Queuing in space: Design of message ferry routes in static ad hoc networks

We study the concept of ferry based wireless local area network (FWLAN), in which a number of isolated nodes are scattered over some area and where communication between a node and the outer world, or communication between the nodes, are made possible via a message ferry. The Ferry has a predetermined cyclic path which collects messages from a node and delivers messages to it when it is in the vicinity of the node. We use the mathematical theory of polling systems to study the performance of the FWLAN. We consider three different architectures and each one of them is mapped to an appropriate polling system. The polling disciplines that are needed for modeling the FWLAN involve non-standard variants of gating disciplines. Our goal is to design the routes of the Ferry as well as the points where it should stop to distribute and collect messages. This mathematical modeling brings another dimension to the classical related vehicle routing problem due to the radio channel: the cyclic path of the ferry need not touch every node. The distance between the node and the fairy at the point when communication occurs determines the transmission rate and hence the service time and thus the system's capacity.