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CprE 458/558: Real-Time Systems. (m, k)-firm tasks and QoS enhancement. (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.
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CprE 458/558: Real-Time Systems (m, k)-firm tasks and QoS enhancement CprE 458/558: Real-Time Systems (G. Manimaran)
(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)
Task model and performance index • Task Model - firm periodic tasks [1,2] • Tasks should meet mi deadlines for every Ki 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)
MK-RMS Schedulability Check [2] • Utilization-based MK-RMS-schedulability check (sufficient, but not necessary) MKLoad <= n(21/n -1) • Classification of mandatory and optional instances - Instances of task Ti activated at times api 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)
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)
Task 1 120 Task 2 120 RMS 120 (a) T1: <4,8,2,10> T2: <4,6,1,5> Task 1 120 Task 2 120 RMS 120 (b) T1: <4,8,4,10> T2: <4,6,2,5> Task 1 120 Task 2 120 RMS 120 Task 1 misses its deadline (c) T1: <4,8,6,10> T2: <4,6,3,5> Scheduling Example CprE 458/558: Real-Time Systems (G. Manimaran)
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)
Control variables disturbance Regulated variables + Controlled RT System Controller Actuators - Sensors Set Points Measured variables Introduction (Cont.) • Feedback control technique CprE 458/558: Real-Time Systems (G. Manimaran)
+ PI Controller Actuator Set point Scheduler Admission Controller Completed tasks CPU - Submitted tasks Accepted tasks Average Dynamic Failure Rate Proposed scheduling architecture [3] CprE 458/558: Real-Time Systems (G. Manimaran)
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)
Feedback control algorithm CprE 458/558: Real-Time Systems (G. Manimaran)
K on-line design Controller parameters Output changing observation Control signal Reference System Controller Output 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 CprE 458/558: Real-Time Systems (G. Manimaran)
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)
Simulation studies • Feedback algorithm vs. iterative algorithm 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 CprE 458/558: Real-Time Systems (G. Manimaran)
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)
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)
References [1] Reference [18] in chapter 4. [2]Overload management in real-time control applications using (m, k)-firm guaranteeRamanathan, 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. CprE 458/558: Real-Time Systems (G. Manimaran)
