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3. 9: Stochastic process size vs. 1 Stochastic Process Size as a Function of the Number of Tasks In the first set of experiments we analysed the impact of the number of tasks on the process size. We considered task sets of 10 to 19 independent tasks. LCM , the least common multiple of the task periods, was 360 for all task sets. 8 (keeping LCM = 360). 9. 10 depicts the maximum size of the sliding window for the same task sets. As it can be seen from the diagram, the increase, both of the process size and of the sliding window, is linear.

S7 ∈ H0 , s8 , s9 , . . 6). In general, let us consider a state s and let Ps be the set of its predecessor states. Let k denote the order of the state s defined as the lowest hyperperiod of the states in Ps (k = min{j : s ∈ Hj , s ∈ Ps }). If s ∈ Hk and s is of order k and k < k, then s is a back state. In our example, s8 , s9 , s14 , and s19 are back states of order 0, while s20 , s25 and s30 are back states of order 1. Obviously, there cannot be any transition from a state belonging to a hyperperiod H to a state belonging to a lower hyperperiod than H (s → s , s ∈ Hk , s ∈ Hk ⇒ Hk ≤ Hk ).

19 CH. 3. 1 Functionality The functionality of an application is modelled as a set of processing tasks, denoted with t1 , t2 , . . , tn . A processing task is a piece of work that has a conceptual unity and is assigned to a processing element. Examples of processing tasks are performing a discrete cosine transform on a stream of data in a video decoding application or the encryption of a stream of data in the baseband processing of a mobile communication application. Let P T denote the set of processing tasks.

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