1624:(ISRs), whether they have a hard real-time deadline or not should be included in RMS analysis to determine schedulability in cases where ISRs have priorities above all scheduler-controlled tasks. An ISR may already be appropriately prioritized under RMS rules if its processing period is shorter than that of the shortest, non-ISR process. However, an ISR with a period/deadline longer than any non-ISR process period with a critical deadline results in a violation of RMS and prevents the use of the calculated bounds for determining schedulability of a task set.
1632:
One method for mitigating a mis-prioritized ISR is to adjust the analysis by reducing the ISR's period to be equal to that of the shortest period, if possible. Imposing this shorter period results in prioritization that conforms to RMS, but also results in a higher utilization factor for the ISR and
1556:
Priority inheritance algorithms can be characterized by two parameters. First, is the inheritance lazy (only when essential) or immediate (boost priority before there is a conflict). Second is the inheritance optimistic (boost a minimum amount) or pessimistic (boost by more than the minimum amount):
1970:
Another method for mitigating a mis-prioritized ISR is to use the ISR to only set a new semaphore/mutex while moving the time-intensive processing to a new process that has been appropriately prioritized using RMS and will block on the new semaphore/mutex. When determining schedulability, a margin
1352:
It has been shown that a randomly generated periodic task system will usually meet all deadlines when the utilization is 88% or less, however this fact depends on knowing the exact task statistics (periods, deadlines) which cannot be guaranteed for all task sets, and in some cases the authors found
1967:. This utilization factor would be used when adding up the total utilization factor for the task set and comparing to the upper bound to prove schedulability. It should be emphasized that adjusting the period of the ISR is for analysis only and that the true period of the ISR remains unchanged.
1543:
to each semaphore, which is the priority of the highest job that will ever access that semaphore. A job cannot preempt a lower priority critical section if its priority is lower than the ceiling priority for that section. This method prevents deadlocks and bounds the blocking time to at most the
1148:. It is acknowledged by Liu and Layland that it is not always feasible to have a harmonic task set and that in practice other mitigation measures, such as buffering for tasks with soft-time deadlines or using a dynamic priority assignment approach may be used instead to allow for a higher bound.
115:
algorithm is also optimal with equal periods and deadlines, in fact in this case the algorithms are identical; in addition, deadline monotonic scheduling is optimal when deadlines are less than periods. For the task model in which deadlines can be greater than periods, Audsley's algorithm endowed
1510:
promotes the priority of the task that holds the resource to the priority of the task that requests that resource at the time the request is made. Upon release of the resource, the original priority level before the promotion is restored. This method does not prevent deadlocks and suffers from
1604:
In practice there is no mathematical difference (in terms of the Liu-Layland system utilization bound) between the lazy and immediate algorithms, and the immediate algorithms are more efficient to implement, and so they are the ones used by most practical systems.
2724:
3181:
283:
4037:
The actual reason for the Mars
Pathfinder Bug, by those who actually dealt with it, rather than someone whose company and therefore stock value depended upon the description of the problem, or someone who heard someone talking about the
98:
schedulers fail to meet the scheduling needs otherwise. Rate monotonic scheduling looks at a run modeling of all threads in the system and determines how much time is needed to meet the guarantees for the set of threads in question.
408:
3418:
795:
1271:
2982:
2519:
2124:
1633:
therefore for the total utilization factor, which may still be below the allowable bound and therefore schedulability can be proven. As an example, consider a hardware ISR that has a computation time,
2911:
2448:
2226:
42:
and have deterministic guarantees with regard to response times. Rate monotonic analysis is used in conjunction with those systems to provide scheduling guarantees for a particular application.
1861:
1428:
35:(RTOS) with a static-priority scheduling class. The static priorities are assigned according to the cycle duration of the job, so a shorter cycle duration results in a higher job priority.
