packets travelling in non-homogeneous networks
This paper considers a probability model for travel of a packet from a source node to a destination node in a large non-homogeneous multiple hop network with unreliable routing tables. Use of a random model is justified by the lack of precise information that can be used in each step of the packet's travel, and randomness can also be useful in exploring alternate paths when a long sequence of hops has not resulted in the packet's arrival to the destination. The packet's travel may also be impeded if certain routers on its path prove to be unreliable, or the packet may be dropped from a buffer or destroyed due to packet loss. The packet also has a limited time-out that allows the source to retransmit a dropped or lost packet. Because the network itself may be extremely large, we consider packet travel in an infinite random non-homogeneous medium, with events that may interrupt, destroy or stop the packet from moving towards its destination. We derive a numerical-analytical solution allowing us to compute the average travel time of the packet from source to destination, as well as to estimate its energy consumption. Two interesting applications are then presented. In the first one a wireless network where areas which are remote from the source and destination nodes may have poor wireless coverage so that the packet losses become more frequent as the packet "unknowingly" (due to poor routing tables for instance) meanders away from the source and destination node. The second application is related to defending a destination node against attacks that take the form of packets that carry a virus or a worm that can be detected via deep packet inspection at intermediate nodes, and as the packet approaches the destination node it is more frequently inspected and dropped if it is a threat.
diffusion process brownian motion multi-hop networks