Traffic-monitoring systems (TMSs) are vital for safety and traffic optimization. However, these systems may compromise the privacy of drivers once they track the position of each driver with a high degree of temporal precision. In this paper, we argue that aggregated data can protect location privacy while providing accurate information for traffic monitoring. We identify a range of aggregate query types. Our proposed privacy-aware monitoring system (PAMS) works as an aggregate query processor that protects the location privacy of drivers as it anonymizes the IDs of cars. Our experiments show that PAMS answers queries with high accuracy and efficiency.