I want to model the case where a particular message is forwarded from a source to multiple nodes with transmission radius r (in multiple hops), until the message reaches a particular destination. The source and the destination are fixed. The other nodes move with known speed and direction of movement (those quantities might be random in general).
Is there any way to model the average number of hops, or the average time it takes for the message to reach the destination? It seems that this is a case of Markov Point Processes (or Strauss Processes) but I can't find a good reference that takes into account the time parameter in order to model the meeting times of the nodes that are in distance less than r apart, or models the inter-meeting times in order to calculate the total average.
In case we use Point processes, we can model the mobile nodes position using a Poisson point process and use random movements (uniformly over each direction) at every time slot for modeling the motion of the nodes on the terrain. Any ideas on how to approach this problem?