Cloud computing market is continually growing in the last years and becoming a new opportunity for business for private and public organisations. The diffusion of multi-tenants distributed systems accessible by clouds leads to the birth of some cross-organisational environments, increasing the organisation efficiency, promoting the business dynamism and reducing the costs. In spite of these advantages, this new business model drives the interest of researchers and practitioners through new critical issues. First of all, the multi-tenant distributed systems need new techniques to improve the traditional resource management distribution along the different tenants. Secondly, new approaches to the process analysis and monitoring analysed since cross-organisational environments allow various organisations to execute the same process in different variants. Hence, information about how each process variant characterised can be collected by the system and stored as process logs. The usefulness of such logs is twofold: these logs can be analysed using some process mining techniques to understand and improve the business processes and can be used to find better resource management and scalability. This paper proposes a cloud computing multi-tenancy architecture to support cross-organisational process executions and to improve resource management distribution. Moreover, the approach supports the systematic extraction/composition of distributed data from the system event logs that are assumed to carry information of each process variant. To this aim, the approach also integrates an online process mining technique for the runtime extraction of business rules from event logs. Declarative processes are used to represent process variants running on the analysed infrastructure as they are particularly suited to represent the business process in a context characterised by low predictability and high variability. In this work, we also present a case study where the proposed architecture is implemented and applied to the execution of a real-life process of online products selling.