Introduction to Real-Time Systems ECE 397-1
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1 Introduction to Real-Time Systems ECE 97-1 Northwestern University Department of Computer Science Department of Electrical and Computer Engineering Teachers: Robert Dick Peter Dinda Office: L477 Tech 8, 1890 Maple Ave. Phone: Webpage: 1
2 Homework index 1 Reading assignment
3 Goals for lecture Resource representations Graph extensions for pre/post-computation and streaming/pipelining Scheduling problem categories Overview of scheduling algorithms Will initially focus on static scheduling Sensor networks
4 Processing resource description Often table-based Price, area For each task Execution time Power consumption Preemption cost etc. etc. Similar characterization for communication resources Wise to use process-based 4
5 Communication resource description Can use bus-bridge based models for distributed systems Some protocols make static analysis difficult Wireless models System-level design, especially for a single chip, depends on wire delays! 5
6 Graph extensions J J1/ J1/ 0 kb 0 kb kb J2/ K1/ 9 kb 9 kb 0 kb 0 kb 0 kb J2/ kb K1/ 0 kb J/ K2/ J/ kb K2/ 0 kb 0 kb K K/ K/ a) conventional b) pre and post computation c) streaming Allows pipelining and pre/post-computation In contrast with book, not difficult to use if conversion automated 6
7 Problem definition A B C D E Given a set of tasks, a cost function, and a set of resources, decide the exact time each task will execute on each resource 7
8 Problem definition A B C D E minimize completion time Given a set of tasks, a cost function, and a set of resources, decide the exact time each task will execute on each resource 8
9 Problem definition A B C D E minimize completion time PE 0 PE 1 Given a set of tasks, a cost function, and a set of resources, decide the exact time each task will execute on each resource 9
10 Problem definition A B C D E minimize completion time PE 0 PE 1 Given a set of tasks, a cost function, and a set of resources, decide the exact time each task will execute on each resource 10
11 Problem definition A B C D E D B C minimize completion time A E PE 0 PE 1 Given a set of tasks, a cost function, and a set of resources, decide the exact time each task will execute on each resource 11
12 Problem definition A B C D E D B C minimize completion time A E PE 0 PE 1 Given a set of tasks, a cost function, and a set of resources, decide the exact time each task will execute on each resource 12
13 Problem definition D B C minimize completion time A E PE 0 PE 1 Given a set of tasks, a cost function, and a set of resources, decide the exact time each task will execute on each resource 1
14 Types of scheduling problems Discrete time Continuous time Hard deadline Soft deadline Unconstrained resources Constrained resources Uni-processor Multi-processor Homogeneous processors Heterogeneous processors Free communication Expensive communication Independent tasks Precedence constraints Homogeneous tasks Heterogeneous tasks One-shot Periodic Single rate Multirate Non-preemptive Preemptive Off-line On-line 14
15 Discrete vs. continuous timing System-level: Continuous Operations are not small integer multiples of the clock cycle High-level: Discrete Operations are small integer multiples of the clock cycle Implications: System-level scheduling is more complicated however, high-level also very difficult. Can we solve this by quantizing time? Why or why not? 15
16 Hard deadline Soft deadline Tasks may have hard or soft deadlines Hard deadline Task must finish by given time or schedule invalid Soft deadline If task finishes after given time, schedule cost increased 16
17 Real-time Best effort Why make decisions about system implementation statically? Allows easy timing analysis, hard real-time guarantees If a system doesn t have hard real-time deadlines, resources can be more efficiently used by making late, dynamic decisions Can combine real-time and best-effort portions within the same specification Reserve time slots Take advantage of slack when tasks complete sooner than their worst-case finish times 17
18 Unconstrained Constrained resources Unconstrained resources Additional resources may be used at will Constrained resources Limited number of devices may be used to execute tasks 18
19 Uni-processor Multi-processor Uni-processor All tasks execute on the same resource This can still be somewhat challenging However, sometimes in P Multi-processor There are multiple resources to which tasks may be scheduled Usually NP-complete 19
20 Homogeneous Heterogeneous processors Homogeneous processors All processors are the same type Heterogeneous processors There are different types of processors Usually NP-complete 20
21 Free Expensive communication Free communication Data transmission between resources has no time cost Expensive communication Data transmission takes time Increases problem complexity Generation of schedules for communication resources necessary Usually NP-complete 21
22 Independent tasks Precedence constraints NEG IOP DCT FIL FT Independent tasks: No previous execution sequence imposed Precedence constraints: Weak order on task execution order 22
23 Independent tasks Precedence constraints NEG IOP DCT FIL FT Independent tasks: No previous execution sequence imposed Precedence constraints: Weak order on task execution order 2
24 Homogeneous Heterogeneous tasks FT FT FT FT FT Homogeneous tasks: All tasks are identical Heterogeneous tasks: Tasks differ 24
25 Homogeneous Heterogeneous tasks NEG IOP DCT FIL FT Homogeneous tasks: All tasks are identical Heterogeneous tasks: Tasks differ 25
26 One-shot Periodic time One-shot: Assume that the task set executes once Periodic: Ensure that the task set can repeatedly execute at some period 26
