The modeling of headway/spacing between two consecutive vehicles in a queue has many appli-cations in traffic flow theory and transport practice. Most known approaches have only studied vehicles on freeways. This paper presents a model for the spacing distribution of queuing vehicles at a signalized junc-tion based on random-matrix theory. The spacing distribution of a Gaussian symplectic ensemble (GSE) fits well with recently measured spacing distribution data. These results are also compared with measured spacing distribution observed for the car parking problem. Vehicle stationary queuing and vehicle parking have different spacing distributions due to different driving patterns.