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**Extra info for Analysis and optimisation of real-time systems with stochastic behaviour**

**Example text**

Hence, it is not sufficient to analyse the system over the interval [0, LCM ) but rather over several consecutive intervals of length LCM . Let an interval of the form [k · LCM, (k + 1) · LCM ) be called the hyperperiod k and denoted Hk . Hk is a lower hyperperiod than Hk (Hk < Hk ) if k < k. Consequently, Hk is a higher hyperperiod than Hk (Hk > Hk ) if k > k . For brevity, we say that a state s belongs to a hyperperiod k (denoted s ∈ Hk ) if its PMI field is a subinterval of the hyperperiod k.

The following example is used throughout this subsection in order to discuss the construction of the stochastic process. e. 2. ANALYSIS ALGORITHM 35 τ1, {τ2}, 0 τ2, Ø, t 1 τ2, Ø, t 2 ... τ2, Ø, t k τ2, {τ1}, tk+1 ... 2: State encoding dent tasks with corresponding periods 3 and 5. The tasks are scheduled according to a non-preemptive EDF scheduling policy [LL73]. LCM , the least common multiple of the task periods is 15. For simplicity, in this example it is assumed that the relative deadlines equal the corresponding periods (δi = πi ).

3. 11: Stochastic process size vs. 12: Stochastic process size vs.