DEADLINE MONOTONIC ALGORITHM (DMA)

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1 CHAPTER 4 By Radu Muresan University of Guelph Page 1 ENGG4420 CHAPTER 4 LECTURE 5 November :07 PM DEADLINE MONOTONIC ALGORITHM (DMA) RMA no longer remains an optimal scheduling algorithm for periodic real time tasks, when task's period pi differs from the relative deadline di. For such task sets DMA is more proficient than RMA DMA is a variant of RMA and assigns priorities to tasks based on their relative deadlines, rather than assigning priorities based on task periods. DMA assigns higher priorities to tasks with shorter relative deadlines When the relative deadline of every task is proportional to its period, RMA and DMA produce identical solutions When the relative deadlines are arbitrary, DMA is more proficient than RMA in that it can sometimes produce a feasible schedule when RMA fails on the other hand RMA always fails when DMA fails.

2 CHAPTER 4 By Radu Muresan University of Guelph Page 2 EXAMPLE 5 Check if the following task set is schedulable by DMA and then by RMA:

3 CHAPTER 4 By Radu Muresan University of Guelph Page 3 CONTEXT SWITCHING OVERHEAD So far, we have ignored in our schedulability tests the switching overhead. Under RMA, whenever a task arrives, at most it preempts one task the task that is currently running. However, there might be situations when we have only one context switch such as: 1) the task arrives when the processor is idle or 2) when a higher priority task executes. We can conclude that in the worst case, each task incurs at most 2 context switches under RMA: one, when it arrives and preempts a lower priority task and the second when it completes. For simplicity we assume that the context switch is constant, and equals c ms. As a result, we can consider that the net effect of context switch increases the execution time of each task Ti to (ei + 2*c). In order to take context switching time into consideration, in all schedulability computations, we need to replace ei by (ei + 2c) for each Ti.

4 CHAPTER 4 By Radu Muresan University of Guelph Page 4 EXAMPLE 6 Check the schedulability under RMA on a uniprocessor for the following task set: T1 = (100, 20); T2 = (150, 30); T3 = (200, 90). Assume that context switching overhead does not exceed 1 ms and is to be taken into account in all computations.

5 CHAPTER 4 By Radu Muresan University of Guelph Page 5 SELF SUSPENSION When a task self suspends, the operating system removes the task from the ready queue, places it in the blocked queue, and takes up the next eligible task for scheduling thus self suspension introduces an additional scheduling point which we did not consider before. Definition. In event driven scheduling, the scheduling points are defined by task completion, task arrival, and self suspension events. Self suspension effect on the schedulability of a task set {T1, T2,..., Tn} when the worst case self suspension time of a task Ti is bi. Let the delay that task Ti might incur due to self suspension and the self suspension of all higher priority tasks be bti

6 CHAPTER 4 By Radu Muresan University of Guelph Page 6 EXERCISE: Explain the self suspension expression (1) by justifying the terms of the right side. SOLUTION

7 CHAPTER 4 By Radu Muresan University of Guelph Page 7 SELF SUSPENSION OF A LOWER PRIORITY TASK Ti A higher priority task Tk may affect the response time of a lower priority task Ti by as much as min (ek, bk), as a caused of self suspension.

8 CHAPTER 4 By Radu Muresan University of Guelph Page 8 EXAMPLE 7 Consider the following set of periodic real time tasks: T1=(50, 10); T2 = (150, 25); T3 = (200, 50). Assume that the self suspension times of T1, T2, and T3 are 3, 3, and 5 respectively. Determine if the task will be RMA schedulable.

9 CHAPTER 4 By Radu Muresan University of Guelph Page 9 SELF SUSPENSION WITH CONTEXT SWITCHING OVERHEAD Let us examine the effect of context switches on the generalized Lehoczky test that consider self suspensions. In a fixed priority preemptable system, each task preempts at most one task if there is no self suspension at most two context switches When a task self suspends, it causes at most two additional context switches As a result, when a task is allowed to self suspend we will incur at most 4 context switches as overhead We need to replace the execution time of a task Ti by (ei + 4c), where c is the maximum context switch time.

10 CHAPTER 4 By Radu Muresan University of Guelph Page 10 ISSUES IN USING RMA IN PRACTICAL SITUATIONS Practical RMA problems that need to be addressed: handling critical tasks with long periods; handling aperiodic and sporadic tasks; coping with limited priority levels; dealing with task jitter. HANDLING CRITICAL TASKS WITH LONG PERIODS Consider a critical task that has a long period in comparison with some task of lower criticality as a result, the critical task could miss at times its deadline due to some transient overload of low critical (but high priority) task. If we raise the priority of critical task to higher level, then the RMA schedulability results would not hold. SOLUTION period transformation technique The critical task Ti is logically divided into k small subtasks of period, deadline, execution times of pi/k; di/k and ei/k The net effect of Ti being logically split into {Ti 1,..., Ti k } is to effectively raise the priority of Ti Each subtasks of Ti would be represented by:

