The document discusses several problems related to real-time embedded systems: 1) A system with 4 scanning tasks that take 5 ms each and a data handling task that takes 20 ms. The maximum periodicity of the heartbeat timer for no overflow is calculated. 2) If one scanner updates at 50 ms instead of 100 ms and its workload increases by 40%, the new timer period is calculated. 3) A system with 3 tasks of varying priorities and execution times, and the response time is calculated assuming interrupt-driven scheduling. 4) Tasks synchronized with a semaphore, and the execution profile and blocked time are drawn. Processor utilization does not depend on semaphore mode.

1. Real-time Embedded Systems Lecture 4 Numerical & Analytical Problems Prof. Dr. Amitava Gupta Department of Power Engineering Jadavpur University, India Real-time Embedded Systems- Lecture 03

2. A real-time system consists of 4 scanner tasks which scan sensor data from the field in a real-life plant and writes on to a buffer which is read by a data handler once in every 100 ms. Each scanner takes 5 ms. and the data handler takes a further 20 ms. If the whole system is controlled by a heart-beat timer which takes 20 micro-sec. each time it is triggered, what should be the maximum periodicity of the timer, so that no overflow occurs. Assume RM scheduling for the tasks. Solution: chalk and board Real-time Embedded Systems- Lecture 03

3. If now, one of the scanners update the data at a higher periodicity, i.e. once in 50 ms. and the data handling load for this increases by 40%, what should be the new period for the heart-beat timer? Solution: chalk and board Real-time Embedded Systems- Lecture 03

4. A real-time embedded system is developed around an intel 8088 based system with a single 8259. It comprises three tasks T 1 , T 2 and T 3 , with priorities in the same sequence which are connected to IRQs 4,5 and 6 respectively, with a default priority assignment for the IRQs. If the tasks are associated with execution times of 20, 25 and 30 msec. respectively, and the interrupt latency is 5 micro-sec., what is the response time of the system, if interrupt driven scheduling is assumed? If the period at which the triggers arrive is same and it is P, what should be the minimum value of P if no overflow occurs, assuming scheduling overhead is 10%? Sketch the execution profile for two cycles if P is reduced below this value. Solution chalk and board Real-time Embedded Systems- Lecture 03

5. 3 tasks T 1 , T 2 and T 3 , with priorities in the same sequence are synchronized using a flag semaphore. Initially,T 1 and T 2 are in the blocked state when T 3 runs for 50 ms after having set the semaphore, when it is pre-empted by T 2 . T 2 runs for 30 ms. more before it is blocked again , while trying to set the same semaphore, and T 3 runs for a further period of 10 ms. when it is pre-empted by T 1 which runs for 20 ms. and gets blocked again when it tries to set the semaphore set by T 1 .T 3 then runs for 15ms. and resets the semaphore. If T 2 and T 1 take further 20 ms. each to complete the activities for the particular cycle, draw the execution profile and calculate the time spent by T 1 in blocked mode assuming a) a burst mode semaphore and b) a FIFO mode semaphore. What is the processor utilization in this case? Does this depend on the execution profile or the semaphore mode? Solution: chalk and board Real-time Embedded Systems- Lecture 03

6. For the problem in slide 3 derive a suitable synchronization mechanism for the application and explain your answer with appropriate pseudocodes. Solution: chalk and board Real-time Embedded Systems- Lecture 03