AIMAC: An Auction-Inspired MAC Protocol Ian Tan 1 I. INTRODUCTION Much attention has been given over the past decade to examining the properties of ad-hoc wireless networks. Current trends, however, show that the proliferation of access point (AP) based wireless networks continues to grow, and impending deployments of large-scale AP-based networks in metropolitan areas (see [?] and [?]) speak volumes for their popularity. Given the continued spread of AP-based WiFi networks, it would be foolish to ignore the role an AP can play in enforcing MAC protocol adherence. As WiFi reaches wider and wider audiences, the potential for protocol-level misbehavior grows tremendously. Fortunately, AP-based and distributed solutions have been proposed to detect MAC-layer misbehavior. In the following sections, we first briefly review previous work in 802.11 MAC misbehavior. In light of this work, we next reconsider the role of the AP within the network. After recasting the AP as an auctioneer of channel resources, we propose an Auction-Inspired MAC protocol (AIMAC) that implicitly discourages greedy nodes from continually occupying the wireless channel (i.e. from misbehaving). Additionally, preliminary simulation results are given. II. MISBEHAVIOR METHODS Raya et. al. in [?] provide a general listing of cheating methods that are feasible in 802.11. Assuming that a wireless node is not malicious (i.e. it misbehaves to gain bandwidth, not solely to deny others access), nearly all misbehavior centers around seizing the channel before other nodes. As such, some methods of cheating are: Scrambling other users frames: Provided the network is in a single collision domain, a misbehaving node can sense the transmissions of other users. By jamming them, he increases the amount of time they back off, thereby leaving him with additional opportunities to occupy the channel. Disregarding interframe spacing parameters: A node could transmit earlier than DIFS, thereby locking out other nodes from the channel. NAV manipulation: By setting a NAV interval much longer than necessary for a given transmission, a cheater can silence nodes around it. Backoff manipulation: A cheater can shorten the size of the distribution out of which it chooses its backoff interval, or it can choose not to backoff at all. Out of these four methods, the last one is the easiest to implement, the least likely to break the protocol, and also the most difficult to detect. It is mainly with this cheating method that the following three works concern themselves. III. BACKOFF DICTATION Within [?], Kyasanur and Vaidya propose a scheme to stem backoff manipulation in an ad-hoc environment. Instead of a sender randomly choosing his own backoff, the receiver specifies a backoff for the sender to use. The receiver then monitors the sender to ensure that the backoff is followed. If the backoff is deviated from, then the receiver retaliates by assigning a penalizing backoff to the sender that is proportional to the extent of the misbehavior. A timing diagram of a sender-receiver data exchange is in Figure 1. Fig. 1. Timing diagram for the backoff dictation scheme. Intially, the sender chooses a random backoff interval, but all subsequent backoffs are governed and monitored by the receiver. The scheme coexists nicely with non-cheaters and is decentralized, but it is still vulnerable to sender-receiver collusion and adaptive misbehavior. It served, however, as the inspiration of the next work.
2 IV. BACKOFF DETECTION Drawing off of [?], Raya et. al. propose a battery of AP-based tests to detect cheaters in [?]. Individual tests are constructed to detect all of the cheating misbehaviors listed in Section II. For example, intentional scrambling is detected by determining if any single node consistently has less retransmissions than the average; if so, it is probably cheating. Other tests measure node backoffs and threshold them against averages for detection. The main advantages of [?] are that all changes are centralized at the AP and that the MAC layer on clients need not be modified. Furthermore, the system relies on passive measurements; over the short term, a node cannot determine whether the AP has the system installed. On the other hand, the system is still vulnerable to adaptive cheaters, and, more importantly, it does not give much insight as to how to fundamentally fix the shortcomings in WiFi that permit misbehavior. V. GAME THEORETIC APPROACH One method to fix the shortcomings in 802.11 (and CSMA protocols in general) is to take a game theoretic approach, such as that in [?]