CprE 458/558: Real-Time Systems (G. Manimaran)1 CprE 458/558: Real-Time Systems (m, k)-firm tasks and QoS enhancement

CprE 458/558: Real-Time Systems (G. Manimaran)2 (m, k) firm real-time tasks A periodic task is said to have an (m,k)-firm guarantee if it is adequate to meet the deadlines of m out of k consecutive instances of the task, where m ≤ k. The adaptive QoS management problem –Admit the tasks to satisfy at least the (m,k) guarantee –Maximize the QoS of admitted tasks beyond the (m,k) property, at run-time, without violating (m,k) property of any of the admitted tasks.

CprE 458/558: Real-Time Systems (G. Manimaran)3 Task model and performance index Task Model - firm periodic tasks [1,2] Tasks should meet m i deadlines for every K i consecutive instances Performance Index –Dynamic Failure Rate (DFR): for a task Ti, it is the percentage of instances of the task miss their (m,k) guarantee. –Marginal Quality Received (MQR): To maximize the quality of tasks during overloading, is increased as much as possible

CprE 458/558: Real-Time Systems (G. Manimaran)4 MK-RMS Schedulability Check [2] Utilization-based MK-RMS-schedulability check (sufficient, but not necessary) MKLoad <= n(2 1/n -1) Classification of mandatory and optional instances - Instances of task T i activated at times ap i is mandatory if Optional instance is assigned the lowest priority Mandatory instances are assigned priority as per RMS

CprE 458/558: Real-Time Systems (G. Manimaran)5 MK-RMS Schedulability - exact analysis [2] Theorem: Given such that Let If, MK-RMS meets the (m,k)-firm guarantee requirement of

CprE 458/558: Real-Time Systems (G. Manimaran)6 Scheduling Example Task 1 Task 2 RMS 120 (a) T 1 : T 2 : Task 1 Task 2 RMS 120 (b) T 1 : T 2 : Task 1 Task 2 RMS 120 (c) T 1 : T 2 : Task 1 misses its deadline

CprE 458/558: Real-Time Systems (G. Manimaran)7 Example (Cont.) We can increase the values to increase the QoS when the system is underloaded, and decrease the values to handle overloading. Feedback method can be used to adjust the values. –Regulated/measured variable: –Set point: desired value of –Control variable: estimation factor,, of

CprE 458/558: Real-Time Systems (G. Manimaran)8 Introduction (Cont.) Feedback control technique ControllerActuators Controlled RT System Sensors Set Points Control variable s Measured variables Regulated variables + - disturbance

CprE 458/558: Real-Time Systems (G. Manimaran)9 Proposed scheduling architecture [3] PI Controller Actuator Scheduler Admission Controller Submitted tasks Accepted tasks Average Dynamic Failure Rate CPU Completed tasks + - Set point

CprE 458/558: Real-Time Systems (G. Manimaran)10 Proposed scheduling architecture (Cont.) Admit tasks based on minimum quality requirement The actual execution time of tasks are normally less than or equal to the worst case execution time used in the admission test –Try to increase the quality as much as possible –Use feedback method to adjust. Non-zero set point is used – achieve high CPU utilization and low dynamic failure rate is zero with respect to – is changed with respect to the current later

CprE 458/558: Real-Time Systems (G. Manimaran)11 Feedback control algorithm

CprE 458/558: Real-Time Systems (G. Manimaran)12 Online controller design Initial Value of K: Halve K when DFR fluctuate across set point K –high value will lead to fluctuation –Low value will lead to a long time to reach the final value K on-line design System Controller Control signal Output Output changing observation Controller parameters Reference

CprE 458/558: Real-Time Systems (G. Manimaran)13 Fairness measure All tasks use the same value of all tasks are the same Fairness index ( ) in terms of : The higher the value of f for a task set, the better the fairness.

CprE 458/558: Real-Time Systems (G. Manimaran)14 MQR performance: Load = 1.1 and MKLoad varied – MQR decreases as MKLoad increases –ACET < WCET can be exploited to increase MQR –Feedback algo offers better MQR than non-feedback algo Simulation studies Feedback algorithm vs. iterative algorithm

CprE 458/558: Real-Time Systems (G. Manimaran)15 Simulation studies (Cont.) Fairness (f): –Fairness obtained by the feedback approach is higher than that obtained by non-feedback algo (MK-RMS)

CprE 458/558: Real-Time Systems (G. Manimaran)16 Imprecise computation - summary Offers scheduling flexibility to achieve graceful degradation (i.e., means to achieve predictable timing faults without violating system spec) Applicable only to a class of applications Models –Imprecise computation - monotone model –Imprecise computation – 0/1 constraint model –(m,k)-firm model

CprE 458/558: Real-Time Systems (G. Manimaran)17 References [1] Reference [18] in chapter 4. [2] Overload management in real-time control applications using (m, k)-firm guarantee Ramanathan, P.; IEEE Transactions on Parallel and Distributed Systems, Volume 10, Issue 6, June 1999 Page(s):549 – 559. [3] Suzhen Lin, Ph.D Dissertation, ISU, 2005.