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Service variability in IP networks creates the need for QoS (quality of service) assessment tools. These tools must provide estimations of the quality of service through different paths in the network. Some existing schemes require a large number of probe packets to be sent to achieve accurate estimates. Others use traffic monitoring with administrative control, the most adopted of which being SNMP (simple network management protocol) and RMON (remote monitoring). We propose a quality of service estimation mechanism for voice over IP (VoIP) that necessitates a small number of probe packets while adding simple queuing delay estimation functionality in core routers. The underlying concept is that variation in delay, jitter and available bandwidth, as seen by a voice application, is due to queuing variations at intermediate hops. Collecting and combining queuing delay estimates from core routers can therefore be used to obtain accurate QoS estimates. Our results indicate better performance than existing QoS estimation tools under similar conditions.