Deflection Routing on a Torus Is Monotone.

Deflection Routing is proposed for all optical core switches because of the lack of optical memory. In Shortest-path Deflection Routing, switches attempt to forward packets along a shortest hop path to their destinations. Each link can send a finite number of packets per time-slot (the link capacity). Incoming packets have to be sent immediately to their next switch along the path. If the number of packets which require a link is larger than the link capacity, only some of them will use the link they ask for and the other ones have to be misdirected or deflected. We build the Markov chain which models a packet routing in an odd torus. We prove that this matrix is $\preceq_{st}$-monotone. The proof is based on increasing sets as we consider a partial ordering on the state space based on the network topology. [ABSTRACT FROM AUTHOR]