slot equals (1 − τ ) denote the channel bandwidth. The maximum throughput N −1 . available to the misbehaving user is given by, B ·(1 − τ ) Now, W is chosen such that,
max W s.t.
B · (1 − τ )
N −1
< T0 .
(12)
Thus the genuine nodes choose a constant contention window size small enough to guarantee that the throughput available to misbehaving user is less than T0 (the genuine throughput share the user would get in the absence of misbehavior). III. A DAPTIVE R EACTION M ECHANISM In this section, we design an adaptive and distributed reaction algorithm for the genuine nodes to react against mildly selfish misbehaviors. Each genuine node measures its throughput degradation with respect to its saturation throughput share T0 given by (11). The reaction aggressiveness is made proportional to the level of suspected selfishness, and in most cases, the reaction is not as strong so as to lower the overall network throughput tremendously. Let us consider the saturation throughput scenario with N nodes. Using Bianchi’s analysis, let the individual fair throughput of each node under saturation conditions equal T0 (as given by (11)). Let us consider that one of the nodes is misbehaving. This would lower the throughput observed by the genuine nodes. Let T0o be the throughput observed by one of the genuine nodes. Clearly, T0o < T0 . A misbehavior is detected if the observed throughput T0o reduces below DtnT hr ∗ 100 %, i.e., T0o < DtnT hr T0 . A. Reaction Algorithm The objective is to reduce the throughput achieved by the misbehaving node to less than T0 . A secondary objective is to
achieve post-reaction fairness among the throughputs achieved by genuine nodes. The genuine nodes use an appropriately chosen constant contention window size (denoted CWf ix ) during the reaction response. The reaction algorithm is described in Algorithm 1. DtnT hr is set to 0.8. Thus, a misbehavior is detected if the observed throughput T0o reduces below 80%, i.e., T0o < 0.8T0 . Note that the choice of 0.8 is made in order to address the tradeoff between the need to (a) apply the reaction early, and (b) to avoid false misbehavior detection. BebP ktT hr is set to 10 packets. Increasing ReaP ktT hr (while keeping BebP ktT hr constant) leads to reaction being employed for a larger fraction of time. Similarly, reducing CWf ix leads to a stronger reaction response. We simulate and observe the impact of this reaction algorithm using NS-2 for various choices of CWf ix and ReaP ktT hr. Network parameters used include N = 10 nodes in a 802.11 wireless LAN, where 9 nodes are sending traffic at the rate of 100 pkts/sec to one common receiver. The channel capacity is 2 Mbps, packet size used is 512 bytes and slot time equals 20μs. Total traffic generated in the network amounts to a load of 3.68 Mbps, which is much higher than the channel capacity. All simulations are performed for a period of 900s. In the absence of misbehavior, average throughput achieved by a genuine node (T0 ) is around 125 Kbps. Next, we introduce selfish misbehavior at one of the sender nodes. Under α-misbehavior, a selfish node chooses its backoff uniformly at random from the interval [0 . . . α(CW − 1)] (instead of the interval [0 . . . (CW − 1)]), where 0 < α < 1. Thus the node ends up choosing a smaller backoff interval than it is supposed to, increasing its chances of accessing the channel next. The lower the value of α, the more aggressive is the misbehavior. Figure 2 depicts the throughput share of all nodes when one of the senders (node 1 in the figure) is configured to misbehave using α-misbehavior, with α = 0.1, while other senders follow standard BEB. We observe that the selfish node is able to get all its data traffic (409 Kbps) successfully transmitted by employing the α-misbehavior. All the genuine nodes suffer a throughput degradation of > 20%, and employ the reaction algorithm. Node 1 represents the misbehaving node in all the figures. With the reaction algorithm, the simulation time is divided into a pre-reaction time of 200s (where the genuine nodes observe their throughputs), and a post-reaction time of 700s
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Algorithm 1 Reaction Algorithm using CWf ix while true do if T0o < DtnT hr T0 then Employ contention window CWf ix to successfully transmit ReaP ktT hr packets else Employ standard BEB to successfully transmit BebP ktT hr packets end if Recompute T0o during the above time interval end while
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(during which all nodes employ the reaction algorithm in a distributed manner). We observe the impact of reaction algorithm for various choices of CWf ix and ReaP ktT hr. Post-reaction throughput of a node is defined as the throughput achieved by the node during the post-reaction time. Figure 3 depicts the post-reaction throughput for (ReaP ktT hr, CWf ix ) tuple of (500, 6). With tuple (500, 6), total LAN throughput equals 1014 Kbps, and total throughput achieved by genuine nodes equals 954 Kbps. We observe that many reaction tuples are able to achieve fairness amongst the post-reaction throughputs achieved by genuine nodes. Therefore, the tuple which maximizes total throughput share of genuine nodes is desirable, and tuple (500, 6) seems to be the best choice among the ones considered. From these results, we infer that a desired reaction mechanism should not only consist of an appropriate reaction response (CWf ix ) but also an appropriate fraction of time that the reaction is applied. Also, the reaction response (in the form of the tuple) would need to vary for different misbehavior types. Next, we describe an adaptive algorithm which allows the genuine nodes to converge to an appropriate reaction response (a tuple) in a distributed manner. B. Design of Adaptive Algorithm We design an adaptive and distributed algorithm which allows the genuine node to dynamically probe the network using different tuples, and to eventually converge to an appropriate tuple. Note that different nodes may converge to different tuples. Once all genuine nodes have converged, the proposed approach is able to achieve the objectives of the reaction mechanism outlined in Section III-A. Figure 4 depicts the operation of a genuine node using the reaction mechanism with a given tuple. According to Algorithm 1, when T0o < 0.8T0 , fixed contention window is employed to successfully transmit ReaP ktT hr packets. We denote the periods of time when CWf ix gets employed as the
Y
N
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Y
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N
Y
time Tn < 0.8 T0
Ty > 0.8 T0
Tn < 0.8 T0
Ty > 0.8 T0
Ty > 0.8 T0
One cycle comprises of 25 Y intervals (Tc) Ty – Throughput observed during Y interval Tn – Throughput observed during N interval Tc – Throughput observed during one cycle
Fig. 4.
