## 1 Introduction  
Recently, there has been increased research on future Internet infrastructures in the field of information and communication technology (ICT), and new basic principles of network management are currently being developed. From the viewpoint of the societal requirements toward a prosperous future communication infrastructure, one goal of the future Internet is to pursue and guarantee reliability and efficiency. In addition, ubiquitous mobility and wireless communication is anticipated to play an even more essential role in the future, due to the high flexibility that mobile systems can provide to users. Hence, reliable and efficient mobile systems are especially important for the future Internet. Moreover, the number and type of mobile nodes, as well as the mobile services and applications have been increasing and diversifying. This phenomenon accelerates the increase of complexity in mobile systems at a large scale. Therefore, future mobile systems should have scalability and cost efficiency from the viewpoint of system performance and business operation.  
Infrastructure-free systems of mobile _ad hoc_ networks (MANETs) are flexible in unstable network connectivity situations, for example after natural disasters, and can cope with highly dynamic network topology changes caused by node mobility. Compared to wired networks, they can be configured and deployed more rapidly, and since they operate without central nodes in a flat network topology, MANETs have better scalability, due to more dynamic and adaptive routing mechanisms. Potential based routing [1] is one of the promising techniques for routing in an autonomous manner. In analogy with thermodynamics, a temperature potential is used for a loop-free and generalized routing method of shortest path routing. There have been several proposals of potential routing variants, and the autonomous exchange of potential information among nearby nodes is the underlying principle for most of these protocols. Since a certain time is needed until the potential information is propagated within the network, the convergence time for potential updates and assurance of node reachability are important indicators for the performance of these protocols.  
Each potential routing scheme has its benefits under certain conditions. However, to the best of our knowledge, none of them can deal well with situations of highly changing topologies caused by the geographic movement of nodes. Therefore, we proposed in [2] a mobility-oriented extension for potential routing, called Mobility Tolerant Firework Routing (MTFR), in order to improve the data transmission reachability among nodes. The potential value of a node is an indicator of its relative distance to the destination, and we include a broadcast-based data replication scheme to improve reachability in combination with a potential threshold to restrict the number of unnecessary broadcasts to the expected vicinity of the destination node. Our method works in an autonomous and self-organizing manner on both cellular systems and infrastructure-free systems, resulting in a higher reachability.  
The rest of this paper is organized as follows. In Section 2, we discuss related work. Then, in Section 3, we first explain the basic mechanism of potential-based routing before describing our firework routing mechanism in detail. In Section 4, the performance of our proposal is compared with conventional potential routing for the random walk mobility model, and the results from the theory of random geometric graphs are briefly discussed. Finally, Section 5 concludes this paper.