To estimate arterial travel time/delay, the key element is to estimate intersection queue length, since travel time, delay, and level of services can be easily derived from queue length information. In this study, we developed a new traffic flow model, named shockwave profile model (SPM), to describe queuing dynamics for congested arterial networks. Taking advantage of the fact that traffic states within a congested link can be simplified as free-flow, saturated, and jammed conditions, the SPM simulates traffic dynamics by analytically deriving the trajectories of four major shockwaves. This model is particularly suitable for simulating congested traffic especially with queue spillover. In the SPM, a novel approach is proposed as part of the SPM, in which queue spillover is treated as either extending a red phase or creating new cycles. Since only the essential features, i.e. queue build-up and dissipation, are considered, the SPM significantly reduces the computational load and improves the numerical efficiency. We further validated the SPM using real-world traffic signal data collected from a major arterial in the Twin Cities. The results clearly demonstrate its effectiveness and accuracy. This model can be applied to estimate arterial travel time and delay and optimize signal timing in real time.