Efficient Admission Control for Enforcing Arbitrary Real-Time Demand-Curve Interfaces Farhana Dewan and Nathan Fisher RTSS, December 6 th, 2012 Sponsors:

Outline 2  Background:  Compositional Real-Time System  Real-Time Interfaces  Problem: Enforcing Interfaces  Setting:  Aperiodic Jobs  Demand-Curve Interfaces  Solution:  Admission Control for MAD Jobs  Simulation  Future Work:  Admission Control for Arbitrary Jobs

Compositional Real-Time System  Component C  Workload W  Component-level Scheduling Algorithm A  Real-time Interface I … … A n n I C W Global Scheduler … … A1A1 1 1 I1I1 C1C1 W1W1 2 2 n n … … A2A2 I2I2 C2C2 W2W n n … … A3A3 I3I3 C3C3 W3W n n 3  Background  Problem  Setting  Solution  Future Work

Real-Time Interfaces … … AiAi IiIi CiCi WiWi τ2τ2 τ2τ2 τ ni Interface Selection (using parameters) Interface Selection (using parameters) Server Global Scheduler τ1τ1 τ1τ1 4  Background  Problem  Setting  Solution  Future Work Server-based interface model Demand-curve interface model … … AkAk IkIk CkCk WkWk τ2τ2 τ2τ2 τ nk τ1τ1 τ1τ1 Interface Selection (using functions) Interface Selection (using functions) Ex- periodic resource model, bounded-delay resource model Ex- Real-Time Calculus, demand-bound server

Real-Time Interfaces  Simple  Schedulabiltiy analysis explicit  Interfaces over-allocates processing resource  Servers enforce strict temporal isolation  Complex  Schedulabiltiy analysis implicit  Interfaces precisely model resource demand  Temporal isolation is not guaranteed Server-Based InterfaceDemand-Curve Interface 5  Background  Problem  Setting  Solution  Future Work

This Work  For demand-based models, achieving efficient resource allocation as well as strict temporal isolation among components is challenging  There is no known “policing” protocol to ensure that a system does not violate its demand-curve interface [Sanjoy Baruah, CRTS2008] 6  Background  Problem  Setting  Solution  Future Work Goal: Design Efficient and near-optimal admission controllers for arbitrary demand-curve interface with aperiodic component workload

This Work … … AiAi IiIi CiCi WiWi τ2τ2 τ2τ2 τnτn τnτn Interface Selection (using parameters) Interface Selection (using parameters) Server Global Scheduler τ1τ1 τ1τ1 7  Background  Problem  Setting  Solution  Future Work Server-based interface model Demand-curve interface model Interface Enforcement (Admission Control) Interface Enforcement (Admission Control) … … AkAk IkIk CkCk WkWk τ2τ2 τ2τ2 τnτn τnτn τ1τ1 τ1τ1 Interface Selection (using functions) Interface Selection (using functions) … … AkAk IkIk CkCk WkWk τ2τ2 τ2τ2 τnτn τnτn τ1τ1 τ1τ1 Interface Selection (using functions) Interface Selection (using functions)

Setting: Aperiodic Jobs Set of Aperiodic Jobs J = { j 1 … j N }  Aperiodic job j i =(A i, D i, E i )  Arrival time A i  Relative deadline D i ; absolute deadline d i = A i +D i  Worst-case execution E i during interval [A i, A i +D i )  Aperiodic job j i =(A i, D i, E i )  Arrival time A i  Relative deadline D i ; absolute deadline d i = A i +D i  Worst-case execution E i during interval [A i, A i +D i ) j1j1 j2j2 j3j3 j4j4 j5j5 t A1A1 A2A2 A3A3 A4A4 A5A5 d4d4 d5d5 d3d3 d1d1 d2d2 t1t1 t2t2 8  Background  Problem  Setting  Solution  Future Work Monotonic absolute deadline (MAD) jobs … … A I C W j1j1 j1j1 j2j2 j2j2

