Real-Time Scheduling
Mehdi Kargahi
School of ECE
University of Tehran
Common Approaches
 Clock-driven (time-driven)
Scheduling decisions are made at specific time instants, which are
typically chosen a priori
 Weighted round-robin (processor-sharing)
 Commonly used for scheduling time-shared applications
 The weights of jobs can speed up or retard the progress of each job
toward its completion
 Priority-driven
 Scheduling decisions are made when particular events in the
system occur, e.g.,
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A job becomes available
Processor becomes idle (a job is completed)
Work-conserving: processor is busy whenever there is work to be
done
Priority driven schedulers can be static or dynamic depending on
the priority assignment at run-time
M. Kargahi (University of Tehran)
Clock-Driven Approaches: Overview
 Scheduling decision time: point in time when scheduler decides which
job to execute next
 Scheduling decision time in clock-driven schedulers is defined a priori
 For example: scheduler periodically wakes up and generates a portion
of the schedule
 Special case: When job parameters are known a priori, schedule can be
pre-computed offline, and stored as a table (table-driven schedulers)
M. Kargahi (University of Tehran)
Weighted Round-Robin Approaches:
Overview
 The WRR algorithm has been used for scheduling real-time traffic in
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high-speed switched networks
A RR scheduler delays the completion of every job
For precedence constrained jobs, the response time of a chain of jobs
can be unduly large
 WRR is not suitable for scheduling such jobs
WRR approach does not require a sorted priority queue, only a RR
queue
suitable for ultrahigh-speed networks, since queues with the
required speed are expensive
M. Kargahi (University of Tehran)
WRR, Sequential, and Piped
Executions
J1,1
P1
J1,2
J2,1
J1,1&J2,1
J1,2&J2,2
P2
WRR
P1
P2
J1,1
J2,1
J1,2
J2,2
Sequential execution
 What if the results could be piped?
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J2,2
Priority-Driven Approaches: Overview
 Never leave processor idle when there is work to be done (such
schedulers are also called work-conserving)
 Based on list-driven, greedy schedulers (tries to make locally optimal
decisions)
 Examples: FIFO, LIFO, SETF, LETF, EDF
 An implementation of preemptive priority-driven scheduling:
 Assign priorities to jobs
 Scheduling decisions are made when
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Job becomes ready
Processor becomes idle
Priority of jobs change
At each scheduling decision time, choose ready task with the
highest priority
 In non-preemptive case, scheduling decisions are made only when
processor becomes idle
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Example: Priority-Driven Scheduling
 Preemptive
 Non-preemptive
J5
J7
J6
J8
Note the dynamic dispatching in the above schedule
M. Kargahi (University of Tehran)
Effective Release Times and Deadlines
 Timing constraints are often inconsistent with precedence
constraints
Example: d1>d2, but J1J2
 Effective timing constraints on a single processor:
eff
eff
 Effective release time: ri : max{ri ,{rj | J j  Ji }}
 Effective deadline: d eff : min{d ,{d eff | J  J }}
i
i
j
i
j
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The effective release time/deadline of all jobs can be
computed in O(n2) where n is the number of jobs
M. Kargahi (University of Tehran)
Effective Release Times and Deadlines
 In the above example, the effective release time of J3 is 2,
and its effective deadline is 8
M. Kargahi (University of Tehran)
Optimality of the EDF Algorithm
 EDF: Earliest Deadline First
 EDF algorithm: At any time, execute the available job with the earliest
deadline
 Theorem: When preemption is allowed and jobs do not contend for
resources, the EDF algorithm can produce a feasible schedule of a set J
of jobs with arbitrary release times and deadlines on a processor if and
only if J has feasible schedules
 Note that the theorem applies even if tasks are not periodic
 If periodic, the task relative deadline, can be <, =, or > its period
M. Kargahi (University of Tehran)
Optimality of the EDF Algorithm
 Proof: Assume that arbitrary schedule S meets timing constraints
For S to not be an EDF schedule, we must have the following situation:
Case 1: L(A)>L(B)
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Optimality of the EDF Algorithm
 Case 2: L(A)L(B)
 If we inductively repeat this procedure, we can eliminate all out-of-
order violations
 The resulting schedule may still fail to be an EDF schedule because it
has idle intervals while some job is ready
 Such idle intervals can be eliminated by moving some jobs forward
M. Kargahi (University of Tehran)
LRT (reverse EDF) Scheduling
 Latest Release Time (LRT)
J1, 3 (0, 6]
J2, 2 (5, 8]
J3, 2 (2, 7]
J1
0
2
J3
4
J2
6
8
 Question: Is LRT a priority-driven scheduling algorithm?
