From Static to Dynamic Routing: Efficient Transformations of Store-and-Forward Protocols

• Authors: Christian Scheideler;Berthold Vöcking
• Venue: SIAM Journal on Computing
• Year: 2000

We investigate how static store-and-forward routing algorithms can be transformed into efficient dynamic algorithms, that is, how algorithms that have been designed for the case that all packets are injected at the same time can be adapted to more realistic scenarios in which packets are continuously injected into the network. Besides describing specific transformations for well-known static routing algorithms, we present a black box transformation scheme applicable to every static, oblivious routing algorithm. We analyze the performance of our protocols under a stochastic and an adversarial model of packet injections.One result of our specific transformations is the first dynamic routing algorithm for leveled networks that is stable for arbitrary admissible injection rates and that works with packet buffers of size depending solely on the injection rate and the node degree, but not on the size of the network. Furthermore, we prove strong delay bounds for the packets. Our results imply, for example, that a throughput of 99% can be achieved on an n-input butterfly network with buffers of constant size while each packet is delivered in time O(log n), with high probability.Our black box transformation ensures that if the static algorithm is pure (i.e., no extra packets apart from the original packets are routed), its dynamic variant is stable up to a maximum possible injection rate. Furthermore, in the stochastic model, the routing time of a packet depends on local parameters such as the length of its routing path, rather than on the maximum possible path length, even if the static algorithm chosen for the transformation does not provide this locality feature and is not pure. In the adversarial model, the delay bound of the packets is closely related to the time bound given for the static algorithm.