Most of the QoS routing schemes proposed so far require periodic exchange of QoS state information among routers, imposing both communication overhead on the network and processing overhead on core routers. Furthermore, stale QoS state information causes the performance of these QoS routing schemes to degrade drastically. In order to circumvent these problems, we focus on localized QoS routing schemes where the edge routers make routing decisions using only "local" information and thus reducing the overhead at core routers. We first describe virtual capacity-based routing (VCR), a theoretical scheme based on the notion of virtual capacity of a route. We then propose proportional sticky routing (PSR), an easily realizable approximation of VCR and analyze its performance. We demonstrate through extensive simulations that adaptive proportional routing is indeed a viable alternative to the global QoS routing approach.