In a packet switching network, congestion is unavoidable and affects the quality of real-time traffic with such problems as delay and packet loss. Packet fair queuing (PFQ) algorithms are well-known solutions for quality-of-service (QoS) guarantee by packet scheduling. Our approach is different from previous algorithms in that it uses hardware time achieved by sampling a counter triggered by a periodic clock signal. This clock signal can be provided to all the modules of a routing system to get synchronization. In this architecture, a variant of the PFQ algorithm, called digitized delay queuing (DDQ), can be distributed on many line interface modules. We derive the delay bounds in a single processor system and in a distributed architecture. The definition of traffic contribution improves the simplicity of the mathematical models. The effect of different time between modules in a distributed architecture is the key idea for understanding the delay behavior of a routing system. The number of bins required for the DDQ algorithm is also derived to make the system configuration clear. The analytical models developed in this paper form the basis of improvement and application to a combined input and output queuing (CIOQ) router architecture for a higher speed QoS network.