A controllable delegation model which is suitable for opening environment, based on usage and trustworthiness (UTCDM) is provided. The new model integrates the merits of both UCON (usage control model) and trust management(TM). In this paper, weight directed graph is used to describe the delegation relationship. An approach for controlling the depth of delegation focusing on the objects and the rights is discussed in this paper. The goal-directed chain discovery algorithm finds and retrieves credentials. The credentials graph which is searchable can be easily established with trust. The arithmetic of access controlling focusing on the depth and width of the delegation is discussed in the process of delegation. Finally, by giving an example to explain the processing of the system, the arithmetic is discussed in detail.