Polynomial Cost Approximations in Markov Decision Theory Based Least Cost Routing

The problem of call admission control and routing in a multi-service circuit-switched loss network can be solved optimally under certain assumptions by the tools of Markov decision theory. However in networks of practical size a number of simplifying approximations are needed to make the solution feasible. Assuming link independence, we propose a new method for approximating the state-dependent link costs accurately and relatively efficiently, even on links with extremely large state spaces. The proposed polynomial approximations are optimal in the sense of minimizing the residual in the continuous-time Howard equations of the Markov decision processes associated with the links. Numerical results are presented, and the proposed approximations are found superior to two earlier link cost approximation methods.