At the end of the cycle, new tuple is chosen based on Tc
Genuine node operation using adaptive algorithm.
Y periods, and when BEB is employed as the N periods. Note that the length of different Y (or N) periods may differ. Also, the sequence of Y and N periods may differ from that shown in Figure 4. Figure 4 depicts the scenario where Ty > 0.8T0 and Tn < 0.8T0 for all Y and N periods. The node employs the same tuple during one cycle of its operation, which is defined as time interval comprising of 25 Y periods. At the end of the cycle, the node checks its throughput over the entire cycle (denoted Tc ), and chooses the next tuple to be employed during the next cycle using Algorithm 2. Initially the node starts with a relatively mild reaction tuple of (100, 16). If the observed throughput Tc is still less than 75% of expected throughput T0 , the node increases the aggressiveness of its reaction quickly by doubling the ReaP ktT hr and cutting its CWf ix into half. Once the throughput of the node is > 80% of T0 and < 90% of T0 , the node increases the reaction aggressiveness slowly by using an additive increase and decrease of the tuple parameters respectively. If the throughput Tc becomes much greater than T0 , the node reduces the level of its reaction. We choose Δ = 10 Kbps. As long as the throughput of the node is satisfactory, i.e., 0.9T0 ≤ Tc ≤ T0 + Δ, the node employs the same tuple during the next cycle of its operation. The node is said to have converged to a tuple when it uses the same tuple for 4 consecutive cycles. Note that the choices made in Algorithm 2 are arrived at after experimenting with various choices, and choosing the ones which lead to faster convergence. The simulation time is increased to 20000 sec to allow all the genuine nodes to converge. C. Convergence Once a node has converged to a tuple, it does not change its tuple, and employs the same tuple thereafter. When all the genuine nodes in the network have converged (to their respective tuples), and the network behavior stabilizes, we refer to the remaining simulation time as the post-convergence period. Post-convergence throughput of a node is defined as the throughput achieved by the node during the post-convergence period. We evaluate the adaptive reaction mechanism in terms of both the post-reaction throughput and the post-convergence throughput achieved in the network.
Algorithm 2 Dynamic computation of the tuple (ReaP ktT hr, CWf ix ) in the adaptive algorithm ReaP ktT hr ← 100; CWf ix ← 16 while not converged do Employ the tuple for the next cycle and compute observed throughput Tc during this cycle if Tc ≤ 34 T0 then ReaP ktT hr ← ReaP ktT hr ∗ 2 CWf ix ← min{CWf ix ∗ 12 , 2} else if 34 T0 < Tc ≤ 45 T0 then ReaP ktT hr ← ReaP ktT hr ∗ 32 CWf ix ← min{CWf ix ∗ 23 , 2} 9 T0 then else if 45 T0 < Tc ≤ 10 ReaP ktT hr ← ReaP ktT hr + 10 CWf ix ← min{CWf ix − 1, 2} else if Tc > T0 + Δ then ReaP ktT hr ← ReaP ktT hr − 20 CWf ix ← CWf ix + 1 else ReaP ktT hr ← ReaP ktT hr; CWf ix ← CWf ix end if end while
Figure 5 depicts the post-reaction throughput achieved in the network using the adaptive algorithm. During the entire course of the reaction, the average throughput of the node is quite close to T0 . The total LAN throughput post-reaction equals 1052.1 Kbps, and the total throughput achieved by genuine nodes equals 959 Kbps. Note that the post-reaction response is quite close to (and slightly better than) the desired behavior with tuple (500, 6) employed by all genuine nodes, as discussed in Section III-A. Figure 6 depicts the postconvergence throughput achieved in the network using the adaptive algorithm. The total throughput post-convergence equals 1048.5 Kbps, and the total throughput achieved by genuine nodes equals 964 Kbps. Thus, once the nodes have converged the genuine nodes’ throughput share increases slightly. Since all the genuine nodes would continue employing the reaction constantly hereafter, this throughput share would remain valid until the misbehaving node changes its behavior (increases the level of misbehavior or leaves the network). The genuine nodes could revisit their tuples from time to time in order to detect and adapt to such changes. Table I shows the converged tuples for all 8 genuine nodes. All the nodes converge to tuple similar to the desired tuple of (500, 6). Note that nodes with aggressive tuples achieve slightly larger post-convergence throughput share compared to nodes with less aggressive tuples (such as nodes 4 and 7), from Figure 6. Nodes with less aggressive tuples typically converge earlier. For instance, in this scenario, node 4 converged first at around 3000 seconds. The post-convergence throughput of the misbehaving node is significantly less than T0 . The Jain’s fairness index [16] computed over the post-convergence throughputs achieved by the genuine nodes equals 0.9988.