630:
683:
2582:
1913:
910:
1965:
3273:
3045:
1780:
3447:
4096:
3212:
3025:
2562:
2268:
1544:
length of one lower priority critical section. This method can be suboptimal, in that it can cause unnecessary blocking. The priority ceiling protocol is available in the
441:
3289:
1701:
1666:
1342:
1310:
1276:
In the instance where for each task, its period is an exact multiple of every other task that has a shorter period, the task set can be thought of as being composed of
945:
1515:. That is, if a high priority task accesses multiple shared resources in sequence, it may have to wait (block) on a lower priority task for each of the resources. The
488:
146:
1730:
1032:
1003:
974:
864:
835:
546:
517:
4063:
2834:
2371:
2149:
111:
under the given assumptions, meaning that if any static-priority scheduling algorithm can meet all the deadlines, then the rate-monotonic algorithm can too. The
1146:
332:
3897:
1469:
or avoid the sharing of a mutex/semaphore across threads with different priorities. This is so that resource conflicts cannot result in the first place.
3275:, tasks 2 and 3 can be considered a harmonic task subset. Task 1 forms its own harmonic task subset. Therefore, the number of harmonic task subsets,
706:
2344:
Under RMS, P2 has the highest release rate (i.e. the shortest release period) and so would have the highest priority, followed by P3 and finally P1.
2050:
Under RMS, P2 has the highest release rate (i.e. the shortest release period) and so would have the highest priority, followed by P1 and finally P3.
4279:
1732:
of 1 millisecond, then the ISR would have a higher priority, but a lower rate, which violates RMS. For the purposes of proving schedulability, set
1170:
4171:
3820:
2922:
4106:
3944:
3697:
3624:
2459:
1441:
is the CPU utilization for each task. It is the tightest upper bound that can be found using only the individual task utilization factors.
2064:
1971:
of CPU utilization due to ISR activity should be subtracted from the least upper bound. ISRs with negligible utilization may be ignored.
4091:
4056:
3571:
3474:
1466:
3680:
Lehoczky, J.; Sha, L.; Ding, Y. (1989), "The rate monotonic scheduling algorithm: exact characterization and average case behavior",
2807:
Under RMS, P2 has the highest rate (i.e. the shortest period) and so would have the highest priority, followed by P3 and finally P1.
4121:
3656:
4186:
1612:
reset bug" which was fixed on Mars by changing the creation flags for the semaphore so as to enable the priority inheritance.
2842:
2379:
2157:
447:, is less than 70%. The other 30% of the CPU can be dedicated to lower-priority, non-real-time tasks. For smaller values of
4035:
1519:
3841:
Sha, L.; Rajkumar, R.; Lehoczky, J. P. (1990), "Priority inheritance protocols: an approach to real-time synchronization",
4258:
4146:
4086:
4049:
3458:
112:
4284:
2270:, and because being below the Least Upper Bound is a sufficient condition, the system is guaranteed to be schedulable.
4126:
3469:
1458:
1785:
1367:
1361:
The hyperbolic bound is a tighter sufficient condition for schedulability than the one presented by Liu and
Layland:
1782:
and recalculate the utilization factor for the ISR (which also raises the total utilization factor). In this case,
3588:
Leung, J. Y.; Whitehead, J. (1982), "On the complexity of fixed-priority scheduling of periodic, real-time tasks",
76:
Static priorities (the task with the highest static priority that is runnable immediately preempts all other tasks)
32:
588:
4212:
4136:
1621:
1536:
4023:
3721:
Enrico Bini; Giorgio C. Buttazzo; Giuseppe M. Buttazzo (2003), "Rate
Monotonic Analysis: the Hyperbolic Bound",
2719:{\displaystyle \prod _{i=1}^{n}(U_{i}+1)=({\frac {3}{16}}+1)*({\frac {2}{5}}+1)*({\frac {2}{10}}+1)=1.995\leq 2}
4141:
3901:
641:
140:
utilization is below a specific bound (depending on the number of tasks). The schedulability test for RMS is:
4166:
137:
63:
3176:{\displaystyle \prod _{i=1}^{n}(U_{i}+1)=({\frac {7}{32}}+1)*({\frac {2}{5}}+1)*({\frac {2}{10}}+1)=2.0475}
1866:
4156:
4072:
3769:
3526:
3485:
869:
91:
39:
1918:
4111:
4101:
3466:, a time and space partitioned real-time operating system containing a working Rate Monotonic Scheduler.
