Deferrable Scheduling for Temporal Consistency: Schedulability Analysis and Overhead Reduction

1. Deferrable Scheduling for Temporal Consistency: Schedulability Analysis andOverhead Reduction Ming Xiong: Lucent Bell Labs Song Han: City University of Hong Kong Deji Chen: Emerson Process Management

2. Outline • Overview and motivation • Deferrable scheduling alg and analysis: • Deferrable Scheduling (DS): A fixed priority scheduling alg for maintaining freshness of real-time data (RTSS05) • A sufficient condition for DS feasibility (schedulability) • DS with Hyper-period algs for reducing on-line scheduling overhead • Performance Studies • Conclusions and Future Work

3. Real-Time Databases RTDB Model for Maintaining Temporal Validity of Real-Time Data Sensor 1 Network Sensor 2 . . . . Sensor N • A real-time object in RTDBs models a real world entity, e.g., position of an aircraft • Values are sampled by sensors, and propagated to RTDBs • Real-time data in RTDBs must remain fresh in order to react to abnormal situations • timely • Transactions may be triggered to deal with abnormal situations

4. What is Data Temporal Validity in RTDBs? Value Temporal Validity: keep data valid relative to real world X 0 1 2 3 4 5 Time • Real-time data values change continuously • Data values are sampled periodically • A validity interval is associated with a data value • Within validity interval, a data value is fresh (temporally valid) • deviation from real world is acceptable

5. D P ML t t t+V/2 t +V V Prior Work: Half-Half (HH) & More-Less (ML) Definition: • X : Real-Time Data • V : Validity Interval Length • T : Trans Updating X • P: Period of T • D: Relative Deadline of T P=D P=D HH t t t +V t+V/2 Observation : Data validity can be guaranteed if Period + Relative Deadline  Validity Length Half-Half : Sample at twice the rate of change (P = D= V/2) More-Less : P  V/2 & D  V/2

6. Intuition of Deferrable Scheduling • More-Less: Periodic approach that is unnecessarily pessimistic • More-Less uses the worst-case response time (WCRT) of a transaction as its relative deadline • Period (Ti) = Validity Length (Ti) - WCRT (Ti) • Relative deadline and period are fixed for all instances of a transaction • DS: Sporadic approach that allows variable separations and relative deadlines for instances of a transaction • DS uses response time of an instance as the relative deadline of the instance • Separation(Ti,j, Ti,j+1) = Validity Length(Ti) – ResponseTime(Ti,j+1) • Relative deadline and separation of two instances are varied for all instances of a transaction • DS increases the average separation of two consecutive instances

7. Di Di ri,1 di,0 d’i,2 di,2 di,1 Vi Vi r’i,1 di,1 Deferrable Scheduling: Example Illustration Ti,0 Ti,1 Validity Length Vi Higher-priority preemption ri,j: Sampling(Release) time of Ti,j di,j: Absolute deadline of Ti,j ri,0 How to determine the response time of Ti,1 if it completes at di,1?

8. Deferrable Scheduling:Key Steps • Release time ri,j fortransaction instance Ti,j is derived backwards from its deadline di,j : • di,j+1 = ri,j + Vi (validity constraint) • ri,j+1 = di,j+1 – ResponseTime(Ti,j+1 ) • ResponseTime(Ti,j+1 ) = HPPreemption(ri,j+1, di,j+1 ) + Ci HPPreemption(ri,j+1, di,j+1) is the total amount of processor demand from higher priority transactions during [ri,j+1, di,j+1]. • HPPreemption(ri,j+1, di,j+1) can be derived only if the schedule of all higher priority transactions of Ti up to di,j+1have been determined • Note that Eq 2) above can be solved by an iterative algorithm in fixed priority scheduling

9. DS Feasibility Analysis: A Sufficient Condition • Theorem: Given a synchronous sensor transaction set T, if T can be scheduled by More-Less, then it can also be scheduled by Deferrable Scheduling. • Synchronous means that the first instances of all transactions are released at the same time

10. Proof Sketch of the Theorem • T can be scheduled by More-Less: WCRTML (Ti) <= Validity Length (Ti)/2 • T can be scheduled by More-Less: WCRT (Ti) <= WCRTML (Ti) • WCRT (Ti) <= Validity Length (Ti)/2:T can be scheduled by Deferrable Scheduling.

11. WCRTML (Ti) <= Validity Length (Ti)/2 • True by the definition of More-Less

12. WCRT (Ti) <= WCRTML (Ti) • Prove by contradiction. • For any 1 < k <= m and WCRT (Tk) > WCRTML (Tk), • we could find 1 <= l < k and WCRT (Tl) > WCRTML (Tl). • Tl could be found from the schedule that produces WCRT (Tk) • But we know: WCRT (T1) = WCRTML (T1)

13. T can be scheduled by Deferrable Scheduling • If ri,k+1 <= di,k, then T is schedulable. • According to DS-FP: ri,k = di,k – Ri,kdi,k+1 = ri,k + Viri,k+1 = di,k+1-Ri,k+1 • We have: ri,k+1 – di,k + Ri,k+1 + Ri,k = Vi • Since: Ri,k+1 + Ri,k <= 2 WCRT (Ti) <= Vi • We have: ri,k+1 – di,k <= 0

14. Reducing DS On-line Scheduling Overhead • Worst-case time complexity of on-line scheduling is O(mVm2) • It is much higher than More-Less (O(1)) • Time complexity of on-line scheduling can be reduced by making DS based hyper-period schedule (off-line) • Periodic on-line scheduling (O(1)) • On-line space overhead to maintain schedule information is low

15. Deferrable Scheduling with Hyper-period (DESH) • Criteria for hyper-period: two consecutive instances of a transaction satisfy the validity constraint • Two instances in the same hyper-period • Two instances across two hyper-periods • Off-line Schedule Adjustment (DESH-SA) Alg • Finds an interval [0, tend] in a partial DS schedule that has its utilization close to Uest • Adjusts the schedule backwards from tend so that the schedule in [0, tend] can be repeated on-line without violating the validity constraint

16. DESH-SA Alg • Finds an idle time t • Repeats the schedule in [0, t] for Ti if Ti and its higher priority transactions satisfy the validity constraint for the last instance before t and the first instance after t • Otherwise, • Pushes back the first Ti instance after t and sets t as its deadline, and computes its release time • If its release time < its prior instance’s absolute deadline, adjusts the schedule of its prior instance (may incur ripple effect)

17. Performance Studies • Experiments are conducted by simulation • Single CPU RTDB with all real-time data in main memory • Sensor and triggered transactions are generated following an air traffic control application

18. Performance Results: DESH Algs • DESH-SA has CPU utilization close to DS

19. Performance Results:Hyper-period Length

20. Conclusions • Introduced Deferrable Scheduling (DS) for fixed priority transactions maintaining real-time data freshness • Proposed a sufficient condition for DS feasibility • Developed DS based algorithm that schedule transactions with hyper-period while reducing on-line scheduling overhead to O(1) • Experimental results demonstrated that DS significantly outperforms More-Less

21. Future Work • Open questions: • Is time 0 a critical instant for synchronous sensor transactions ? • What is a sufficient and necessary condition for DS feasibility ? • What is processor utilization bound for DS feasibility ? • How much can DS improve the feasibility of More-Less ?