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misbehavior with α = 0.5), the convergence time reduces significantly (to 2400 sec). If adaptive reaction is used with aggressive misbehaviors, the genuine nodes may not be able to achieve a respectable throughput share even with the reaction, and may not converge. In such cases, the genuine nodes should switch to the reaction mechanism specified in Section II. IV. C ONCLUSIONS
Fig. 5.
Post-reaction throughput with adaptive algorithm.
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We proposed two reaction mechanisms based entirely upon local information, to prevent selfish misbehaviors in wireless networks. The non-adaptive reaction mechanism is suitable when a node suffers significant throughput degradation (> 50%). The adaptive reaction mechanism allows the genuine nodes to achieve satisfactory throughput in the presence of selfish misbehaviors, and to reduce the throughput of misbehaving node to less than what it would achieve without misbehavior. The reaction also leads to fairness among the post-reaction throughputs of genuine nodes.
Post-convergence throughput with adaptive algorithm.
R EFERENCES D. Discussion and Open Issues The adaptive and distributed reaction algorithm outlined above is based entirely upon a node’s observed throughput, and hence is easily implementable in practice. The mechanism only relies upon the knowledge of T0 at genuine nodes, which could be obtained by keeping track of one’s throughput or computing T0 (using (11)). Since genuine nodes make no assumption regarding the type or level of misbehavior, the mechanism is suitable for reacting towards many selfish misbehaviors. This mechanism is different from other reaction mechanisms which are geared towards specific misbehavior types [5], or rely upon reliable collaborations with other nodes in the network [8], [9]. The mechanism allows the genuine nodes to detect and adapt to changes, such as increase in level of misbehavior or misbehaving node leaving the network, by revisiting their tuples from time to time. Typically it takes around 18 decision instances (with decision instances around 10 minutes apart) for all genuine nodes to converge. Thus, one possible improvement could be to reduce the convergence time of the algorithm. However, since average post-reaction throughput for a genuine node is quite close to T0 , rate of convergence does not impact the objectives significantly. Also, when the node misbehavior is milder (αTABLE I C ONVERGED REACTION TUPLE FOR ALL GENUINE NODES . Node Number 2 3 4 5 6 7 8 9
ReaP ktT hr, CWf ix 445, 3 480, 5 400, 3 410, 4 450, 3 602, 6 410, 4 860, 7
[1] N. Mandayam, “Talk of cognitive radio networks & the future internet,” in DIMACS workshop on Next Generation Networks, August 2007. [2] L. Guang, C. Assi, and A. Benslimane, “Mac layer misbehavior in wireless networks: Challenges and solutions,” IEEE Wireless Communications, vol. 15, no. 4, pp. 6–14, Aug. 2008. [3] M. Dillinger, K. Madani, and N. Alonistioti, Software Defined Radio: Architectures, Systems and Functions. Wiley, 2003. [4] L. Giupponi and C. Ibars, “Misbehavior detection in cognitive and cooperative networks,” in Proc. IEEE GLOBECOM, Honolulu, HI, Nov. 2009, pp. 1–6. [5] L. Guang, C. Assi, and Y. Ye, “Dream: A system for detection and reaction against mac layer misbehavior in ad hoc networks,” Elsevier Computer Communications, vol. 30, no. 8, pp. 1841–1853, Jun. 2007. [6] V. R. Giri and N. Jaggi, “Mac layer misbehavior effectiveness and collective aggressive reaction approach,” in Proc. 33rd IEEE Sarnoff Symposium, Princeton, NJ, Apr. 2010, pp. 1–5. [7] A. A. C´ardenas, S. Radosavac, and J. S. Baras, “Evaluation of detection algorithms for mac layer misbehavior: theory and experiments,” IEEE/ACM Trans. Netw., vol. 17, no. 2, pp. 605–617, 2009. [8] P. Kyasanur and N. H. Vaidya, “Selfish mac layer misbehavior in wireless networks,” IEEE Transactions on Mobile Computing, vol. 4, no. 5, pp. 502–516, Sep. 2005. [9] L. Guang, C. Assi, and A. Benslimane, “Modeling and analysis of predictable random backoff in selfish environments,” in Proc. 9th ACM international symposium on Modeling analysis and simulation of wireless and mobile systems, Terromolinos, Spain, 2006, pp. 86–90. [10] M. Cagalj, S. Ganeriwal, I. Aad, and J.-P. Hubaux, “On selfish behavior in csma/ca networks,” in Proc. IEEE INFOCOM, Miami, USA, Mar. 2005, pp. 2513–2524. [11] M. Raya, I. Aad, J.-P. Hubaux, and A. E. Fawal, “Domino: Detecting mac layer greedy behavior in ieee 802.11 hotspots,” IEEE Transactions on Mobile Computing, vol. 5, no. 12, pp. 1691–1705, Dec. 2006. [12] S. Radosavac, J. S. Baras, and I. Koutsopoulos, “A framework for mac protocol misbehavior detection in wireless networks,” in 4th ACM workshop on Wireless security, Cologne, Germany, 2005, pp. 33–42. [13] Y. Rong, S.-K. Lee, and H.-A. Choi, “Detecting stations cheating on backoff rules in 802.11 networks using sequential analysis,” in Proc. 25th IEEE International Conference on Computer Communications (INFOCOM), Barcelona, Spain, Apr. 2006, pp. 1–13. [14] G. Bianchi, “Performance analysis of the ieee 802.11 distributed coordination function,” IEEE Journal on Selected Areas in Communications, vol. 18, no. 3, pp. 535–547, Mar. 2000. [15] G. Bianchi, L. Fratta, and M. Oliveri, “Performance evaluation and enhancement of the csma/ca mac protocol for 802.11 wireless lans,” in Proc. IEEE PIMRC, Taipei, Taiwan, Oct. 1996, pp. 392–396. [16] D.-M. Chiu and R. Jain, “Analysis of the increase and decrease algorithms for congestion avoidance in computer networks,” Computer Networks and ISDN Systems, vol. 17, no. 1, pp. 1–14, Jun. 1989.
