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When investigating the performance of running scientific/commercial workflows in parallel and distributed systems, we often take into account only the resources allocated to the tasks constituting the workflow, assuming that computational resources will accept the tasks and execute them to completion once the processors are available. In reality, and in particular in grid or e-business environments, security policies may be implemented in the individual organisations in which the computational resources reside. It is therefore expedient to have methods to calculate the performance of executing workflows under security policies. Authorisation control, which specifies who is allowed to perform which tasks when, is one of the most fundamental security considerations in distributed systems such as grids. Role-based access control (RBAC), under which the users are assigned to certain roles while the roles are associated with prescribed permissions, remains one of the most popular authorisation control mechanisms. This paper presents a mechanism to theoretically compute the performance of running scientific workflows under RBAC authorisation control. Various performance metrics are calculated, including both system-oriented metrics, (such as system utilisation, throughput and mean response time) and user-oriented metrics (such as mean response time of the workflows submitted by a particular client). With this work, if a client informs an organisation of the workflows they are going to submit, the organisation is able to predict the performance of these workflows running in its local computational resources (e.g. a high-performance cluster) enforced with RBAC authorisation control, and can also report client-oriented performance to each individual user.