Middleware tools are generally used to glue together distributed, heterogeneous systems into a coherent composite whole. Unfortunately, there is no clear conceptual framework in which to reason about transactional correctness in such an environment. This paper is a first attempt at developing such framework. Unlike most existing systems, where concurrent executions are controlled by a centralized scheduler, we will assume that each element in the system has its own independent scheduler receiving input from the schedulers of other elements and producing output for the schedules of yet other elements in the system. In this paper we analyze basic configurations of such composite systems and develop correctness criteria for each case. Moreover, we also show how these ideas can be used to characterize and improve different transaction models such as distributed transactions, sagas, and federated database transactions.
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