I. I NTRODUCTION Contention for wireless spectrum has never been higher with rapid increase in wireless enabled devices. These devices compete for bandwidth in a wireless LAN leading to increased congestion (and increased contention in channel access). A user could employ the following two basic approaches to obtain better performance in the presence of increasing resource constraints in wireless channels: (i) rely on the cognitive radio paradigm to seek better spectrums to use, and move away from congested channels [1], or (ii) behave selfishly to gain unfair access to the channel at the expense of other users [2]. The first approach involves hardware and infrastructure upgrades, and is expensive. However, the latter approach can be achieved by modifying the radio to disobey standard protocol mechanisms, and is becoming easier to incorporate with increased programmability of network devices [2] and with software defined radios [3]. Today, selfish misbehavior is an easy way out for users to improve their performance, for instance in a 802.11 hotspot. Moreover, such misbehaviors are also a matter of concern in cognitive radio networks [4]. Selfish misbehavior employed by one or more users could starve other genuine nodes of throughput, depending upon the level or aggressiveness of such misbehavior [5], [6], [7]. A selfish user could employ mildly aggressive cheating with respect to backoff rules [8], [9], or the choice of contention window [10], DIFS or SIFS. Note that selfish misbehavior is mild (compared to malicious misbehavior, such as jamming or DoS attacks) and is employed to increase one’s own throughput share at the expense of other genuine users. Thwarting This work was supported in part by the Army Research Office under DEPSCoR ARO Grant W911NF-08-1-0256.
such misbehavior requires the network to both detect the misbehavior, and then react towards it [7]. Most prior work has focused only towards the detection problem, with many of them relying upon a centralized infrastructure or protocol modifications for detection [9], [11], [12], [13]. In this paper, we focus towards distributed reaction mechanisms to prevent selfish misbehaviors. Existing reaction mechanisms at genuine nodes attempt to penalize [8], [9] or isolate [5] the selfish user. Among these [8], [9] rely upon reliable collaborations with the receiver nodes in the network to be effective, and thus assume that the receiver is a genuine (non-misbehaving) node. [5] suggests that isolation of misbehaving nodes is not the best strategy to react, as it affects the performance at network and higher layers, as more and more nodes get isolated. This paper considers selfish misbehavior achieved via modifications to IEEE 802.11 Binary Exponential Backoff (BEB) algorithm employed in Distributed Coordination Function (DCF) mode, and proposes two reaction mechanisms that provide the much needed disincentive to misbehaving node(s), in order to prevent selfish misbehaviors. The first mechanism is an analytical, non-adaptive and aggressive reaction strategy, and is applicable to aggressive misbehaviors. The second mechanism is an adaptive and distributed algorithm, which allows genuine nodes to adjust their reaction over time in response to the level of misbehavior detected in the network. Different types of MAC layer misbehaviors are possible using modifications to the BEB algorithm [6]. In addition, the misbehaving user may alter its behavior (either become more aggressive or leave the network), and the number of misbehaving users could change over time. Thus, there is a need for a uniform, adaptive, and distributed reaction mechanism, wherein the genuine users are able to adjust their reaction over time. Many mild misbehaviors do not yield additional throughput to the misbehaving node, and do not cause significant throughput degradation at genuine users (particularly in lightly loaded network scenarios) [6]. The reaction should thus focus towards misbehaviors which are effectively measured or detected using a genuine node’s throughput degradation. Therefore, the proposed mechanisms are based upon the node’s own throughput, do not require any coordination among the genuine nodes, and are thus easy to implement and deploy. The proposed reaction mechanisms strive to achieve the following objectives – (a) guarantee that the misbehaving user’s throughput reduces below what it would have been if the user had not misbehaved, and
1-p 0,0 00 0,
1
...
1
...
i-1, 0
1
i, 0
1
... m,, 0
0,00,1 1
i-1, 1
1
i, 1
1
m, 1
Fig. 1.
1
...
... 1
0,00,2 22
i-1, 2
i, 2
1 1
... 1
m, 2
1
... ... ... ... ... ... ... ...
0,W 0 ,W W1 0,00,W W00-2 1 0, W00-1 2 1
...
