## Applying New Scheduling Theory to Static Priority Pre-Emptive Scheduling (1993)

Venue: | Software Engineering Journal |

Citations: | 312 - 56 self |

### BibTeX

@ARTICLE{Audsley93applyingnew,

author = {N. Audsley and A. Burns and M. Richardson and K. Tindell and A. J. Wellings},

title = {Applying New Scheduling Theory to Static Priority Pre-Emptive Scheduling},

journal = {Software Engineering Journal},

year = {1993},

volume = {8},

pages = {284--292}

}

### Years of Citing Articles

### OpenURL

### Abstract

The paper presents exact schedulability analyses for real-time systems scheduled at run-time with a static priority pre-emptive dispatcher. The tasks to be scheduled are allowed to experience internal blocking (from other tasks with which they share resources) and (with certain restrictions) release jitter — such as waiting for a message to arrive. The analysis presented is more general than that previously published, and subsumes, for example, techniques based on the Rate Monotonic approach. In addition to presenting the theory, an existing avionics case study is described and analysed. The predictions that follow from this analysis are seen to be in close agreement with the behaviour exhibited during simulation studies. 1.

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Citation Context ...uter periods completing within the window of size r i is bounded by: # # # T j r i ### # # # The total interference due to full outer arrivals is therefore bounded by: n j # # # T j r i ### # # # C j =-=(7)-=- At most one partially complete outer arrival can interfere over the remaining part of the window not already accounted for by whole arrivals. This remaining time amounts to: r i - T j # # # T j r i #... |

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Citation Context ... hp (i ) S # # # # # min # # # # # # # # # # t j J j + r i - T j # # # T j J j + r i ####### # # # #################### # # # # # , n j # # # # # + n j # # # T j J j + r i ####### # # # # # # # # C j =-=(12)-=-s- As with Equation (3) an iterative equation to find r i can be formulated. Again, the worst-case response time of a task, measured from arrival to termination, is given by J i + r i . 6. DISCUSSION ... |

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Citation Context ... to: r i - T j # # # T j r i ### # # # and lies in the range (0 .. T j ]. We shall denote this value by Q i j . The interference over this remaining time is bounded by: # # # t j Q i j #### # # # C j =-=(8)-=- The above equation assumes that task j executes as a continual periodic task (with period t j ) over the remaining interval. However, task j cannot execute for more than n j periods in this interval ... |

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On the Complexity of Fixed-priority Scheduling of Periodic, Real-Time Tasks. Performance Evaluation, 2:237-250, 1982. Nok831 WB991 @SL89] Andrew Lyons. UML for Real-Time Overview. White Paper, Published by ObjecTime, and available from www.objectime.com
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Citation Context ...ombining Equations (10) and (7) and summing over all higher priority tasks we obtain: I i = "j hp (i ) S # # # min # # # # # # t j Q i j #### # # # , n j # # # + n j # # # T j r i ### # # # # # #=-= C j (11)-=- If a task j is not sporadically periodic then we choose n j = 1 and t j = T j . As a check for Equation (11) we assume that all tasks are not sporadically periodic, and hence for all tasks j n j = 1 ... |

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Citation Context ...e point at which task i is released. A more reasonable and useful measure might be from the time task i arrives, so that the worstcase time from arrival to completion of task i is given by: J i + r i =-=(6)-=- Note that Equation (5) still allows semaphores to be locked and unlocked according to the Priority Ceiling Protocol. Having extended the scheduling analysis to handle release jitter, we now indicate ... |

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Citation Context ...vers only a partially complete outer arrival), and another bound can be obtained: n j C j (9)s- The least upper bound can therefore be used, i.e.: min # # # # # # t j Q i j #### # # # , n j # # # C j =-=(10) Comb-=-ining Equations (10) and (7) and summing over all higher priority tasks we obtain: I i = "j hp (i ) S # # # min # # # # # # t j Q i j #### # # # , n j # # # + n j # # # T j r i ### # # # # # # C ... |

