Three periodic tasks run under fixed-priority interrupts on a controller

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Digital electronics, embedded systems and data acquisition · Digital electronics, embedded systems and data acquisition

Inside the Instrument, Ch Microcontrollers and programmable logic for measurement

Problem

Three periodic tasks run under fixed-priority interrupts on a controller, with periods

T_1 = 2\,\mathrm{ms}

T_2 = 8\,\mathrm{ms}

T_3 = 20\,\mathrm{ms}

and worst-case execution times

C_1 = 0.3\,\mathrm{ms}

C_2 = 1.0\,\mathrm{ms}

C_3 = 3.0\,\mathrm{ms}

. The controller nests interrupts, so every task is fully pre-emptive and none is ever blocked; each deadline equals its period, and priorities are in rate-monotonic order. ((a)) Compute the total utilisation

\sum C_i/T_i

. ((b)) Compare it with the rate-monotonic bound

n(2^{1/n}-1)

for

n=3

(quoted as

0.780

), and state whether the set is guaranteed schedulable. ((c)) Now run the same tasks on a controller that does not nest interrupts, so a task already running cannot be pre-empted. Find task 1's worst-case response time and decide whether it meets its deadline.

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