Continuous polling with rerouting and applications to ferry assisted wireless LANs

In almost all studied polling systems, the user leaves the system after his service is completed. There are interesting applications, in which the users demand a second service (or more). For example, in a ferry assisted sparse wireless network, for every local data transfer the ferry has to collect the data from the source and then deliver the same to the sink. This type of application can be modeled by polling systems with rerouting. In polling systems with continuum of queues (on a circle), a moving server attends the users as and when it encounters one. When rerouting is supported, after the service is completed, the users can reroute to a different point in the same circle to await another service. We obtain the performance of such a system under quite general conditions. We come up with a special way of discretizing the continuous rerouting system such that: 1) the existing Pseudo conservation laws can be applied to obtain the expected workload of the discrete systems; 2) the limit of these ’discretized’ expected workloads equals the stationary expected work load of the continuous system. The results are applied to study a ferry assisted wireless local area network. Our results rely heavily on fixed point analysis of infinite dimensional operators.