. Cagalj begins by observing that, if channel access is treated as a one-shot game, the situation degrades into the Tragedy of the Commons; namely, either one node obtains all the bandwidth (by seizing the channel first), or no nodes obtain any bandwidth due to repeated collisions. These two outcomes characterize the possible Nash equilibria (NE) of the static game. He then analyzes the channel seizure process as a dynamic game. By exploiting the static game NE as a credible threat, he constructs a distributed protocol that encourages rational nodes to adjust their backoffs. Through these adjustments, nodes come to operate at a more beneficial Nash bargaining equilibrium. The scheme has merit based on its distributed implementation and high throughput for rational (i.e. cheating) nodes. However, its one significant downfall is its great unfairness to non-cheating nodes, as they attain significantly lower throughput than cheaters (between 5x and 10x less). A. Design Observations and Assumptions VI. AIMAC As reviewed in the previous three sections, various methods have been proposed to prevent the easiest form of cheating - backoff manipulation. [?] attempts to specify backoff explicitly between sender and receiver, [?] makes use of an AP as a detection mechanism, and [?] has nodes enforce cooperation in a distributed manner. However, none capitalize fully upon the observation that the wireless medium is a shared resource that can be allocated by a centralized authority such as an AP. At a fundamental level, the AP acts as a aggregator of data. To communicate with any other node inside or outside the wireless network, a sending node s traffic must pass through the AP. Usually, it has no more right to access the shared wireless medium than any other user node. Given the central role it plays, though, one can easily imagine the AP as a scheduler or controller for the wireless channel. If cast in this manner, the AP acts much like an auctioneer. The goods he auctions off are channel access slots, and the people he sells slots to are nodes. The more a node values a slot or slots, the more likely he is to outbid other users for the purchase of those slots. The question, then, becomes: How do we quantify the value of a slot to a node? Obviously, if nodes are to bid on slots, they must be willing to exchange something of value in return. To determine what constitutes an item of value, we make a second observation - that 802.11 rewards nodes that have smaller backoffs with sustained channel access. In most analyses, increased probability of channel access directly translates into higher throughput. Backoff therefore appears to be a candidate for this valuable item. Of course, in general most traffic patterns would benefit from higher throughput with lower delay. However, having a node obtain more throughput than it reasonably requires is not fair to other users and is essentially cheating. With this in mind, we force a node to tradeoff the quantities of delay and data it demands. Together, these two elements constitute a traffic pattern, as will be explained in the following sections. By forcing nodes to balance the amount of data they wish to send with the delay (backoff) they are willing to suffer, we fundamentally change the direct relationship between backoff and throughput typically assumed in CSMA MAC protocols. In formulating the AIMAC, we wish to ensure the following hold true: 1) Nodes should be forced to balance the data they need to transmit with the backoff (delay) they are willing to suffer 2) Nodes with a higher utility (to be specified) should be guaranteed better performance than nodes with utilities lower than them. 3) Incentive-compatability: Nodes should be encouraged to reveal their minimum requirements for their desired traffic pattern. 4) Misbehaving nodes should never be treated better than obedient nodes. With these criteria, we wish to reward nodes that reveal their minimum traffic requirements by issuing some sort of guarantee on their performance. In our formulation, we assume a trusted AP serving untrustworthy nodes. Bids are always sealed, as some form of encryption is enabled between each node and the AP. However, it is possible for nodes to sense the channel and empirically deduce the winner of past auctions.
3 B. Bids and Utilities We begin by defining a standard format for nodes to specify their desired traffic pattern. Based on information from higher layers, the MAC layer for node i submits a bid to the AP in the form (b i, δ i ). b i is the backoff volunteered between data transmissions and δ i is the data burst size following each backoff. The relation between these two quantities is illustrated in Figure??. Both quantities are measured in terms of slots. Fig. 2. The diagram illustrates the traffic pattern formed by a bid of (7, 6). To account for both downlink and uplink traffic, a bidding node should estimate the data requirements of its downlink traffic and merge that with its uplink traffic requirements. Next, a utility function must be defined on the bid so that the AP can rank nodes. In light of objectives (1) and (3), the ultimate goal is to have nodes backoff as long as possible before transmitting as little data as possible. Therefore, define the utility function as: U(b i, δ i ) = b i δ i (1) Notice that higher utility values correspond to either greater backoffs or smaller data bursts. Based on the utility it calculates for each node s bid, the AP ranks nodes from highest utility to lowest. The node with the highest utility is said to win the auction, and is guaranteed the traffic pattern it bid or better. A better traffic pattern is one with higher throughput than the one originally bid. C. Overview AIMAC consists of three primary stages. The first is a solicitation period by the AP. In this stage, the AP gathers new bids from newly entered and existing nodes and ranks them according to their calculated utilities. Next, the AP enters a scheduling mode that assigns data transmission slots to each node, starting with the node with highest utility (the auction winner ). This will