1 i-1,W -2 1 i-1,W -1 i-1 i-1
1
i, Wi-2
1
bi−1,0 · p = bi,0
=⇒
bm−1,0 · p = (1 − p)bm,0
=⇒
Now, for each k ∈ (1, Wi − 1), bi,k can be expressed as, ⎧ m ⎨ (1 − p) j=0 bj,0 i = 0, (3) bi,k = 0 < i < m, p · bi−1,0 ⎩ p (bm−1,0 + bm,0 ) i = m. m b0,0 Using (2), and the fact that i=0 bi,0 = 1−p , we have
i, Wi-1
...
1 m, W -22 1 m, W -1 m m
bi,k = bi,0 ∀i ∈ (0, m), ∀k ∈ (0, Wi − 1). (4) m Wi −1 b0,0 is determined using: i=0 k=0 bi,k = 1, which simplifies to (assuming 2p < 1),
Worst Case Access Probability.
(b) provide fairness amongst the post-reaction throughputs achieved by genuine nodes.
m W i −1
In the presence of aggressive misbehaviors, the genuine nodes’ throughput degrades severely. We outline conditions to detect such extreme scenarios, and propose a reaction mechanism which could be employed in these scenarios. Detection Scheme: Consider an IEEE 802.11 wireless LAN with N nodes, where all nodes are genuine, i.e. they correctly follow BEB. We derive a lower bound on the channel access probability of a node (and thus its throughput). Every time a node chooses a backoff value uniformly at random from 1 . [0 . . . CW − 1], it could choose CW − 1 with probability CW Let node A choose backoff values in this way every time. The channel access probability (τ ) and conditional collision probability (p) are obtained using equations (7) and (9) in [14]. The access probability of node A, denoted τA , is minimum (= τmin ) since the node chooses the largest backoff value in the allowed interval every time. Using Markov Chain analysis, we characterize the steady state probability τmin . The Discrete-time Markov Chain model for the backoff window size is given in [14]. Let Wi denote the contention window size during stage i. The state of the system is characterized as (s, b), where s ∈ (0, m) is the backoff stage of the node and b is the current backoff value of the node. Figure 1 depicts the state evolution for the DTMC for the node A. The transition probabilities for node A are given by:
m
bi,k = bi,0 Wi i=0 k=0 i=0 m−1 pm b0,0 2m W0 pi b0,0 2i W0 + 1 − p i=0 m−1 (2p)m i W0 b0,0 (2p) + 1−p i=0
m m
1 =
II. N ON - ADAPTIVE R EACTION M ECHANISM = =
1 − (2p) (2p) + 1 − 2p 1−p 1 − p(1 + (2p)m ) . = W0 b0,0 (1 − 2p)(1 − p) = W0 b0,0
(5)
This implies, b0,0 =
(1 − 2p)(1 − p) . W0 [1 − p(1 + (2p)m )]
(6)
Now, we can express the transmission probability of node A, denoted τA , as τA =
m i=0
bi,0 =
1 − 2p b0,0 = . 1−p W0 [1 − p(1 + (2p)m )]
(7)
Note that τA is less than the steady-state transmission probability τ of a general node in the network, given by (from equation (7) in [14]), τ=
2(1 − 2p) , (1 − 2p)(W0 + 1) + pW0 (1 − (2p)m )
(8)
The conditional collision probability is given by [14],
P {i, k|i, k + 1} = 1, i ∈ (0, m), k ∈ (0, Wi − 2) P {0, W0 − 1|i, 0} = 1 − p, i ∈ (0, m) P {i, Wi − 1|i − 1, 0} = p, P {m, Wm − 1|m, 0} = p.
bi,0 = pi b0,0 0 < i < m pm b0,0 . bm,0 = (2) 1−p
p = 1 − (1 − τ )N −1 .
i ∈ (1, m) (1)
Let bi,k denote the steady-state probability of state (i, k) for node A. We have,
(9)
Note that τA < τ since (2p)m < 1. It is interesting to observe that when m = 0, i.e. no exponential backoff is considered, τA = W10 < τ = W02+1 for W0 > 1. Here W0 = CWmin . As m increases, the difference between τA and τ increases. Since τA is the minimum transmission probability
possible for a node in the presence of all genuine nodes (i.e. in the absence of misbehavior), we also denote τA as τmin . 1 Lemma 1: For all m ≥ 0 and W0 ≥ 1, the worst case transmission probability τmin of a node in the network satisfies the following bound: τmin > τ2 . Proof: From equations (7) and (8), we have, τmin 1 (1 − 2p) = + . τ 2 2W0 [(1 − p) − p(2p)m ] Now using the assumption that 2p < 1, τmin > 12 . τ Let us compute the worst case throughput of node A in the network in the presence of all genuine nodes. Node A achieves the least throughput when the N −1 nodes in the network have access probability τ (given by (8)), and the node A has access probability τA (given by (7)). Using the arguments in [14], the throughput achieved in the network is given by, T =
Ps Ptr E[P ] . (1 − Ptr )σ + Ptr Ps Ts + Ptr (1 − Ps )Tc
(10)
where, Ptr is the probability that there is at least one transmission in the considered time slot, and equals 1 − (1 − τ )N , and Ps is the probability that a transmission is successful, and )N −1 equals nτ (1−τ . Here, E[P ] denotes the average packet Ptr length, and σ, Ts and Tc denote empty slot time, average time taken for a successful transmission and average time taken for an unsuccessful transmission respectively. The denominator in (10) denotes the average length of a time slot. Assuming each node gets a fair share of the LAN throughput, the throughput achieved by a node (other than A), denoted T0 , is given by, T0 =
T . N
(11)
With node A having access probability τA < τ , let the A and PsA (PsA denotes corresponding parameters be denoted Ptr the probability that node A’s transmission is successful), given by, A Ptr = 1 − (1 − τA )(1 − τ )N −1 ,
PsA =
τA (1 − τ )N −1 . A Ptr
Lemma 2: The worst case throughput achieved by a node in the network, denoted Tmin , satisfies the following bound: Tmin ≥
τmin 1 T0 > T0 τ 2
. Proof: Assuming, σ, Ts and Tc remain the same, the throughput achieved by node A, denoted Tmin , is given by, Tmin =
A E[P ] PsA Ptr . A A A (1 − P A )T A (1 − Ptr )σ + Ptr Ps Ts + Ptr c s
1 Note that this analysis is applicable if the number of nodes N is sufficiently large, and thus p is still approximately given by (9).