3229:
808:
Liu and
Layland noted that this bound may be relaxed to the maximum possible value of 1.0, if for tasks
1735:
1035:
3426:
136:
periodic tasks with unique periods, a feasible schedule that will always meet deadlines exists if the
90:
It is a mathematical model that contains a calculated simulation of periods in a closed system, where
4207:
4181:
3495:
3189:
1462:
3517:; Layland, J. (1973), "Scheduling algorithms for multiprogramming in a hard real-time environment",
548:
should represent the worst-case deadline (i.e. shortest period) in which all processing must occur.
3774:
3531:
1005:, which is to say that all tasks have a period that is not just a multiple of the shortest period,
2991:
2528:
2234:
416:
4253:
4131:
4006:
3787:
3703:
3662:
3568:
3544:
1454:
278:{\displaystyle U=\sum _{i=1}^{n}{U_{i}}=\sum _{i=1}^{n}{\frac {C_{i}}{T_{i}}}\leq n({2}^{1/n}-1)}
1034:, but instead that any task's period is a multiple of all shorter periods. This is known as an
50:
A simple version of rate-monotonic analysis assumes that threads have the following properties:
1671:
1636:
1315:
1283:
915:
4176:
4161:
3940:
3693:
3652:
3620:
461:
59:
1706:
1008:
979:
950:
840:
811:
522:
493:
3998:
3975:
3850:
3779:
3738:
3730:
3685:
3644:
3597:
3536:
20:
1312:, which makes this generalization equivalent to Liu and Layland's least upper bound. When
4116:
3575:
3514:
3490:
3482:, an open source real-time operating system containing a working Rate Monotonic Scheduler.
1609:
1523:
557:
2818:
2355:
2133:
86:
Context switch times and other thread operations are free and have no impact on the model
403:{\displaystyle \lim _{n\rightarrow \infty }n({\sqrt{2}}-1)=\ln 2\approx 0.693147\ldots }
4227:
4222:
4217:
3757:
1041:
116:
with an exact schedulability test for this model finds an optimal priority assignment.
3883:
4273:
4191:
3707:
3601:
3548:
4010:
3927:
Hard Real-Time
Computing Systems: Predictable Scheduling Algorithms and Applications
3870:
Hard Real-Time
Computing Systems: Predictable Scheduling Algorithms and Applications
3807:
Hard Real-Time
Computing Systems: Predictable Scheduling Algorithms and Applications
3666:
3413:{\displaystyle {U_{lub,harmonic}}=K(2^{\frac {1}{K}}-1)=2(2^{\frac {1}{2}}-1)=0.828}
4237:
3989:
Sha, Lui; Goodenough, John B. (April 1990), "Real-Time
Scheduling Theory and Ada",
3791:
1527:
1496:
family of primitives which nest the locking of device interrupts (FreeBSD 5.x/6.x),
1487:
95:
67:
4029:
2836:
processes, under which we can conclude that the task set is schedulable, remains:
2373:
processes, under which we can conclude that the task set is schedulable, remains:
1516:
1353:
that the utilization reached the least upper bound presented by Liu and
Layland.
