modeling hybrid systems wine fermentation and cells differeniation

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A multi-tiered system might start with requests from Web Clients that flow through a front-end Web-Server and then to a Web Application Server, which may in turn makes calls to other servers. Modeling the behavior of such distributed systems is a challenge, especially when the behavior consists of several collaborations of different parties, each involving possibly several starting(input) and ending(output) events of the involved components. We characterize a collaboration as a partial order of input and output events, and the performance of the collaboration is defined by the minimum delays required for a given output event with respect to an input event. We define the semantics of the dynamic behavior using the control flow operators from UML Activity diagrams, in terms of partial order relationships among the involved input and output events. Based on these semantics, we provide formulas for calculating the performance of composed collaborations in terms of the performance of the sub-collaborations, where each delay is characterized by a fixed value, a range of values and a distribution. We also propose approximations for the stochastic behavior with Normal Distributions.

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