1 \emph{A vessel where some chemical reaction takes place can be cooled by
2 inserting two different rods, each with different cooling capacities. Only one
3 rod can be inserted at a certain time. The vessel can be in three different
5 \textbf{no rods:
} then the temperature T evolves according to the differential
6 equation $T'=
0.1T −
10.0$.\\
7 \textbf{with rod1
}: equation is $T'=
0.1T −
11.2$\\
8 \textbf{with rod2
}: equation is $T'=
0.1T −
12.0$ (so rod2 cools better than
10 A rod will be inserted if the temperature reaches
110 degrees. A rod that is in
11 the vessel will be removed from the vessel if the temperature is between
102
12 and
105 degrees. When a rod is removed, it cannot be used for
20 time units.\\
13 Initial temperature is
102 degrees. The objective is to keep the temperature
14 between
102 and
110 degrees. If the temperature is going up to
110 degrees but
15 no rod is yet available, the system goes into a state Overheating.
}
17 \emph{Specify the system in
\UPPAAL. Show that unfortunately it may reach state
18 \texttt{Overheating
}. What is the chance this happens within
100 time units?
}
21 \emph{Someone forwards the idea that the fact that the
\texttt{Overheating
}
22 state can be reached is due to rod2 cooling too well, and proposes to replace
23 rod2 by a rod that is similar to rod1. What do you think of this idea?
}