790:{\displaystyle \rho _{i}={\lambda _{i} \over \mu _{i}}={C_{i} \over T_{i}}=U_{i}}
2815:
Using the Liu and
Layland bound, as in Example 1, the sufficient condition for
2352:
Using the Liu and Layland bound, as in Example 1, the sufficient condition for
4232:
3980:
3966:
Joseph, M.; Pandya, P. (1986), "Finding response times in real-time systems",
1703:, of 4 milliseconds. If the shortest scheduler-controlled task has a period,
83:
conventions (tasks with shorter periods/deadlines are given higher priorities)
3648:
3639:
T.-W. Kuo; A.K. Mok (1991). "Load adjustment in adaptive real-time systems".
3734:
3689:
455:
is close to this estimate, the calculated utilization bound should be used.
3783:
3760:; Redell, D. D. (1980), "Experience with processes and monitors in Mesa",
3540:
2151:
processes, under which we can conclude that the system is schedulable is:
1266:{\displaystyle U=\sum _{i=1}^{n}{\frac {C_{i}}{T_{i}}}\leq K({2}^{1/K}-1)}
3953:
323:
3743:
2977:{\displaystyle U={\frac {7}{32}}+{\frac {2}{5}}+{\frac {2}{10}}=0.81875}
1449:
In many practical applications, resources are shared and the unmodified
4041:
2514:{\displaystyle U={\frac {3}{16}}+{\frac {2}{5}}+{\frac {2}{10}}=0.7875}
1545:
3854:
3423:
Using the total utilization factor calculated above (0.81875), since
2119:{\displaystyle U={\frac {1}{8}}+{\frac {2}{5}}+{\frac {2}{10}}=0.725}
1608:
An example of usage of basic priority inheritance is related to the "
4002:
519:
should represent the worst-case (i.e. longest) computation time and
443:
is that RMS can meet all of the deadlines if total CPU utilization,
1461:
hazards. In practice, this is solved by disabling preemption or by
310:
is the release period (with deadline one period later) for process
3479:
3031:
to be guaranteed to be schedulable by the Liu and Layland bound.
2568:
to be guaranteed to be schedulable by the Liu and Layland bound.
3463:
1539:
enhances the basic priority inheritance protocol by assigning a
1486:
primitives that lock CPU interrupts in a real-time kernel, e.g.
4045:
1598:
priority ceiling protocol, basic priority inheritance protocol
3641:[1991] Proceedings Twelfth Real-Time Systems Symposium
3569:
http://oreilly.com/catalog/linuxkernel/chapter/ch10.html#85347
1344:, the upper bound becomes 1.0, representing full utilization.
322:
for two processes. When the number of processes tends towards
4030:
What really happened on Mars Rover Pathfinder by Mike Jones
3218:
be guaranteed to be schedulable by the Hyperbolic bound.
318:
is the number of processes to be scheduled. For example,
2906:{\displaystyle {U_{lub}}=3(2^{\frac {1}{3}}-1)=0.77976}
2443:{\displaystyle {U_{lub}}=3(2^{\frac {1}{3}}-1)=0.77976}
2221:{\displaystyle {U_{lub}}=3(2^{\frac {1}{3}}-1)=0.77976}
54:
No resource sharing (processes do not share resources,
582:. These two parameters are often specified as rates:
3872:(Third ed.), New York, NY: Springer, p. 212
3809:(Third ed.), New York, NY: Springer, p. 225
3429:
3292:
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3192:
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149:
73:
Deterministic deadlines are exactly equal to periods
4246:
4200:
4079:
3898:"Mars Pathfinder Reset Bug - Anthology of Interest"
3619:(4th ed.), Addison-Wesley, pp. 391, 397,
3441:
3412:
3267:
3206:
3175:
3019:
2976:
2905:
2828:
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1959:
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1265:
1156:Kuo and Mok showed that for a task set made up of
1140:
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997:
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939:
904:
858:
829:
789:
677:
624:
540:
511:
482:
435:
402:
277:
337:
3039:Using the tighter Hyperbolic bound as follows:
2576:Using the tighter Hyperbolic bound as follows:
1856:{\displaystyle {U_{isr}}{=}{C_{isr}}/{T_{isr}}}
1423:{\displaystyle \prod _{i=1}^{n}(U_{i}+1)\leq 2}
1280:harmonic task subsets of size 1 and therefore
4057:
31:) is a priority assignment algorithm used in
8:
3449:the system is determined to be schedulable.
