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

2. 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. 3 RTDB Model for Maintaining Temporal Validity of Real-Time Data Real-Time Databases Network Sensor 1 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. 4 What is Data Temporal Validity in RTDBs? Temporal Validity: keep data valid relative to real world Time Value X 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 0 1 2 3 4 5

5. 5 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 V t P=D t+V/2 t +V t 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 P=D D t t+V/2 t +V t P ML HH

6. 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 (T i ) = Validity Length (T i ) - WCRT (T i ) –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(T i,j, T i,j+1 ) = Validity Length(T i ) – ResponseTime(T i,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. 7 Deferrable Scheduling: Example Illustration Validity Length V i r i,0 d i,1 r i,1 d i,1 r’ i,1 T i,0 T i,1 Higher-priority preemption d i,0 DiDi DiDi How to determine the response time of T i,1 if it completes at d i,1 ? r i,j : Sampling(Release) time of T i,j d i,j : Absolute deadline of T i,j ViVi d i,2 ViVi d’ i,2

8. 8 Deferrable Scheduling: Key Steps Release time r i,j for transaction instance T i,j is derived backwards from its deadline d i,j : 1)d i,j+1 = r i,j + V i (validity constraint) 2)r i,j+1 = d i,j+1 – ResponseTime(T i,j+1 ) 3)ResponseTime(T i,j+1 ) = HPPreemption(r i,j+1, d i,j+1 ) + C i HPPreemption(r i,j+1, d i,j+1 ) is the total amount of processor demand from higher priority transactions during [r i,j+1, d i,j+1 ]. 4)HPPreemption(r i,j+1, d i,j+1 ) can be derived only if the schedule of all higher priority transactions of T i up to d i,j+1 have been determined Note that Eq 2) above can be solved by an iterative algorithm in fixed priority scheduling

9. 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. 10 Proof Sketch of the Theorem T can be scheduled by More-Less: WCRT ML (T i ) <= Validity Length (T i )/2 T can be scheduled by More-Less: WCRT (T i ) <= WCRT ML (T i ) WCRT (T i ) <= Validity Length (T i )/2: T can be scheduled by Deferrable Scheduling.

11. 11 WCRT ML (T i ) <= Validity Length (T i )/2 True by the definition of More-Less

12. 12 WCRT (T i ) <= WCRT ML (T i ) Prove by contradiction. For any 1 WCRT ML (T k ), we could find 1 WCRT ML (T l ). T l could be found from the schedule that produces WCRT (T k ) But we know: WCRT (T 1 ) = WCRT ML (T 1 )

13. 13 T can be scheduled by Deferrable Scheduling If r i,k+1 <= d i,k, then T is schedulable. According to DS-FP: r i,k = d i,k – R i,k d i,k+1 = r i,k + V i r i,k+1 = d i,k+1 -R i,k+1 We have: r i,k+1 – d i,k + R i,k+1 + R i,k = V i Since: R i,k+1 + R i,k <= 2 WCRT (T i ) <= V i We have: r i,k+1 – d i,k <= 0

14. 14 Reducing DS On-line Scheduling Overhead Worst-case time complexity of on-line scheduling is O(mV m 2 ) –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. 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, t end ] in a partial DS schedule that has its utilization close to U est –Adjusts the schedule backwards from t end so that the schedule in [0, t end ] can be repeated on-line without violating the validity constraint

16. 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. 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. 18 Performance Results: DESH Algs DESH-SA has CPU utilization close to DS

19. 19 Performance Results: Hyper-period Length

20. 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. 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 ?