6.2.1. Anonymity Set Size

Anonymity is one of the significant metrics for evaluation of location privacy. It is the process of the grouping of users of similar status in a vicinity that hides the identity of a user in the group. Anonymity Set Size (ASS) is defined is the set of users/vehicles, including target users that are indistinguishable among the group of users. ASS achieves the anonymisation of the vehicle in a group of vehicles of similar status. In the road network, ASS is preferred, which hides the actual identities of a target vehicle during communication. Its value affects the location privacy of vehicles. The higher the ASS, the higher will be the level of vehicle privacy. We consider the arrival of vehicles at a particular point at the road is the Poisson process with rate *λ* and *X* is a random variable that denotes the number of vehicles gathered at the congested area for an interval of time *T*; then, the probability is calculated as follows [12]:

$$P(X = x) = \frac{(\lambda T)^x}{x!}e^{-(\lambda T)},\tag{21}$$

where *λT* is the expected number of vehicles that change pseudonyms cooperatively. This can improve the anonymity of vehicles in the vicinity by updating pseudonyms at the same time. Hence, the expected number of vehicles during the time *T* is denoted as:

$$E(X=x) = \sum\_{\mathbf{x}=1}^{\infty} \mathbf{x} \frac{(\lambda T)^{\mathbf{x}}}{\mathbf{x}!} e^{-(\lambda T)} = \lambda T. \tag{22}$$

After the computation of probability and the expected number of vehicles at a certain time, the anonymity set size is calculated as follows:

$$\left|ASS\right| = \sum\_{i,j=1}^{n} V\_i\\PC\_j = \sum\_{i=1}^{n} E(X\_i = x) = \sum\_{j=1}^{n} \lambda\_j T. \tag{23}$$

where *ViPC<sup>j</sup>* is the number of vehicle update pseudonyms that anonymize the target vehicle in the region.