be detailed in the following section. Finally, all the nodes accept and run their schedules during the activation stage, the length of which is determined by the AP and/or network administrator. Once the activation stage is complete, bid solicitation begins once again and the access algorithm repeats. D. Scheduling To ensure that a winning node attains at least the traffic pattern he bids, the auction winner is scheduled first. Assuming a first-price auction, the winner receives his desired traffic pattern during the following activation stage. He is assigned a pattern of data transmission slots interleaved with backoff slots where he should not transmit. These backoff slots are left open for the scheduling of other nodes. The data slots may be used for either uplink or downlink traffic as the node dynamically desires. If a data slot is scheduled for node n, say that it is occupied by node n. The AP then schedules other nodes in descending order of their utilities. The scheduling proceeds in a similar manner to that of the winner, with one caveat. The AP cannot schedule new data slots into those that are already occupied. Since scheduling proceeds in descending utility order, higher-ranked nodes maintain their slot occupations in case of scheduling conflicts with lower-ranked nodes. Therefore, the lower a node s rank, the less likely it is to attain its desired traffic pattern. After all nodes are scheduled or all slots in the given activation stage are filled, the AP sends each node their schedule. The activation stage then commences, with the winner having channel occupancy first. Pseudocode for the scheduling algorithm is shown in Algorithm??. E. Bid Solicitation Along with a schedule, the AP also tells nodes in what order they can bid during the subsequent solicitation stage. No node knows the complete ordering of bids - they only know what position they are in the sequence. The order should be randomized to reduce the probability that one node could intentionally disrupt the bid of another node. If a node knew when other nodes were placing their bids, he could strategically disrupt the bids of nodes that had historically outbid him. This would increase his chances of winning the auction unfairly.
4 Algorithm 1 Scheduling Algorithm 1: procedure SCHEDULE(B) B is the set of all bids 2: U U will be the set of corresponding utilities 3: for all B i B do 4: U i u(b i, δ i ) 5: U U {U i } where B i is a bid (b i, δ i ) 6: end for 7: while U = 0 do 8: currentslot 1 9: k = arg k max U k U 10: while currentslot < activationstagelength do 11: top lace δ k Extract δ k and b k from bid leading to utility U k 12: backoff b k 13: while top lace > 0 do 14: if currentslot is unoccupied then 15: Place one data slot for node k 16: top lace T op lace 1 17: end if 18: currentslot currentslot + 1 19: end while 20: currentslot currentslot+ backoff 21: end while 22: U = U \ {U k } 23: end while 24: end procedure F. Incentive Compatibility A precise formulation of the incentive compatibility of this scheme is difficult to show, mainly because the utility a node derives from the schedule returned to it is unknown. The utility function presented previously in Section?? acts more as a ranking function for the AP, and does not represent true nodal utility quite as well. This is because, all other things being equal, most nodes desire higher throughput, which corresponds to lower values of b and higher values of δ. Intuitively, then, we still wish to justify that a node has incentive to reveal its lowest tolerable traffic pattern. This is the pattern with the least amount of data to send and the most amount of time between transmissions. Assume a second-price structure, such that the auction winner actually obtains the traffic pattern of the 2nd place bidder (which presumably has higher throughput than his own bid). ( ) Let (b i, δ i ) be the original bid of a node with associated utility U i. Say that, instead of this bid, he bids b i, δ i, where b i < b i and/or δ i > δ i. In either case, the AP calculates a utility U i that is less than the original bid. Thus, by being greedy, this node has decreased his chances of obtaining a favorable traffic pattern because his rank will drop. Consequently, he will be scheduled later and have fewer data slots available to him. However, by bidding his minimum tolerable traffic pattern (b i, δ i ), he maximizes the chance he will be ranked higher and scheduled earlier. The second-price mechanism is instrumental in encouraging this behavior because, provided node i s utility is higher than that of j, i has no reason to bid anything other than his minimum traffic pattern. If i tries to be greedy (and thus lower his U i ), but manages to still maintain U i > U j, the second-price mechanism will still allocate him the traffic pattern specified by j s bid. For i, this is the best traffic pattern he can obtain without losing to j. Therefore, i wishes to maintain U i as high as possible. G. Simulations In the following simulations, a 30 node network is represented. All thirty nodes choose their b i values from a discrete U[1, 25] distribution and their δ i values from another independent U[1, 25] distribution. The length of the activation stage varies from 50 to 2000 slots between plots. We simulate AIMAC under a first-price auction model, so that winners receive exactly the traffic pattern they bid for. The quantity of interest here is the fractional gain, which we define as: fracgain i = T attained,i T desired,i T desired,i (2) T attained and T desired are the throughputs a node achieves and desires, respectively. T desired is calculated directly from the bid submitted to the AP:
5 T desired,i = δ i δ i + b i (3) The simulation results are shown in Figures?? through??. For each network size (x-axis value), the simulation is run 800 times and the average fractional gain for the winner, 2 nd place, 3 rd place, etc. are plotted. Each run simulates a single activation stage with randomly generated traffic patterns. Note that the simulations do not care nor show which nodes specifically win or lose. It is only concerned about the average fractional gain is if, say, we examine the i th place node in a n node network. Also note that this gain is almost always negative, indicating a loss in performance. Under the first-price scheme, no node should ordinarily attain above a 0 fractional gain in the long term. However, since our activation interval is not necessarily an integer multiple of any δ i + b i, effects such as those illustrated in Figure?? could occur, leading to a positive fractional gain. Fig. 3. Illustrates possible overestimation of throughput for a big of (4,2). Long-term throughput is 1 5, but estimate throughput here is 3 13 > 1 3. Certainly, the winner should not suffer any loss or gain compared to its bid. Generally, this holds true, except when the length of the activation stage is on the order of the distribution from which b i s and δ i s are taken. In this case (Figure??), the effects noted in the previous paragraph occur for both the winner, 2 nd, and 3 rd place bidders. In reading the plots, the uppermost line (colored blue) indicates the gains of the auction winner. Working downwards leads to the gains of the 2 nd place (green), 3 rd place (red), etc. nodes. One apparent property is that as network size grows, only a limited number of nodes can be supported with non-zero throughput. For even a modest network size of 30, if all nodes are in contention, only 7 nodes can be supported with less than 80% loss. However, this bears further examination since a smaller network size appears to support even fewer nodes adequately (about 5 for a 10 node network). The growth in supportable nodes with network size may be due to the increased likelihood of less intensive traffic patterns being demanded of the AP. It also appears that the length of the activation period does not affect the loss suffered by the losing node. For example, in a 2 node network, the 2 nd place node always appears to lose about 27% of its desired throughput, regardless of the activation period. A similar observation holds for the 3 rd place node - he seems to lose about 60-65% of his target performance in a 3 node network. Fig. 4. Fractional gains as a function of network size for various bidders. The winning node is represented by the top curve, and rank decreases going downwards. Activation period is 50 slots. VII. CONCLUSION Ensuring that wireless users obey MAC protocol rules is a valid concern, especially considering the overwhelming popularity of IEEE 802.11. Several approaches, focusing on detecting and correcting backoff-based misbehavior, have been briefly
6 Fig. 5. Fractional gains as a function of network size for various bidders. Activation period of 500 slots. Fig. 6. Fractional gains as a function of network size for various bidders. Activation period of 2000 slots. reviewed. Based on these approaches and a rethinking of the role of the AP in an infrastructure network, we propose an auction-inspired MAC protocol. By casting the AP as an auctioneer of channel resources, we avoid the tendency to link channel seizure with increased bandwidth. Instead, we force nodes to trade off between the amount of data they send and how long they wait to send it. Sparse data patterns are encouraged, while greedy ones are discouraged, thereby giving nodes an incentive to bid their minimum tolerable traffic pattern. In the immediate future, we hope to continue simulating the scheme with more realistic traffic patterns and/or the secondprice auction methodology. Also, the fact that the auction is repeated may impact the bidding strategies nodes use. From a conceptual standpoint, AIMAC is a first step towards exploring the potential in auction-based MAC mechanisms. Future work in this vein will examine how such schemes should be constructed, and what tradeoffs nodes should be forced to make in order to ensure system-wide fairness. REFERENCES [1] M. Cagalj, S. Ganeriwal, I. Aad and J.-P. Hubaux, On Selfish Behavior in CSMA/CA Networks. IEEE Infocom 05, March 2005.
[2] P. Kyasanur and N. Vaidya, Detection and handling of MAC layer misbehavior in wireless networks. Dependable Systems and Networks, June 2003. [3] D. McCullagh, EarthLink wins Philly Wi-Fi contract. 4 October 2005. http://news.com.com/earthlink+wins+philly+wi-fi+contract/2100-7351 3-5888494.html [4] E. Mills, Google in San Francisco: Wireless Overlord?. 1 October 2005. http://news.com.com/google+in+san+francisco+wireless+overlord/2100-1039 3-5886968.html [5] M. Raya, J.-P. Hubaux, and I. Aad, DOMINO: A system to detect greedy behavior in IEEE 802.11 hotspots. ACM MobiSys, June 2004. 7