625:{\displaystyle \lambda _{i}={1 \over T_{i}}}
79:Static priorities assigned according to the
3937:Real-Time Systems and Programming Languages
3617:Real-Time Systems and Programming Languages
1530:includes an implementation of this formula.
4064:
4050:
4042:
129:
107:The rate-monotonic priority assignment is
3979:
3773:
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3530:
3428:
3384:
3351:
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3293:
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3257:
3252:
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148:
4097:Earliest eligible virtual deadline first
4032:from The Risks Digest, Vol. 19, Issue 49
2740:
2277:
1983:
1559:
678:{\displaystyle \mu _{i}={1 \over C_{i}}}
16:Scheduling technique in computer science
3960:, Upper Saddle River, NJ: Prentice Hall
3506:
1164:), the least upper bound test becomes:
693:The utilization for each task, denoted
4172:Statistical time-division multiplexing
1548:real-time kernel. It is also known as
38:These operating systems are generally
3935:Alan Burns and Andy Wellings (2009),
3615:Alan Burns and Andy Wellings (2009),
1908:{\displaystyle {0.5ms}/{4ms}{=}0.125}
326:, this expression will tend towards:
7:
905:{\displaystyle {T_{m}}{>}{T_{i}}}
299:is the computation time for process
1960:{\displaystyle {0.5ms}/{1ms}{=}0.5}
1508:basic priority inheritance protocol
3884:"Mike Jones at Microsoft Research"
3475:Earliest deadline first scheduling
3268:{\displaystyle {T_{3}}={2{T_{2}}}}
1668:of 500 microseconds and a period,
1550:Highest Locker's Priority Protocol
804:Upper bound for harmonic task sets
347:
62:resource, a queue, or any kind of
14:
4122:Generalized foreground-background
3562:Bovet, Daniel P.; Cesati, Marco,
1775:{\displaystyle {T_{isr}}={T_{1}}}
1465:. Alternative methods are to use
1152:Generalization to harmonic chains
1038:. An example of this would be:
413:Therefore, a rough estimate when
3939:(4th ed.), Addison-Wesley,
3682:IEEE Real-Time Systems Symposium
3442:{\displaystyle 0.81875<0.828}
2916:The total utilization will be:
2453:The total utilization will be:
1160:harmonic task subsets (known as
4280:Processor scheduling algorithms
3207:{\displaystyle 2.0{<}2.0475}
1628:Mitigating mis-prioritized ISRs
552:Relationship to queueing theory
3843:IEEE Transactions on Computers
3723:IEEE Transactions on Computers
3564:Understanding the Linux Kernel
3401:
3377:
3368:
3344:
3164:
3145:
3139:
3120:
3114:
3095:
3089:
3070:
2894:
2870:
2729:it is found that the task set
2701:
2682:
2676:
2657:
2651:
2632:
2626:
2607:
2431:
2407:
2209:
2185:
1411:
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1231:
1135:
1111:
1105:
1045:
376:
355:
344:
272:
243:
1:
3459:Deadline-monotonic scheduling
2130:The sufficient condition for
113:deadline-monotonic scheduling
3602:10.1016/0166-5316(82)90024-4
3214:the system is determined to