τA A A We have, Ptr Ps = τA (1 − τ )N −1 = N τ Ptr Ps . The expected length of a time slot would reduce when node A has transmission probability τA < τ , compared to the case where all nodes have same transmission probability τ . Therefore, denominator in the above expression is less than denominator in (10). Thus, τA τA 1 Tmin ≥ N τ T = τ T0 > 2 T0 , from Lemma 1. τmin is the minimum access probability a genuine node could possibly have in the absence of any misbehavior. Therefore, if a node’s throughput falls below T20 , it implies misbehavior almost surely, and hence the node declares detection of a misbehavior. Note that this detection rule can be used to detect the presence of any misbehavior type, as long as the throughput degradation caused is severe. For mild misbehaviors, we design a distributed algorithm in Section III. Reaction Mechanism: Once a misbehavior has been detected using the above policy (and hence an aggressive misbehavior is assumed), following reaction mechanism is employed to penalize the misbehaving user(s). All the N − 1 genuine nodes, upon detection of misbehavior, choose a constant contention window size = W , and do not vary the window size. From [15], each node transmits in a slot with probability τ = W 2+1 . The probability that none of the N − 1 genuine N −1 . Let B nodes transmits in a time slot equals (1 − τ ) denote the channel bandwidth. The maximum throughput N −1 . available to the misbehaving user is given by, B ·(1 − τ ) Now, W is chosen such that,
max W s.t.
B · (1 − τ )
N −1
< T0 .
(12)
Thus the genuine nodes choose a constant contention window size small enough to guarantee that the throughput available to misbehaving user is less than T0 (the genuine throughput share the user would get in the absence of misbehavior). III. A DAPTIVE R EACTION M ECHANISM In this section, we design an adaptive and distributed reaction algorithm for the genuine nodes to react against mildly selfish misbehaviors. Each genuine node measures its throughput degradation with respect to its saturation throughput share T0 given by (11). The reaction aggressiveness is made proportional to the level of suspected selfishness, and in most cases, the reaction is not as strong so as to lower the overall network throughput tremendously. Let us consider the saturation throughput scenario with N nodes. Using Bianchi’s analysis, let the individual fair throughput of each node under saturation conditions equal T0 (as given by (11)). Let us consider that one of the nodes is misbehaving. This would lower the throughput observed by the genuine nodes. Let T0o be the throughput observed by one of the genuine nodes. Clearly, T0o < T0 . A misbehavior is detected if the observed throughput T0o reduces below DtnT hr ∗ 100 %, i.e., T0o < DtnT hr T0 . A. Reaction Algorithm The objective is to reduce the throughput achieved by the misbehaving node to less than T0 . A secondary objective is to
achieve post-reaction fairness among the throughputs achieved by genuine nodes. The genuine nodes use an appropriately chosen constant contention window size (denoted CWf ix ) during the reaction response. The reaction algorithm is described in Algorithm 1. DtnT hr is set to 0.8. Thus, a misbehavior is detected if the observed throughput T0o reduces below 80%, i.e., T0o < 0.8T0 . Note that the choice of 0.8 is made in order to address the tradeoff between the need to (a) apply the reaction early, and (b) to avoid false misbehavior detection. BebP ktT hr is set to 10 packets. Increasing ReaP ktT hr (while keeping BebP ktT hr constant) leads to reaction being employed for a larger fraction of time. Similarly, reducing CWf ix leads to a stronger reaction response. We simulate and observe the impact of this reaction algorithm using NS-2 for various choices of CWf ix and ReaP ktT hr. Network parameters used include N = 10 nodes in a 802.11 wireless LAN, where 9 nodes are sending traffic at the rate of 100 pkts/sec to one common receiver. The channel capacity is 2 Mbps, packet size used is 512 bytes and slot time equals 20μs. Total traffic generated in the network amounts to a load of 3.68 Mbps, which is much higher than the channel capacity. All simulations are performed for a period of 900s. In the absence of misbehavior, average throughput achieved by a genuine node (T0 ) is around 125 Kbps. Next, we introduce selfish misbehavior at one of the sender nodes. Under α-misbehavior, a selfish node chooses its backoff uniformly at random from the interval [0 . . . α(CW − 1)] (instead of the interval [0 . . . (CW − 1)]), where 0 < α < 1. Thus the node ends up choosing a smaller backoff interval than it is supposed to, increasing its chances of accessing the channel next. The lower the value of α, the more aggressive is the misbehavior. Figure 2 depicts the throughput share of all nodes when one of the senders (node 1 in the figure) is configured to misbehave using α-misbehavior, with α = 0.1, while other senders follow standard BEB. We observe that the selfish node is able to get all its data traffic (409 Kbps) successfully transmitted by employing the α-misbehavior. All the genuine nodes suffer a throughput degradation of > 20%, and employ the reaction algorithm. Node 1 represents the misbehaving node in all the figures. With the reaction algorithm, the simulation time is divided into a pre-reaction time of 200s (where the genuine nodes observe their throughputs), and a post-reaction time of 700s
Throughput (Kbps)
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Fig. 2.