27 One-shot Periodic time One-shot: Assume that the task set executes once Periodic: Ensure that the task set can repeatedly execute at some period 27
28 One-shot Periodic time One-shot: Assume that the task set executes once Periodic: Ensure that the task set can repeatedly execute at some period 28
29 Single rate Multirate time period = 20 ms Single rate: All tasks have the same period Multirate: Different tasks have different periods Complicates scheduling Can copy out to the least common multiple of the periods (hyperperiod) 29
30 Single rate Multirate time copies period = 20 ms period = 0 ms 2 copies system hyperperiod = 60 ms Single rate: All tasks have the same period Multirate: Different tasks have different periods Complicates scheduling Can copy out to the least common multiple of the periods (hyperperiod) 0
31 Periodic graphs time copies period = 20 ms deadline = 20 ms period = 0 ms deadline = 40 ms 2 copies system hyperperiod = 60 ms 1
32 Periodic graphs time copies period = 20 ms deadline = 20 ms period = 0 ms deadline = 40 ms 2 copies system hyperperiod = 60 ms 2
33 Periodic graphs time copies period = 20 ms deadline = 20 ms period = 0 ms deadline = 40 ms 2 copies system hyperperiod = 60 ms
34 Aperiodic/sporadic graphs No precise periods imposed on task execution Useful for representing reactive systems Difficult to guarantee hard deadlines in such systems Possible if minimum inter-arrival time known 4
35 Periodic vs. aperiodic Periodic applications Power electronics Transportation applications Engine controllers Brake controllers Many multimedia applications Video frame rate Audio sample rate Many digital signal processing (DSP) applications However, devices which react to unpredictable external stimuli have aperiodic behavior Many applications contain periodic and aperiodic components 5
36 Aperiodic to periodic Can design periodic specifications that meet requirements posed by aperiodic/sporadic specifications Some resources will be wasted Example: At most one aperiodic task can arrive every 50 ms It must complete execution within 100 ms of its arrival time 6
37 Aperiodic to periodic Can easily build a periodic representation with a deadline and period of 50 ms Problem, requires a 50 ms execution time when 100 ms should be sufficient Can use overlapping graphs to allow an increase in execution time Parallelism required The main problem with representing aperiodic problems with periodic representations is that the tradeoff between deadline and period must be made at design/synthesis time 7
38 Non-preemptive Preemptive A ready B ready B deadline A deadline Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 8
39 Non-preemptive Preemptive A ready B ready A B deadline A deadline non preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 9
40 Non-preemptive Preemptive A ready B ready B deadline A B A deadline non preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 40
41 Non-preemptive Preemptive A ready B ready B deadline A B A deadline non preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 41
42 Non-preemptive Preemptive A ready B ready B deadline A B A1 A deadline non preempt. ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 42
43 Non-preemptive Preemptive A ready B ready B deadline A B A1 B A deadline non preempt. ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 4
44 Non-preemptive Preemptive A ready B ready B deadline A B A1 B A2 A deadline non preempt. ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 44
45 Non-preemptive Preemptive A ready B ready B deadline A deadline A B non preempt. A1 B A2 O.K. ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 45
46 Non-preemptive Preemptive A ready B ready B deadline A deadline A B A1 B A2 O.K. A1 non preempt. ideal preempt. non ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 46
47 Non-preemptive Preemptive A ready B ready B deadline A B A1 B A2 A1 P O.K. A deadline non preempt. ideal preempt. non ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 47
48 Non-preemptive Preemptive A ready B ready B deadline A B A1 B A2 A1 P B O.K. A deadline non preempt. ideal preempt. non ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 48
49 Non-preemptive Preemptive A ready B ready B deadline A B A1 B A2 A1 P B P O.K. A deadline non preempt. ideal preempt. non ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 49
50 Non-preemptive Preemptive A ready B ready B deadline A B A1 B A2 O.K. A1 P B P A2 A deadline non preempt. ideal preempt. non ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 50
51 Non-preemptive Preemptive A ready B ready B deadline A B A1 B A2 O.K. A1 P B P A2 A deadline non preempt. ideal preempt. non ideal preempt. Non-preemptive: Tasks must run to completion Ideal preemptive: Tasks can be interrupted without cost Non-ideal preemptive: Tasks can be interrupted with cost 51
52 Off-line On-line Off-line Schedule generated before system execution Stored, e.g., in dispatch table. for later use Allows strong design/synthesis/compile-time guarantees to be made Not well-suited to strongly reactive systems On-line Scheduling decisions made during the execution of the system More difficult to analyze than off-line Making hard deadline guarantees requires high idle time No known guarantee for some problem types Well-suited to reactive systems 52
53 Hardware-software co-synthesis scheduling Automatic allocation, assignment, and scheduling of system-level specification to hardware and software Scheduling problem is hard Hard and soft deadlines Constrained resources, but resources unknown (cost functions) Multi-processor Strongly heterogeneous processors and tasks No linear relationship between the execution times of a tasks on processors 5
