Attribute-based access control (ABAC) is well known for flexible policy specification and dynamic decision-making capabilities. Unlike the other access control models, in ABAC, privileges are granted on the basis of the values (e.g., manager, deputy manager, secret, etc.) of the attributes (e.g., role, security level, etc.) of various entities (e.g., users, objects, environment, etc.). Therefore, it is imperative to associate the appropriate values of attributes to entities for ensuring proper access. Although ample amount of research has been done on ABAC, there is a lack of literature that addresses both constraints and the hierarchies of the values of the attributes of users and objects. This paper explores a family of ABAC models, which presents the multiple variations of ABAC, and also proposes a consolidated ABAC model, known as AHCSABAC, which specifies the hierarchies of the values of the attributes of users and various constraints on the values of the attributes of users. The usefulness of AHCSABAC model is then demonstrated.