409
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Pre-reaction throughput with α-misbehavior (α = 0.1). 150 123
Throughput (Kbps)
Algorithm 1 Reaction Algorithm using CWf ix while true do if T0o < DtnT hr T0 then Employ contention window CWf ix to successfully transmit ReaP ktT hr packets else Employ standard BEB to successfully transmit BebP ktT hr packets end if Recompute T0o during the above time interval end while
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Fig. 3.
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Post-reaction throughput with tuple (500, 6).
(during which all nodes employ the reaction algorithm in a distributed manner). We observe the impact of reaction algorithm for various choices of CWf ix and ReaP ktT hr. Post-reaction throughput of a node is defined as the throughput achieved by the node during the post-reaction time. Figure 3 depicts the post-reaction throughput for (ReaP ktT hr, CWf ix ) tuple of (500, 6). With tuple (500, 6), total LAN throughput equals 1014 Kbps, and total throughput achieved by genuine nodes equals 954 Kbps. We observe that many reaction tuples are able to achieve fairness amongst the post-reaction throughputs achieved by genuine nodes. Therefore, the tuple which maximizes total throughput share of genuine nodes is desirable, and tuple (500, 6) seems to be the best choice among the ones considered. From these results, we infer that a desired reaction mechanism should not only consist of an appropriate reaction response (CWf ix ) but also an appropriate fraction of time that the reaction is applied. Also, the reaction response (in the form of the tuple) would need to vary for different misbehavior types. Next, we describe an adaptive algorithm which allows the genuine nodes to converge to an appropriate reaction response (a tuple) in a distributed manner. B. Design of Adaptive Algorithm We design an adaptive and distributed algorithm which allows the genuine node to dynamically probe the network using different tuples, and to eventually converge to an appropriate tuple. Note that different nodes may converge to different tuples. Once all genuine nodes have converged, the proposed approach is able to achieve the objectives of the reaction mechanism outlined in Section III-A. Figure 4 depicts the operation of a genuine node using the reaction mechanism with a given tuple. According to Algorithm 1, when T0o < 0.8T0 , fixed contention window is employed to successfully transmit ReaP ktT hr packets. We denote the periods of time when CWf ix gets employed as the
Y
N
N
Y
N
Y
N
Y
time Tn < 0.8 T0
Ty > 0.8 T0
Tn < 0.8 T0
Ty > 0.8 T0
Ty > 0.8 T0
One cycle comprises of 25 Y intervals (Tc) Ty – Throughput observed during Y interval Tn – Throughput observed during N interval Tc – Throughput observed during one cycle
Fig. 4.
At the end of the cycle, new tuple is chosen based on Tc
Genuine node operation using adaptive algorithm.
Y periods, and when BEB is employed as the N periods. Note that the length of different Y (or N) periods may differ. Also, the sequence of Y and N periods may differ from that shown in Figure 4. Figure 4 depicts the scenario where Ty > 0.8T0 and Tn < 0.8T0 for all Y and N periods. The node employs the same tuple during one cycle of its operation, which is defined as time interval comprising of 25 Y periods. At the end of the cycle, the node checks its throughput over the entire cycle (denoted Tc ), and chooses the next tuple to be employed during the next cycle using Algorithm 2. Initially the node starts with a relatively mild reaction tuple of (100, 16). If the observed throughput Tc is still less than 75% of expected throughput T0 , the node increases the aggressiveness of its reaction quickly by doubling the ReaP ktT hr and cutting its CWf ix into half. Once the throughput of the node is > 80% of T0 and < 90% of T0 , the node increases the reaction aggressiveness slowly by using an additive increase and decrease of the tuple parameters respectively. If the throughput Tc becomes much greater than T0 , the node reduces the level of its reaction. We choose Δ = 10 Kbps. As long as the throughput of the node is satisfactory, i.e., 0.9T0 ≤ Tc ≤ T0 + Δ, the node employs the same tuple during the next cycle of its operation. The node is said to have converged to a tuple when it uses the same tuple for 4 consecutive cycles. Note that the choices made in Algorithm 2 are arrived at after experimenting with various choices, and choosing the ones which lead to faster convergence. The simulation time is increased to 20000 sec to allow all the genuine nodes to converge. C. Convergence Once a node has converged to a tuple, it does not change its tuple, and employs the same tuple thereafter. When all the genuine nodes in the network have converged (to their respective tuples), and the network behavior stabilizes, we refer to the remaining simulation time as the post-convergence period. Post-convergence throughput of a node is defined as the throughput achieved by the node during the post-convergence period. We evaluate the adaptive reaction mechanism in terms of both the post-reaction throughput and the post-convergence throughput achieved in the network.
