A Simple Analytical Model for Ad Hoc Networks with Cooperative Nodes

A crucial issue of civilian applications of ad-hoc networks is cooperation of nodes. More precisely, each node has its own authority and may try to maximize the benefits it gets from the network without participating to its services (e.g. without forwarding packets of other nodes). To conquer with this problem, a virtual currency, namely nuglet (Buttyan and Hubaux, 2003), is used to provide an incentive for cooperation by having a node to send its traffic at a given cost, while allowing it to profit every time it forwards others´ traffic. Several papers have shown that such a model encourages individual node cooperation. In this paper, we consider a network whose nodes use nuglets except that when a node empties out of nuglets, as a penalty and to enforce more cooperation, it can not forward its own traffic again until forwarding K packets of other nodes. Once the node begins to send its own packets, it proceeds normally until the node becomes empty again. We develop a Markov model of the network to evaluate the system performance in terms of network capacity, data generation delay and the probability that a node empties out of nuglets. We use these performance parameters to show that how the proposed scheme encourages nodes to cooperate with the network. We also show the trade-off between increasing node cooperation and data generation delay and analyze it by defining a total cost function due to non-cooperative behavior and data generation delay. At last, a comparison between our scheme and the scheme proposed in the work by Buttyan and Hubaux (2003), as the most well-known protocol in node cooperation schemes, is presented.