Car path, platoon length, and flow rate equations are developed for the purpose of studying the platoon dynamics at signalized traffic links. The basic modeling is macroscopic in nature and is based on the formation of shock waves generated within the link due to the intermittent service of traffic by the signals. The analysis reveals not only platoon dispersion but also platoon compression, a phenomenon already observed but not previously described mathematically. It is demonstrated that compression does not only occur to platoons entering the link in red but also to those entering in green even in the absence of a downstream signal. Numerical examples are also presented for demonstrating the applicability of the theory.