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Citation Context ...r 2 would be 8, and since 8 + 4 12, no extra `hit' occurs. Equation (3) can thus be modified to allow for release jitter:s- r i n +1 = C i + B i + "j hp (i ) S # # # T j r i n + J j ####### # # #=-= C j (5)-=- Recall that r i is the worst-case response time measured from the point at which task i is released. A more reasonable and useful measure might be from the time task i arrives, so that the worstcase ... |

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Citation Context ...ing interval. However, task j cannot execute for more than n j periods in this interval (since the interval covers only a partially complete outer arrival), and another bound can be obtained: n j C j =-=(9)-=-s- The least upper bound can therefore be used, i.e.: min # # # # # # t j Q i j #### # # # , n j # # # C j (10) Combining Equations (10) and (7) and summing over all higher priority tasks we obtain: I... |

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Citation Context ...d all computation for T2 would be complete before T1 re-arrived and pre-empted T2. The extra `hit' only occurs if r i + J j > T j , and hence: I i = "j hp (i ) S # # # T j r i + J j ####### # # #=-= C j (4)-=- In Figure 4, r 2 would be 9, according to Equation (3). Since r 2 + J 1 > T 1 (or 9 + 4 > 12), T2 gets an extra `hit'. But if C 2 = 5 then r 2 would be 8, and since 8 + 4 12, no extra `hit' occurs. E... |

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Citation Context ...amount of computation equal to C i , and be delayed when locking semaphores by at most B i . Additionally, task i could be pre-empted by at most I i . Therefore we can say that: r i = C i + B i + I i =-=(1)-=- If a task i has a deadline then we must have r isD i . The worst-case computation time C i is constant and known a priori by some means 14, 15 . The worst-case blocking time B i is found according to... |

38 | STRESS—A simulator for hard real-time systems
- Audsley, Burns, et al.
- 1994
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Citation Context ...technique. Let r i n be the n th approximation to the true value of r i . These approximations are generated from the above equation: r i n +1 = C i + B i + "j hp (i ) S # # # T j r i n ### # # #=-= C j (3)-=- The iteration starts with r i 0 = 0, and terminates when r i n +1 = r i n . It can easily be shown that r i n +1sr i n and so the iteration can be halted early if either r i n +1 > D i or if r i n +1... |

34 |
Real-Time Scheduling: The Deadline Monotonic Approach
- Audsley, Burns, et al.
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(Show Context)
Citation Context ...m shows part of a schedule of a system consisting of three tasks, displayed in priority order. Task 1 is a task with worst-case computational requirement of C 1 = 1, a deadline of D 1 = 4, and a worst=-=(1)-=-scase inter-arrival time of T 1 = 50. Tasks 2 and 3 have their characteristics defined in Table 1. Figure 1 shows the worst-case scheduling point described by Liu and Layland, where all tasks are rele... |

15 | Building a Predictable Avionics Platform in Ada: A Case - Study”, Vogel, et al. - 1991 |

6 | Real-time synchronisation protocols for shared memory multiprocessors - Rajkumar |

4 | Resource Control for Hard Real-Time Systems: A Review
- Audsley
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(Show Context)
Citation Context ...are not needed. In fact, a periodic task can be regarded as a sporadic task, released by a regular timing event. The total interference I i is given by: I i = "j hp (i ) S # # # T j r i ### # # #=-= C j (2)-=- where hp (i ) is the set of tasks with higher base priorities. Unfortunately, when equations (1) and (2) are combined, the unknown term r i appears on both the left and the right hand sides of the eq... |

1 |
STRESS: A Simulator For Real-Time
- Audsley, Burns, et al.
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Citation Context ... ri ≥ ri and so the iteration can be halted early if either ri >Di or if ri >Ti . It can also be shown that the iteration is guaranteed to converge if the processor utilisation is ≤ 100% 6 . Equation =-=(3)-=- can be embodied into a software tool that analyses a task set. Note that if the priority of task a is greater than the priority of task b then rb >ra ; thus the task set should be analysed in 0 prior... |

1 | Computer Society Press (28 May - 1 - Systems, Paris - 1990 |