3020:{\displaystyle U>U_{lub}}
2557:{\displaystyle U>U_{lub}}
2263:{\displaystyle U<U_{lub}}
436:{\displaystyle {n}\geq {10}}
4127:Highest response ratio next
3470:Dynamic priority scheduling
3027:, the system is determined
2564:, the system is determined
292:is the utilization factor,
120:Upper bounds on utilization
33:real-time operating systems
4301:
4107:Fixed-priority pre-emptive
3925:Buttazzo, Giorgio (2011),
3868:Buttazzo, Giorgio (2011),
3805:Buttazzo, Giorgio (2011),
3222:Harmonic Task Set Analysis
2058:The utilization will be:
1622:interrupt service routines
1616:Interrupt Service Routines
976:is an integer multiple of
66:blocking or non-blocking (
4137:Multilevel feedback queue
4026:from Research @ Microsoft
3762:Communications of the ACM
1696:{\displaystyle {T_{isr}}}
1661:{\displaystyle {C_{isr}}}
1537:priority ceiling protocol
1337:{\displaystyle {K}{=}{1}}
1305:{\displaystyle {K}{=}{n}}
940:{\displaystyle i=1...m-1}
132:proved that for a set of
25:rate-monotonic scheduling
4142:Process Contention Scope
3929:, New York, NY: Springer
3823:. kernel.org. 2008-03-26
3649:10.1109/REAL.1991.160369
483:{\displaystyle {i^{th}}}
130:Liu & Layland (1973)
4167:Shortest remaining time
3981:10.1093/comjnl/29.5.390
3735:10.1109/TC.2003.1214341
3690:10.1109/REAL.1989.63567
1725:{\displaystyle {T_{1}}}
1473:Disabling of preemption
1027:{\displaystyle {T_{1}}}
998:{\displaystyle {T_{i}}}
969:{\displaystyle {T_{m}}}
859:{\displaystyle {T_{i}}}
830:{\displaystyle {T_{m}}}
541:{\displaystyle {T_{i}}}
512:{\displaystyle {C_{i}}}
3821:"Real-Time Linux Wiki"
3590:Performance Evaluation
3486:Scheduling (computing)
3443:
3414:
3269:
3208:
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2907:
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831:
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626:
542:
513:
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404:
279:
212:
176:
4112:Foreground-background
3784:10.1145/358818.358824
3541:10.1145/321738.321743
3444:
3415:
3270:
3209:
3178:
3049:
3022:
2979:
2908:
2831:
2721:
2586:
2559:
2516:
2445:
2368:
2265:
2223:
2146:
2121:
1962:
1910:
1858:
1777:
1727:
1698:
1663:
1425:
1371:
1339:
1307:
1268:
1180:
1143:
1029:
1000:
971:
942:
907:
861:
832:
792:
680:
627:
543:
514:
485:
458:In practice, for the
438:
405:
280:
192:
156:
4073:Processor scheduling
3968:BCS Computer Journal
3684:, pp. 166–171,
3643:. pp. 160–170.
3427:
3290:
3230:
3190:
3046:
2992:
2923:
2843:
2819:
2583:
2529:
2460:
2380:
2356:
2235:
2158:
2134:
2065:
1919:
1867:
1786:
1736:
1707:
1672:
1637:
1501:Priority inheritance
1467:lock-free algorithms
1463:priority inheritance
1368:
1316:
1284:
1171:
1042:
1009:
980:
951:
916:
870:
841:
812:
707:
642:
589:
523:
494:
462:
417:
333:
320:U ≤ 0.8284
147:
4285:Real-time computing
4024:Mars Pathfinder Bug
2829:{\displaystyle 3\,}
2366:{\displaystyle 3\,}
