Timed Simulation with Multiple Resource Schedulability Analysis

Yang Zhao and Slobodan Matic

University of California, Berkeley Dec 10, 2004

Introduction

Embedded software for control determinism both in value and time multiple resources

Simulation environment timing constraints resource utilization component interactions

Multi-domain timed simulation Discreteness of software in CT domain Timed Multitasking Ptolemy domain [LL03]

Simulink RTWorkshop Model: periodic multi-rate patterns

• no fast reaction to external triggers Code: rate-monotonic schedule (almost)

• no specification and analysis of timing constraints

Motivating Example

[KHM03]

Advanced automotivecontrol applications withend-to-end deadlines

TM Software Architecture Concurrent interaction in TM actors

Atomic actors (tasks):• Task execution times (estimates)• Resource(s)

Composite actors: • Task graph• Deadline• Invocation trigger condition (pattern)

set of TM composite actors in other domain

Schedulers Static table-based

• Schedulability analysis• schedule generation off-, dispatching on-

line Dynamic priority EDF-based

• No schedulability analysis• scheduling and dispatching on-line

Schedulability Analysis

[CCLL95] Mixed-integer programming techniques Branch and Bound global scheduling

h

multiple

processors

h1

h2

h1

h2

+ no intertask

communication

1)(

)(

i i

i

tperiod

twcet

single

processor+

intertask

communication

multiple

processors

+ intertask

communication

topological order

in linear time

NP-complete

[BKS99]

set of periodic events A 8 a2 A . p(a)=T

time function :A![0,T) span constraint S: interval D=[d-,d+], integer k

event pair (a1,a2) satisfies S if d- · (a2) - (a1) + kT · d+

T=12, D=[5,7]

PESP instanceT2 R , (A,E), d+,d-:E![0,T)

PESP algorithm [SU89] find minimum spanning tree of (A,E) successively satisfy constraints on each chord of the tree

• otherwise find blocking cycle with tight constraints

Periodic Event Scheduling Problem (PESP)

2

0

3

76

9

5

1

PESP solution

:A![0,T), k:E! Z

20

3

76

9

5

1

k=0 k=1

Static TM Model Scheduling

Invocation pattern known All release times known and periodic

t(a) execution time, r(a) resource ! (a) start time in [0,T)

two types of span constraints mutual exclusion: 8 a1,a2. 8 r2 R. r(a1)=r(a2)

• t(a1) · (a2)-(a1)+k(a1,a2)T· T-t(a2)

precedence constraint for each path of task graph • t(ai) · (ai+1)-(ai)+k(ai,ai+1)T· t(ai)+D, D=T-i=1: nt(ai)

• t(an) · (a1)-(an)+(1-i=1: n-1k(ai,ai+1))T· t(an)+D

Multi-rate solution:

Deadline less than period: D=deadline - i=1:nt(ai) Multiple (exclusive) resources

],[ ba],[ ba ],[ ba

],[ TT

],[ TT

T T2

Static TM Demo

This demo uses a TMController to control a Car model to drive at the Cruise Speed. The TM model contains tasksperiodically execute on a set of computing resources (processes). A PESPScheduler is used to statically check whether the TM model is schedulable for a given period and schedule the execution of these tasks.

Invocation pattern unknown task release times determined by model execution task execution order dynamic and suboptimal

• deadline miss detection

Composite end-to-end deadline Deadline assignment (distribution) for intermediate tasks

Maximize minimal laxity: Li = [Di - j=1:n t(aj)]/n

Assign deadlines whenever composite actor is triggeredUse Earliest Deadline First strategy on each resource

Dynamic TM Model Scheduling

1T250

2T200

3T150

4T150

5T200

2000D

1T250

2T200

3T150

4T150

5T200

550

1050

1500

2000

1T250

2T200

3T150

4T150

5T200

550

1050

1500

2000

1050

Some tasks are preempted

Compare to the periodic demo, the TM model here is not periodically executed: some input happens randomlly. The TM model is executed when it istriggered by an event. When it is triggered, it calcultes deadlines for related tasks. In this case, a task is released when it receives an event and an EDF scheduler is used to schedule the released tasks on the computing resource.

Dynamic TM Demo

TM with Multi-Resources in Ptolemy

Several scheduling algorithm is implemented.

Support modeling and simulation with multi-resources (processes).

Refactor the Director to several modules:

Director

Scheduler

Resource

ExecutionTime Estimator

XXX

<<Interface>>

Sceduler

+GenerateSchedule()

+Schedule()

PESPScheduler

SimpleSchedulerTMDirector

EDFScheduler<<Interface>>

Resource

+available()

ComputingResource

TM with Multi-Resources in Ptolemy

+execute()

AtomicActor