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Test of Discrete Event Systems - 12.11.2019

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Test of Discrete Event Systems - 12.11.2019

Exercise 1

Consider the stochastic timed automaton represented in the figure,

where E = {a, d

1

, d

2

}, X = {1, 2, 3, 4, 5, 6, 7}, p = 3/5, and the initial state is x

0

= 1. Using Matlab, simulate the model and estimate the limit probabilities

• lim

k→∞

P(X

k

= x)

• lim

k→∞

P(E

k

= e)

for all states x ∈ X and events e ∈ E, under the following different assumptions on the stochastic clock structure.

1. The lifetimes of events a, d

1

and d

2

follow uniform distributions over the intervals [15, 25], [12, 18], and [16, 20] min, respectively.

2. The lifetimes of event a follow an exponential distribution with expected value 20 min, while for events d

1

and d

2

the lifetimes are generated as above.

3. The lifetimes of event a follow an exponential distribution with expected value 20 min, while

d

1

and d

2

have deterministic lifetimes, all equal to 15 and 18 min, respectively.

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