54 Hardware-software co-synthesis scheduling Expensive communication Complicated set of communication resources Precedence constraints Periodic Multirate Strong interaction between NP-complete allocation-assignment and NP-complete scheduling problems Will revisit problem later in course if time permits 54
55 Behavioral synthesis scheduling Difficult real-world scheduling problem Not multirate Discrete notion of time Generally less heterogeneity among resources and tasks What scheduling algorithms should be used for these problems? 55
56 Scheduling methods Clock Weighted round-robbin List scheduling Priority EDF, LST Slack RMS Multiple costs MILP Force-directed 56
57 Clock-driven scheduling Clock-driven: Pre-schedule, repeat schedule Music box: Periodic Multi-rate Heterogeneous Off-line Clock-driven 57
58 Weighted round robbin A D B C Time Weighted round-robbin: Time-sliced with variable time slots 58
59 List scheduling Pseudo-code: Keep a list of ready jobs Order by priority metric Schedule Repeat Simple to implement Can be made very fast Difficult to beat quality 59
60 Priority-driven Impose linear order based on priority metric Possible metrics Earliest start time (EST) Latest start time * Danger! LST also stands for least slack time. Shortest execution time first (SETF) Longest execution time first (LETF) Slack (LFT - EFT) 60
61 List scheduling Assigns priorities to nodes Sequentially schedules them in order of priority Usually very fast Can be high-quality Prioritization metric is important 61
62 Prioritization As soon as possible (ASAP) As late as possible (ALAP) Slack-based Dynamic slack-based Multiple considerations 62
63 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 6
64 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 64
65 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 65
66 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 66
67 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 67
68 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 68
69 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 69
70 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 70
71 As soon as possible (ASAP) max(7, 11) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 71
72 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 72
73 As soon as possible (ASAP) From root, topological sort on the precedence graph Propagate execution times, taking the max at reconverging paths Schedule in order of increasing earliest start time (EST) 7
74 As late as possible (ALAP) From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 74
75 As late as possible (ALAP) 2 6 deadline = deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 75
76 As late as possible (ALAP) 2 6 deadline = deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 76
77 As late as possible (ALAP) 2 6 deadline = deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 77
78 As late as possible (ALAP) 2 6 deadline = deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 78
79 As late as possible (ALAP) 2 6 deadline = deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 79
80 As late as possible (ALAP) 2 min(12, 2) 6 deadline = deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 80
81 As late as possible (ALAP) deadline = deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 81
82 As late as possible (ALAP) deadline = deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 82
83 As late as possible (ALAP) deadline = min(7, 22) deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 8
84 As late as possible (ALAP) deadline = deadline = 7 From deadlines, topological sort on the precedence graph Propagate execution times, taking the min at reconverging paths Consider precedence-constraint satisfied tasks Schedule in order of increasing latest start time (LST) 84
85 Slack-based Compute EFT, LFT For all tasks, find the difference, LFT EFT This is the slack Schedule precedence-constraint satisfied tasks in order of increasing slack Can recompute slack each step, expensive but higher-quality result Dynamic critical path scheduling 85
86 Multiple considerations Nothing prevents multiple prioritization methods from being used Try one method, if it fails to produce an acceptable schedule, reschedule with another method 86
87 Effective release times Ignore the book on this Considers simplified, uniprocessor, case Use EFT, LFT computation Example? 87
88 EDF, LST optimality EDF optimal if zero-cost preemption, uniprocessor assumed Why? What happens when preemption has cost? Same is true for slack-based list scheduling in absence of preemption cost 88
89 Breaking EDF, LST optimality Non-zero preemption cost Multiprocessor Why? 89
90 Rate mononotic scheduling (RMS) Single processor Independent tasks Differing arrival periods Schedule in order of increasing periods No fixed-priority schedule will do better than RMS Guaranteed valid for loading ln2 = 0.69 For loading > ln2 and < 1, correctness unknown Usually works up to a loading of 0.88 More detail in later lectures 90
91 Reading assignment Skim and refer to K. Ramamritham and J. Stankovic, Scheduling algorithms and operating systems support for real-time systems, Proc. IEEE, vol. 82, pp , Jan Skim and refer to Y.-K. Kwok and I. Ahmad, Static scheduling algorithms for allocating directed task graphs to multiprocessors, ACM Computing Surveys, vol. 1, no. 4, pp , 1999 J. W. S. Liu, Real-Time Systems. Prentice-Hall, Englewood Cliffs, NJ, 2000 Finish Chapter 5, read Chapter 6 by Thursday 91
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Introduction to Real-Time Systems ECE 97-1 Homework index 1 Reading assignment.............. 4 Northwestern University Department of Computer Science Department of Electrical and Computer Engineering Teachers:
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