Transmission Costs, Selfish Nodes, and Protocol Design

Abstract

Abstract-We study the influence of transmission costs on the behavior of selfish nodes in wireless local area networks. Intuitively, it seems that transmission costs should have a stabilizing effect as (rational) nodes will defer packet transmissions when congestion develops and the cost for (successfully) transmitting a packet becomes high. In this paper we investigate whether this intuition is true. We use slotted Aloha to model the communication channel where we model the interaction among nodes as a non-cooperative game. For this game, we study the existence and properties of a (symmetric) Nash equilibrium. We show that the existence of a transmission cost is not always sufficient to guarantee stability. In particular, a stable equilibrium strategy will not exist if the transmission cost is too small. We then propose and analyze a price-based mechanism to guarantee stability and to optimize system performance in terms of throughput and delay. I. INTRODUCTIONAn important feature of wireless networks is that packet transmissions incur a cost in terms of battery energy. Intuitively, it seems that transmission costs should have a stabilizing effect as nodes will defer packet transmissions when congestion occurs and the cost for (successfully) transmitting a packet becomes high. In this paper we investigate this intuition and its implication for the design of protocols.For our analysis, we consider the situation where wireless nodes communicate over a random access channel. That is, whenever a node has a new packet to send, it will do so immediately. If the packet collides (interferes) with a packet sent by another node at the same time, then it is lost and has to retransmitted at a later time. Here, we assume that nodes are selfish and make the decision of (a) when to accept a new packet and (b) when to retransmit a backlogged packet in order to maximize their net benefit. To characterize the net benefit, we assume that (a) nodes obtain a reward for successfully transmitting a packet (where different packets can have different rewards) and (b) each transmission attempt incurs a cost (which is the same for all packets).Note that under the above model, nodes will try to avoid to transmit/retransmit packets during periods when collisions are likely to occur, as this would decrease the likelihood of a successful transmission and increase the expect cost for successfully transmitting a packet. This observation suggests that transmission costs have a stabilizing effect in the sense that during time of congestion (i.e. when collisions occur frequently) nodes will back-off and hence prevent that the channel becomes clogged. In order to investigate whether this intuition is indeed true, we model the interaction among nodes as a non-cooperative game, and study the existence and properties of a (symmetric) Nash equilibrium. In particular, we are

A Game-Theoretic Analysis of Denial of Service Attacks in Wireless Random Access

“…Theorem 2: The cooperative equilibrium strategies that maximize Z' 1 3iui are given by Pi _2 (q212 (r2 + D2) -E2) P= i(q1 I-q1 1,2)(ri + DI) + 02(q212 -q211,2)(r2 + D2) (10) P* /3i(q111 /i(q 1 I(ri + D1) F1 E =l(q,Iq 1,2)(r, + DI) + 02(q212 -q21l,2)(r2 + D2) Proof: The total weighted utility sum can be expressed as UE = /31ul +/32u2 = /31 (pu (T, P2) + (1 -P1)u1 (W, P2)) + ui(pi*,P*-i)>-ui(pi,p*i) , t = 1 2 /32(P2U2(T, pi) + (1-P2)U2(W, Pl)) = ,=2 1/3i(-PlP2(qili-qiI1,2)(ri + Di) + piqiIi(ri + Di) -piEi-Di).…”

“…Since uY is concave in pi, i = 1, 2, the optimal solutions should satisfy au9p 0 for i = 1, 2 such that the total utility is optimized by cooperative equilibrium strategies (10) and (11) to the maximum value of u = Bl (q, I (r± +DI) -EI)32 (q2 2 (r2+D2)-E2) 1 (q iI-ql ,2)(r±+DI)±+2(q212-q2II,2)(r,+D2) 1 1 /32D2. U The non-cooperative equilibrium utility of node i is ui = -Di.…”

“…For finite number of transmitter nodes without queue buffers, the problem of non-cooperative random access has been studied in [7]- [10] for collision channels under the assumption that each packet arrives at a new node, and whenever a packet is successfully transmitted, it leaves the system. The effects of packet captures in non-cooperative random access have been evaluated in [11], and the stability properties have been discussed in [12] for the Aloha system model without queue buffers and in [13] by taking into account the interactions among individual packet queues, as studied in [1]- [6] for cooperative stability region optimization.…”

Modeling Slotted Aloha as a Stochastic Game with Random Discrete Power Selection Algorithms

“…Another way to reduce the access contention is to introduce a transmission cost. Indeed, it was shown in [18] that costs have a stabilizing effect; being rational, users will defer packet transmissions when congestion develops and the cost for successful transmission becomes high. This way, users will drop packets when the total transmission costs are high which can cause a huge delay and then the analysis seems to be not applicable to delay-sensitive traffic.…”