On the stability of shuffle-exchange and bidirectional shuffle-exchange deflection networks

In a stable packet-switched network, throughput equals offered load and packet backlogs do not build up in an unbounded manner. A network with an unstable operating region poses the problem that it may evolve eventually to a stable but saturated operating point with a low throughput. This paper considers the shuffle-exchange and bidirectional shuffle networks when operated with deflection routing. It is shown that both networks exhibit instability when packet contention is resolved in a random manner. However, instability can be avoided if contention is resolved in a manner that favors packets closest to their destinations. This obviates the need for complicated network access control to prevent instability.