On Quadratic Adaptive Routing Algorithms Two analytic models of a store-and-forward communications network are constructed, one to find the optimal message routing and the other to illustrate the equilibrium (stationary state) maintained by an adaptive routing algorithm. These models show that adaptive routing does not satisfy the necessary conditions for an optimal routing, Adaptive routing tends to overuse the direct path and underuse alternate routes because it does not consider the impact of its current routing decision on the future state of the network. The form of the optimality conditions suggests that a modification of the adaptive algorithm will result in optimality. The modification requires the substitution of a quadratic bias term instead of a linear one in the routing table maintained at each network node. Simulation results are presented which confirm the theoretical analysis for a simple network. CACM January, 1976 Agnew, C. E. routing algorithms, adaptive routing, quadratic routing, alternate routing, store-and-forward network, distributed network, computer network, message switching 3.81 8.0 8.1 8.3 CA760103 JB January 5, 1978 10:37 AM 2890 5 2890 2890 5 2890 2890 5 2890