Algorithm 2 Dynamic computation of the tuple (ReaP ktT hr, CWf ix ) in the adaptive algorithm ReaP ktT hr ← 100; CWf ix ← 16 while not converged do Employ the tuple for the next cycle and compute observed throughput Tc during this cycle if Tc ≤ 34 T0 then ReaP ktT hr ← ReaP ktT hr ∗ 2 CWf ix ← min{CWf ix ∗ 12 , 2} else if 34 T0 < Tc ≤ 45 T0 then ReaP ktT hr ← ReaP ktT hr ∗ 32 CWf ix ← min{CWf ix ∗ 23 , 2} 9 T0 then else if 45 T0 < Tc ≤ 10 ReaP ktT hr ← ReaP ktT hr + 10 CWf ix ← min{CWf ix − 1, 2} else if Tc > T0 + Δ then ReaP ktT hr ← ReaP ktT hr − 20 CWf ix ← CWf ix + 1 else ReaP ktT hr ← ReaP ktT hr; CWf ix ← CWf ix end if end while
Figure 5 depicts the post-reaction throughput achieved in the network using the adaptive algorithm. During the entire course of the reaction, the average throughput of the node is quite close to T0 . The total LAN throughput post-reaction equals 1052.1 Kbps, and the total throughput achieved by genuine nodes equals 959 Kbps. Note that the post-reaction response is quite close to (and slightly better than) the desired behavior with tuple (500, 6) employed by all genuine nodes, as discussed in Section III-A. Figure 6 depicts the postconvergence throughput achieved in the network using the adaptive algorithm. The total throughput post-convergence equals 1048.5 Kbps, and the total throughput achieved by genuine nodes equals 964 Kbps. Thus, once the nodes have converged the genuine nodes’ throughput share increases slightly. Since all the genuine nodes would continue employing the reaction constantly hereafter, this throughput share would remain valid until the misbehaving node changes its behavior (increases the level of misbehavior or leaves the network). The genuine nodes could revisit their tuples from time to time in order to detect and adapt to such changes. Table I shows the converged tuples for all 8 genuine nodes. All the nodes converge to tuple similar to the desired tuple of (500, 6). Note that nodes with aggressive tuples achieve slightly larger post-convergence throughput share compared to nodes with less aggressive tuples (such as nodes 4 and 7), from Figure 6. Nodes with less aggressive tuples typically converge earlier. For instance, in this scenario, node 4 converged first at around 3000 seconds. The post-convergence throughput of the misbehaving node is significantly less than T0 . The Jain’s fairness index [16] computed over the post-convergence throughputs achieved by the genuine nodes equals 0.9988.
150 Throughput (Kbps)
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misbehavior with α = 0.5), the convergence time reduces significantly (to 2400 sec). If adaptive reaction is used with aggressive misbehaviors, the genuine nodes may not be able to achieve a respectable throughput share even with the reaction, and may not converge. In such cases, the genuine nodes should switch to the reaction mechanism specified in Section II. IV. C ONCLUSIONS
Fig. 5.
Post-reaction throughput with adaptive algorithm.
Throughput (Kbps)
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Fig. 6.
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We proposed two reaction mechanisms based entirely upon local information, to prevent selfish misbehaviors in wireless networks. The non-adaptive reaction mechanism is suitable when a node suffers significant throughput degradation (> 50%). The adaptive reaction mechanism allows the genuine nodes to achieve satisfactory throughput in the presence of selfish misbehaviors, and to reduce the throughput of misbehaving node to less than what it would achieve without misbehavior. The reaction also leads to fairness among the post-reaction throughputs of genuine nodes.
Post-convergence throughput with adaptive algorithm.
R EFERENCES D. Discussion and Open Issues The adaptive and distributed reaction algorithm outlined above is based entirely upon a node’s observed throughput, and hence is easily implementable in practice. The mechanism only relies upon the knowledge of T0 at genuine nodes, which could be obtained by keeping track of one’s throughput or computing T0 (using (11)). Since genuine nodes make no assumption regarding the type or level of misbehavior, the mechanism is suitable for reacting towards many selfish misbehaviors. This mechanism is different from other reaction mechanisms which are geared towards specific misbehavior types [5], or rely upon reliable collaborations with other nodes in the network [8], [9]. The mechanism allows the genuine nodes to detect and adapt to changes, such as increase in level of misbehavior or misbehaving node leaving the network, by revisiting their tuples from time to time. Typically it takes around 18 decision instances (with decision instances around 10 minutes apart) for all genuine nodes to converge. Thus, one possible improvement could be to reduce the convergence time of the algorithm. However, since average post-reaction throughput for a genuine node is quite close to T0 , rate of convergence does not impact the objectives significantly. Also, when the node misbehavior is milder (αTABLE I C ONVERGED REACTION TUPLE FOR ALL GENUINE NODES . Node Number 2 3 4 5 6 7 8 9
ReaP ktT hr, CWf ix 445, 3 480, 5 400, 3 410, 4 450, 3 602, 6 410, 4 860, 7
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