sched/dl/Documentation: Add some references

 maximum tardiness of each task is smaller or equal than

	((M − 1) · WCET_max − WCET_min)/(M − (M − 2) · U_max) + WCET_max

 where WCET_max = max{WCET_i} is the maximum WCET, WCET_min=min{WCET_i}

 is the minimum WCET, and U_max = max{WCET_i/P_i} is the maximum utilization.

 is the minimum WCET, and U_max = max{WCET_i/P_i} is the maximum

 utilization[12].

 If M=1 (uniprocessor system), or in case of partitioned scheduling (each

 real-time task is statically assigned to one and only one CPU), it is

 On multiprocessor systems with global EDF scheduling (non partitioned

 systems), a sufficient test for schedulability can not be based on the

 utilizations (it can be shown that task sets with utilizations slightly

 larger than 1 can miss deadlines regardless of the number of CPUs M).

 However, as previously stated, enforcing that the total utilization is smaller

 than M is enough to guarantee that non real-time tasks are not starved and

 that the tardiness of real-time tasks has an upper bound.

 utilizations or densities: it can be shown that even if D_i = P_i task

 sets with utilizations slightly larger than 1 can miss deadlines regardless

 of the number of CPUs.

 Consider a set {Task_1,...Task_{M+1}} of M+1 tasks on a system with M

 CPUs, with the first task Task_1=(P,P,P) having period, relative deadline

 and WCET equal to P. The remaining M tasks Task_i=(e,P-1,P-1) have an

 arbitrarily small worst case execution time (indicated as "e" here) and a

 period smaller than the one of the first task. Hence, if all the tasks

 activate at the same time t, global EDF schedules these M tasks first

 (because their absolute deadlines are equal to t + P - 1, hence they are

 smaller than the absolute deadline of Task_1, which is t + P). As a

 result, Task_1 can be scheduled only at time t + e, and will finish at

 time t + e + P, after its absolute deadline. The total utilization of the

 task set is U = M · e / (P - 1) + P / P = M · e / (P - 1) + 1, and for small

 values of e this can become very close to 1. This is known as "Dhall's

 effect"[7]. Note: the example in the original paper by Dhall has been

 slightly simplified here (for example, Dhall more correctly computed

 lim_{e->0}U).

 More complex schedulability tests for global EDF have been developed in

 real-time literature[8,9], but they are not based on a simple comparison

 between total utilization (or density) and a fixed constant. If all tasks

 have D_i = P_i, a sufficient schedulability condition can be expressed in

 a simple way:

	sum(WCET_i / P_i) <= M - (M - 1) · U_max

 where U_max = max{WCET_i / P_i}[10]. Notice that for U_max = 1,

 M - (M - 1) · U_max becomes M - M + 1 = 1 and this schedulability condition

 just confirms the Dhall's effect. A more complete survey of the literature

 about schedulability tests for multi-processor real-time scheduling can be

 found in [11].

 As seen, enforcing that the total utilization is smaller than M does not

 guarantee that global EDF schedules the tasks without missing any deadline

 (in other words, global EDF is not an optimal scheduling algorithm). However,

 a total utilization smaller than M is enough to guarantee that non real-time

 tasks are not starved and that the tardiness of real-time tasks has an upper

 bound[12] (as previously noted). Different bounds on the maximum tardiness

 experienced by real-time tasks have been developed in various papers[13,14],

 but the theoretical result that is important for SCHED_DEADLINE is that if

 the total utilization is smaller or equal than M then the response times of

 the tasks are limited.

 SCHED_DEADLINE can be used to schedule real-time tasks guaranteeing that

 the jobs' deadlines of a task are respected. In order to do this, a task

      Concerning the Preemptive Scheduling of Periodic Real-Time tasks on

      One Processor. Real-Time Systems Journal, vol. 4, no. 2, pp 301-324,

      1990.

  7 - S. J. Dhall and C. L. Liu. On a real-time scheduling problem. Operations

      research, vol. 26, no. 1, pp 127-140, 1978.

  8 - T. Baker. Multiprocessor EDF and Deadline Monotonic Schedulability

      Analysis. Proceedings of the 24th IEEE Real-Time Systems Symposium, 2003.

  9 - T. Baker. An Analysis of EDF Schedulability on a Multiprocessor.

      IEEE Transactions on Parallel and Distributed Systems, vol. 16, no. 8,

      pp 760-768, 2005.

  10 - J. Goossens, S. Funk and S. Baruah, Priority-Driven Scheduling of

       Periodic Task Systems on Multiprocessors. Real-Time Systems Journal,

       vol. 25, no. 2–3, pp. 187–205, 2003.

  11 - R. Davis and A. Burns. A Survey of Hard Real-Time Scheduling for

       Multiprocessor Systems. ACM Computing Surveys, vol. 43, no. 4, 2011.

       http://www-users.cs.york.ac.uk/~robdavis/papers/MPSurveyv5.0.pdf

  12 - U. C. Devi and J. H. Anderson. Tardiness Bounds under Global EDF

       Scheduling on a Multiprocessor. Real-Time Systems Journal, vol. 32,

       no. 2, pp 133-189, 2008.

  13 - P. Valente and G. Lipari. An Upper Bound to the Lateness of Soft

       Real-Time Tasks Scheduled by EDF on Multiprocessors. Proceedings of

       the 26th IEEE Real-Time Systems Symposium, 2005.

  14 - J. Erickson, U. Devi and S. Baruah. Improved tardiness bounds for

       Global EDF. Proceedings of the 22nd Euromicro Conference on

       Real-Time Systems, 2010.

4. Bandwidth management

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