Demand-Curve Interfaces Single-Step Demand InterfaceArbitrary Demand Interface α ∆ t σ dbi α1α1 ∆1∆1 t σ1σ1 σ2σ2 σ3σ3 σ4σ4 ∆2∆2 ∆3∆3 ∆4∆4 α2α2 α3α3 α4α4 9  Background  Problem  Setting  Solution  Future Work

Example: Periodic Demand-Curve Interface 10  dbi can be generated from dbf  Consider τ contains 3 tasks:  τ 1 (1,3,3)  τ 2 (2,5,5)  τ 3 (2,8,8) t DBF Cumulative Demand Bound Function, DBF( τ,t) dbf( τ 2,t) t dbf( τ 3,t) t dbf( τ 1,t) t  Background  Problem  Setting  Solution  Future Work

 Exact admission control  Approximate admission control Admission Control 11  Background  Problem  Setting  Solution  Future Work

Admission Control 12  Background  Problem  Setting  Solution  Future Work t dbi Interval demand  Demand-point: In the XY-plane, a demand-point P(x,y) is represented by any interval length (x) and demand (y) over that interval P(x,y)

Step 1 Store demand-points corresponding to admitted jobs in a list Step 2 Insert demand-point corre- sponding to new job Exact Admission Control 13  Background  Problem  Setting  Solution  Future Work t j1j1 A1A1 d1d1 j2j2 A2A2 d2d2 A3A3 j3j3 d3d3 E2E2 E 1 + E 2 E1E1 E3E3 E 1 + E 2 + E 3 t dbi E 2 + E 3 Step 3 Update existing demand- points w.r.t new interval Step 4 ACCEPT the job if no demand-point violates dbi Infeasible for long running online system! Challenges  No assumption on interface  Store all demand-points with interval of all accepted job’s arrival and most recently accepted job’s deadline  Complexity linear in number of accepted jobs  No assumption on interface  Store all demand-points with interval of all accepted job’s arrival and most recently accepted job’s deadline  Complexity linear in number of accepted jobs

Approximate Admission Control t dbi 1 1+ ϵ (1+ ϵ) 2 (1+ ϵ) 3 Step 1 Approximation regions Step 2 Merge points within region to get approximate points Merge points within region to get approximate points Step 3 Remove redundant points Step 4 Merge approximate points 14  Background  Problem  Setting  Solution  Future Work

Approximate Admission Control t dbi 1 1+ ϵ (1+ ϵ) 2 (1+ ϵ) 3 Step 1 Approximation regions Step 2 Merge points within region to get approximate points Merge points within region to get approximate points Step 3 Remove redundant points Step 4 Merge approximate points 15  Background  Problem  Setting  Solution  Future Work Polynomial complexity in number of bits to represent max dbi and ϵ

Approximate Admission Control 16 Theorem [Correctness] Given a demand-curve interface Λ, ϵ, and set of previously- admitted jobs J, when new job j k arrives in the system, if APPROXIMATEAC returns “Accept”, then j k may be admitted without violating Λ Theorem [Approximation Ratio] Given a demand-curve interface Λ, ϵ, and set of previously- admitted jobs J, if APPROXIMATEAC returns “Reject” for a new job j k, then EXACTAC also returns “Reject” for a demand-curve (1/1+ ϵ )dbi( Λ, ・ ) on the same previously-admitted job set

Reducing Demand Points for Periodic Demand-Curve Interface 17  DBI-WrapCheck  Background  Problem  Setting  Solution  Future Work t dbi H2H4H 3H uH 2uH 3uH 2uH 4H Observation 1  Any demand-point in the XY-plane with demand (y- value) greater 2u.H can be mapped to previous region Observation 2  Any demand-point in the XY-plane with interval length (x-value) greater 4H can be discarded