11 CHAPTER 4 By Radu Muresan University of Guelph Page 11 HANDLING APERIODIC AND SPORADIC TASKS Under RMA it is difficult to assign high priority values to sporadic tasks a burst of sporadic task arrivals would overload the system The RMA schedulability analysis presented are no longer applicable when aperiodic and sporadic tasks are assigned high priority values therefore these type of tasks have very low priority values However, in practical applications sometimes we need high priority for sporadic tasks. SOLUTION: APERIODIC SERVER Handles aperiodic and sporadic tasks and passes them to an RMA scheduler. The server deposits a "ticket" which is replenished at the expiration of a certain replenishment period. When an aperiodic event occurs, the server checks to see whether any ticket is available. Based on the ticket creation policies we have: 1) deferrable servers; 2) sporadic servers Deferrable servers: tickets are replenished at regular intervals, completely independent of the actual ticket usage if an aperiodic task arrives, the system will process it immediately if it has enough tickets, and wait until the tickets are replenished if it does not. Sporadic server: the replenishment time depends on exact ticket usage time as soon as a ticket is used, the system set a timer that replaces any used tickets when the timer goes off (in this way a minimum separation between sporadic tasks is guaranteed.

12 CHAPTER 4 By Radu Muresan University of Guelph Page 12 COPING WITH LIMITED PRIORITY LEVELS As the number of priority levels increases, the number of feedback queues to be maintained by the operating system also increases. As a result, increased memory requirement and processing overhead at every scheduling point. To reduce OS overload and to improve task response times, some RTOS support only a restricted number of priority levels (i.e. Real Time LabView) PROBLEM: more tasks than priority levels => more tasks need to share same priority level RMA analysis differ in this case HOW LEHOCZKY'S TEST CHANGES when priority sharing among tasks? Let SP(Ti) be the set of tasks sharing a single priority value with the task Ti

13 CHAPTER 4 By Radu Muresan University of Guelph Page 13 PRIORITY ASSIGNMENT TO TASKS 1) 2) 3) There are various schemes available for assigning priority values to tasks when the number of real time tasks to be scheduled exceed the distinct real time priority levels supported by the underlying OS Uniform Scheme: all tasks in the application are divided uniformly among the available priority levels if uniform division is not possible, then more tasks should be made to share the lower priority levels for better schedulability; Arithmetic scheme: the number of tasks assigned to different priority levels form an arithmetic progression a possible scenario would be that r tasks are assigned to the highest priority level, 2r to the next highest priority level, etc. for a total of N tasks in an application N = r + 2r + 3r +... nr; where n is the total number of priority levels; Geometric scheme: the number of tasks assigned to different priority levels form a geometric progression the r task having the shortest periods are assigned to the highest priority level, kr 2 tasks are assigned to the next highest priority level, etc.

14 CHAPTER 4 By Radu Muresan University of Guelph Page Logarithmic scheme or logarithmic grid assignment scheme The scheme requires that the shorter period tasks should be allotted distinct priority levels as much as possible while the lower priority tasks should be combined together at the same priority levels the high priority tasks will be assured schedulability. PROCEDURE: arrange task in increasing order of their periods; the range of task periods are divided into a sequence of logarithmic intervals; the tasks are assigned to priority levels based on the logarithmic intervals they belong to EXAMPLE. Consider an OS with 4 priority levels. An application with 10 periodic real time tasks are to be scheduled on this OS using RMA. It is known that pmax = 10,000 ms and pmin = 1 ms. Other task periods are distributed uniformly over this interval. Assign the tasks to priority levels using the logarithmic scheme

15 CHAPTER 4 By Radu Muresan University of Guelph Page 15 DEALING WITH TASK JITTER (Arrival jitter) = (latest arrival time among all instances of a task) (earliest arrival time among all instances of a task); (Completion time jitter) = (latest completion time) (the earliest completion time of the task). CAUSES FOR ARRIVAL JITTER physical clock skew CAUSES FOR COMPLETION JITTER basic nature of RMA the response time of a task depends on how many higher priority tasks arrive (or were waiting) during the execution of the task. Real time developers commonly handle tasks with tight completion time jitter requirements following one of these techniques: 1. If only one or two actions (tasks) have tight jitter requirements, these actions are assigned very high 2. priority works well for small applications If jitter must be minimized for an application that is barely schedulable, each task needs to be split into two parts: one part that computes the output but does not passes it on, and one which passes the output on. a. This method involves setting the second task's priority to very high values and its period to be the same as that of the first task an action scheduled with this approach will run one cycle behind, but the task will have tight completion time jitter.

16 CHAPTER 4 By Radu Muresan University of Guelph Page 16 END OF CHAPTER 4

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