One of the key challenges in the success of vehicular ad hoc networks (VANETs) is to consider the location privacy of drivers. Although, the pseudonym changing approach is suggested by standardization development organizations such as IEEE and ETSI, the development of an effective pseudonym changing strategy is still an open issue. The existing pseudonym changing strategies are either not effective to protect against the pseudonyms linking attacks or can have a negative impact on the VANETs’ applications. To address these issues, this paper proposes a new pseudonym changing strategy based on the Vehicular Location Privacy Zone (VLPZ), which is a roadside infrastructure designed and dedicated to change the pseudonyms. Existing roadside infrastructures such as gas stations and toll booths are considered as typical places to implement a VLPZ. An analytical model based on queuing theory is developed to evaluate the location privacy protection achieved at a VLPZ using the size of vehicles’ anonymity set as a metric.