Continuous Polling with Rerouting: Performance and Modeling of Ferry assisted Wireless LANs

In this paper we focus on a class of polling systems encountered while modeling a class of ferry based wireless local area networks (FWLAN). A ferry facilitates local communication between the nodes (or users) as well as the communication between the nodes and a base station (BS) that serves as the gateway with the external world. The ferry, while walking in a predetermined cyclic path, communicates with the static nodes of the network via a wireless link. The ferry is assumed to stop and communicate with a node that has a packet to send or to receive, when it is closest to that node. The location distribution of the node to which (or from which) a packet arrives is assumed to have a support of positive Lebesgue measure. These features imply that polling models with finite number of queues cannot be used to model the system. Further, in almost all studied continuous polling systems, the user leaves the system after his service is completed. But for every local data transfer, the ferry has to collect the data from the source and then deliver the same to the sink. It either delivers the data to the sink on its own or has to be guided by the BS for the same. Thus each transfer may require services at two or three independent locations. Such an application can be modeled by polling systems with rerouting. We study the continuous polling models with rerouting, via discretization approach and by using the known Pseudo conservation laws of discrete systems. We obtain its stationary expected workload as the limit of the same for a discrete system. Our results rely heavily on fixed point analysis of infinite dimensional operators.