2014/02/12 by William F. Bradley, Bradley, William F.
Business, Management and Accounting · Computer Science · Mathematics · #Advanced Queuing Theory Analysis #Mobile Ad Hoc Networks #Network Traffic and Congestion Control #cs.NI #math.PR
paper · pdf · doi:10.48550/arxiv.1402.2963
Bradley, William F. (2002). Running in circles: packet routing on ring networks (Doctoral dissertation, Massachusetts Institute of Technology)
arxiv created 2014/02/12 · arxiv updated 2014/02/13
I analyze packet routing on unidirectional ring networks, with an eye towards establishing bounds on the expected length of the queues. Suppose we route packets by a greedy "hot potato" protocol. If packets are inserted by a Bernoulli process and have uniform destinations around the ring, and if the nominal load is kept fixed, then I can construct an upper bound on the expected queue length per node that is independent of the size of the ring. If the packets only travel one or two steps, I can calculate the exact expected queue length for rings of any size. I also show some stability results under more general circumstances. If the packets are inserted by any ergodic hidden Markov process with nominal loads less than one, and routed by any greedy protocol, I prove that the ring is ergodic.