A central problem in Delay Tolerant Networks (DTNs) is to persuade mobile nodes to participate in relaying messages. Indeed, the delivery of a message incurs a certain number of costs for a relay. We consider a twohop DTN in which a source node, wanting to get its message across to the destination as fast as possible, promises each relay it meets a reward. This reward is the minimum amount that offsets the expected delivery cost, as estimated by the relay from the information given by the source (number of existing copies of the message, age of these copies). A reward is given only to the relay that is the first one to deliver the message to the destination. We show that under fairly weak assumptions the expected reward the source pays remains the same irrespective of the information it conveys, provided that the type of information does not vary dynamically over time. On the other hand, the source can gain by adapting the information it conveys to a meeting relay. For the particular cases of two relays or exponentially distributed inter-contact times, we give some structural results of the optimal adaptive policy.Index terms -delay tolerant networks, reward incentive mechanism, adaptive strategy *

The literature on airlines presents few studies analyzing the airlines network evolution. We believe that this gap is due to the difficulty of capturing the network complexity in a simple manner. This paper proposes new simple and continuous indicators to measure the airlines' network structure. The methodology to build them is based on graph theory and principal component analysis. We apply this approach to the US domestic market for 2005-2018, and obtain three network indicators. The first one measures how close the network is to a single-center structure. The second indicator measures the airline's ability to provide alternative routes. The third indicator captures the network size. We analyze the indicators evolution across time and show their robustness under different scenarios.

We investigate the convergence of sequential best-response dynamics in a routing game over parallel links. Each player controls a nonnegligible portion of the total traffic, and seeks to split its flow over the links of the network so as to minimize its own cost. We prove that best-response operators are lipschitz continuous, which implies that a sufficient condition for the convergence of the best-response dynamics is that the joint spectral radius of Jacobian matrices of best-response operators be strictly less than unity. We establish the specific structure of these Jacobian matrices for our game, and show that this condition is met in two cases: (a) two-player game for an arbitrary number of links and for a wide class of cost functions; and (b) for arbitrary numbers of players and links in the case of linear latency functions. For latency functions satisfying reasonable convexity assumptions, we conjecture that the proposed sufficient condition is met for arbitrary numbers of players and links.