On the asymptote of the optimal routing policy for two service stations

Abstract

It has been previously proved that the optimal routing control of a two-station Markovian network with linear cost is described by a monotone switching curve. With the discounted cost objective function, it is proven in this paper that the optimal switching curve has a finite asymptotic limit when c/sub 1/ not=c/sub 2/, where c/sub i/ is the unit inventory cost at station i. Whereas, for the case with c/sub 1/=c/sub 2/, as well as the case with the long-run average objective function, the switching curve does not have a finite asymptote. >