M. Kargahi (University of Tehran)
LST (MLF or LLF) Scheduling
 Least Slack-Time First (LST)
 Minimum Laxity First (MLF) or Least Laxity First (LLF)
 Slack (laxity): at any time t, the slack (or laxity) of a job with deadline
d is equal to d - t minus the time required to complete the remaining
portion of the job
 MLF scheduling: The job with the smallest slack (laxity) has the
highest priority at all times
 MLF is also optimal (proof is similar to EDF)
 Question: Which of EDF or MLF is preferable in practice?
M. Kargahi (University of Tehran)
Non-Optimality of EDF and LST
 Case 1: When preemption is not allowed
 Ji=(ri, di, ei)
J1
J2
0
2
4
6
 J1=(0, 10, 3)
 J2=(2, 14, 6)
J1
J3
 J3=(4, 12, 4)
0
2
4
6
J3
8
10
12
14
12
14
J2
8
10
No NP priority-driven alg. is optimal when jobs have arbitrary ri, di, ei
 Case 2: On more than one processor
J1
 J1=(0, 4, 1)
P1
0
2
 J2=(0, 4, 1)
J2
 J3=(0, 5, 5)
P2
0
2
J1
J2
P1
0
2
P2
J3
0
2
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4
5
J3
4
6
4
6
Anomaly with NP-Priority Sch.
 When jobs have arbitrary release times and share
resources, scheduling anomalies can occur even
with one processor and preemptable jobs
 Whether a set of jobs has predictable execution
behavior depends not only on the parameters of
jobs but also on the algorithm used to schedule the
jobs
M. Kargahi (University of Tehran)
Offline vs. Online Scheduling
 Offline scheduling
Inflexibility
 Deterministic timing behavior for a deterministic system
 Complexity is not important
 Low run-time overhead
 Online scheduling
 The parameters of each job are known only after the job is released
 The only option for unpredictable workloads
 Flexibility and adaptability
 Reduced ability for best using of resources
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M. Kargahi (University of Tehran)
Example for an online scheduler
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Assume a non-preemptive job J1,1 (0, 2]
 Two options
1.
Start executing J1 at time 0
2.
Postpone the execution of J1 to some later time x1
 Selecting option 1: we may have J2,1-x (x<1, 1]miss J2
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Selecting option 2: we may have J3,1 (x<1, 2]miss J3
 A clairvoyant scheduler is required
 No optimal online scheduling algorithm exists when some
jobs are non-preemptable
 When all jobs are preemptable and there is only 1 processor
we have optimal online algorithms such as EDF and LST
M. Kargahi (University of Tehran)
Overloaded systems
 A system is overloaded when the jobs offered to the scheduler cannot be
feasibly scheduled even by a clairvoyant scheduler
 Some measures
 Value of Ji = ei if Ji meets its deadline, or 0 otherwise
 V (schedule) = sum of the values of all jobs in the schedule
 Competitive factor for an online algorithm = c iff
V (schedule) of any finite sequence of jobs produced by the alg. is at
least c times of V (schedule) produced by an optimal clairvoyant alg.
 c=1 for EDF and LST, when jobs are preemptable, there is one
processor, and the processor is not overloaded
 c=0 for EDF and LST, when the processor is overloaded
 Ex.: J1,2(0, ] & J2,e(, +e]
 V (EDF)=0, while V (Best)=e
M. Kargahi (University of Tehran)