Enforcing Temporal Isolation 18  Component-level temporal isolation  Lightweight server to execute each admitted job  The server will discontinue executing a job j k when it has executed upto its E k  Enforce temporal isolation in component level  Reclaim unused execution  Keep a buffer of active jobs  Instead of updating the demand-points in the list at the time of job arrival, update after a job has finished execution  Background  Problem  Setting  Solution  Future Work

Simulation: Exact Vs Approximate 19  Demand-curve interface (periodic dbi):  8 periodic tasks with randomly generated parameters are used to generate periodic dbi  Workload:  For MAD jobs, inter-arrival time, deadline and execution time are generated from uniform distribution  Approximation parameter: ϵ = 0.01, 0.1, 0.2  Simulation process:  A 2.33 GHz Intel Core 2 Duo E6550 machine with 2.0GB RAM is used  The simulation runs until A i ≥ 4H  Metrics:  Execution time trace  Number of accepted jobs  Background  Problem  Setting  Solution  Future Work

Simulation: Exact Vs Approximate Execution Time Trace 20  Background  Problem  Setting  Solution  Future Work Observation  Approximate algorithm significantly reduces runtime as it does not depend on number of jobs in the system  After 0.9s, exact algorithm takes 19ms, approximate algorithm ( ϵ=0.01 ) takes 0.5ms  Approximate algorithm significantly reduces runtime as it does not depend on number of jobs in the system  After 0.9s, exact algorithm takes 19ms, approximate algorithm ( ϵ=0.01 ) takes 0.5ms

Simulation: Exact Vs Approximate Accepted Jobs Vs Execution Time 21  Background  Problem  Setting  Solution  Future Work Observation  Number of accepted jobs for ϵ =0.01 is very close to the number of accepted jobs by the exact algorithm

Admission Control for Arbitrary Jobs 22  A simple extension to arbitrary aperiodic jobs is given in [Dewan and Fisher, WSU-CS-TR 2012]  Keep a buffer to store active jobs  Insert demand-point corresponding to the newly admitted job in the list in absolute deadline order  Other operations are modified accordingly  Currently working on improving space/time complexity  Background  Problem  Setting  Solution  Future Work

Summary 23  Focused on: Enforcing demand-curve interfaces for compositional real-time systems  Developed: Exact and approximate AC for arbitrary demand-interface  Proved: Given an accuracy parameter ϵ, t he approximate AC runs in polynomial in terms of the dbi representation and ϵ  Verified: Simulation results show significant improvement of performance of the approximate AC with respect to the exact AC  Background  Problem  Setting  Solution  Future Work

Future Work  Uniprocessor:  Admission control for arbitrary demand-curve interface with arbitrary job arrival Reduce space/time complexity  Implementation of admission controller in operating system Verify practicality of admission controller  Multiprocessor:  Enforcing demand-curve interface for multiprocessor 24  Background  Problem  Setting  Solution  Future Work

THANK YOU! 25 Questions?

Resetting Admission Controller 26  Not possible to reset at arbitrary subsystem idle point  Requires global system knowledge  Example  S with interface dbi( Λ,t)=0.9t  j 1 = (0,0.9,1), j 2 = (0.91,0.9,1)  If j 1 is contiguously executed at its release time by the processor, S will be idle at time 0.9  If S is reset at 0.9, j 2 will be admitted at time 0.91  However, j 1 + j 2 together violates S (1.91x0.9 = 1.719< =1.8)  Background  Problem  Setting  Solution  Future Work

Simulation: Exact Vs Approximate 27  Demand-curve interface (periodic dbi):  8 periodic tasks with total utilization = 0.5  Periods in the range [5,40]  Task utilizations using UUniFast [Bini and Buttazzo, ECRTS’2004]  Hyperperiod H =  Workload:  Uniform distribution is used to generate random parameters  Inter-arrival time in the range [0,20]  Relative-deadline in the range [0,50]  Execution-time in the range [0, D i ]  Approximation parameter: ϵ = 0.01, 0.1, 0.2  Background  Problem  Setting  Solution  Future Work p e