The paper proposes novel algorithms for Quality of Service (QoS) routing in IP networks. The new algorithms can handle incomplete information, when link measures (e.g. link delays, bandwidths... etc.) are assumed to be random variables. Incomplete information can arise due to aggregated information in PNNI and OSPF routing protocols, which make link measures characterized by their corresponding p.d.f. It will be demonstrated that the task of QoS routing can be viewed as quadratic optimization. Therefore, neural based optimization algorithms implemented on an analog computer (CNN) can provide fast routing algorithms even in the case of incomplete information. As a result, real-time routing can be carried out to meet end-to-end QoS (such as end-to-end delay) requirements.