Performance of a Fixed Reward Incentive Scheme for Two-hop DTNs with Competing Relays

Abstract

We analyse the performance of an incentive scheme for two-hop DTNs in which a backlogged source proposes a xed reward to the relays to deliver a message. Only one message at a time is proposed by the source. For a given message, only the rst relay to deliver it gets the reward corresponding to this message thereby inducing a competition between the relays. The relays seek to maximize the expected reward for each message whereas the objective of the source is to satisfy a given constraint on the probability of message delivery. We show that the optimal policy of a relay is of threshold type: it accepts a message until a rst threshold and then keeps the message until it either meets the destination or reaches the second threshold. Formulas for computing the thresholds as well as probability of message delivery are derived for a backlogged source.

A Mixed Strategy for a Competitive Game in Delay Tolerant Networks

“…The equilibrium obtained is a mixed one in which a relay accepts a message with a certain probability. This contrasts with the threshold-based equilibrium in [18] in which the source gave message generation information to the relays. Simulations suggest giving no information on the message generation times can be advantageous to the source compared to giving information.…”

“…Denote by δ x (t) the Dirac delta function at point x. Following the same approach as in [18], we can the following result.…”

“…Many incentive mechanisms have been proposed to avoid the free-rider problem in DTNs, including reputationbased schemes [12,16,[22][23][24], barter-based schemes [4,5,20] and credit-based schemes [7,8,14,19,25,26]. In contrast to most of the incentive mechanisms proposed in the literature, explicit guarantees on the probability of message delivery and on the mean time to deliver a message have been obtained for the credit-based scheme considered in [17,18] (see also [19] for a closely-related mechanism).…”

“…The authors of [17,18] consider a source which promises a fixed reward to the relay who first delivers a message to the destination. The source is backlogged and only one message at a time is proposed by the source.…”

“…The analysis in [17,18] implicitly assumes that the source tells the relays when a message was proposed for the first time, or, in other words, when this message was generated. Our objective in the present paper is to understand whether it is profitable for the source to give this information to the relays.…”