2144:{\displaystyle 3\,}
1577:OS_ENTER_CRITICAL()
1480:OS_ENTER_CRITICAL()
1453:will be subject to
4254:Processor affinity
4147:Proportional share
4087:Deadline-monotonic
3574:2014-09-21 at the
3519:Journal of the ACM
3439:
3410:
3265:
3204:
3173:
3017:
2974:
2903:
2826:
2716:
2554:
2511:
2440:
2363:
2260:
2218:
2141:
2116:
1957:
1905:
1853:
1772:
1722:
1693:
1658:
1581:OS_EXIT_CRITICAL()
1522:2020-10-13 at the
1484:OS_EXIT_CRITICAL()
1455:priority inversion
1420:
1334:
1302:
1263:
1138:
1024:
995:
966:
937:
902:
856:
827:
787:
675:
622:
538:
509:
480:
451:or in cases where
433:
400:
351:
275:
4267:
4266:
4162:Shortest job next
4092:Earliest deadline
3958:Real-time systems
3946:978-0-321-41745-9
3699:978-0-8186-2004-1
3626:978-0-321-41745-9
3496:Kingman's formula
3392:
3359:
3156:
3131:
3106:
2966:
2953:
2940:
2885:
2811:Least Upper Bound
2805:
2804:
2747:Computation time
2693:
2668:
2643:
2503:
2490:
2477:
2422:
2348:Least Upper Bound
2342:
2341:
2284:Computation time
2200:
2108:
2095:
2082:
2054:Least Upper Bound
2048:
2047:
1990:Computation time
1863:will change from
1602:
1601:
1588:, highest locker
1348:Stochastic bounds
1223:
1141:{\displaystyle =}
1036:harmonic task set
772:
745:
673:
620:
569:interarrival time
368:
336:
235:
125:Least upper bound
4292:
4066:
4059:
4052:
4043:
4013:
3984:
3983:
3961:
3949:
3930:
3913:
3912:
3910:
3909:
3900:. Archived from
3894:
3888:
3887:
3880:
3874:
3873:
3865:
3859:
3857:
3855:10.1109/12.57058
3849:(9): 1175–1185,
3838:
3832:
3831:
3829:
3828:
3817:
3811:
3810:
3802:
3796:
3794:
3777:
3754:
3748:
3747:
3746:
3718:
3712:
3710:
3677:
3671:
3670:
3636:
3630:
3629:
3612:
3606:
3604:
3585:
3579:
3566:
3559:
3553:
3551:
3534:
3511:
3448:
3446:
3445:
3440:
3419:
3417:
3416:
3411:
3394:
3393:
3385:
3361:
3360:
3352:
3337:
3336:
3335:
3282:
3278:
3274:
3272:
3271:
3266:
3264:
3263:
3262:
3261:
3244:
3243:
3242:
3213:
3211:
3210:
3205:
3200:
3182:
3180:
3179:
3174:
3157:
3149:
3132:
3124:
3107:
3099:
3082:
3081:
3068:
3063:
3035:Hyperbolic Bound
3026:
3024:
3023:
3018:
3016:
3015:
2983:
2981:
2980:
2975:
2967:
2959:
2954:
2946:
2941:
2933:
2912:
2910:
2909:
2904:
2887:
2886:
2878:
2863:
2862:
2861:
2835:
2833:
2832:
2827:
2741:
2725:
2723:
2722:
2717:
2694:
2686:
2669:
2661:
2644:
2636:
2619:
2618:
2605:
2600:
2572:Hyperbolic Bound
2563:
2561:
2560:
2555:
2553:
2552:
2520:
2518:
2517:
2512:
2504:
2496:
2491:
2483:
2478:
2470:
2449:
2447:
2446:
2441:
2424:
2423:
2415:
2400:
2399:
2398:
2372:
2370:
2369:
2364:
2278:
2269:
2267:
2266:
2261:
2259:
2258:
2227:
2225:
2224:
2219:
2202:
2201:
2193:
2178:
2177:
2176:
2150:
2148:
2147:
2142:
2125:
2123:
2122:
2117:
2109:
2101:
2096:
2088:
2083:
2075:
1984:
1966:
1964:
1963:
1958:
1953:
1948:
1937:
1932:
1914:
1912:
1911:
1906:
1901:
1896:
1885:
1880:
1862:
1860:
1859:
1854:
1852:
1851:
1850:
1834:
1829:
1828:
1827:
1811:
1806:
1805:
1804:
1781:
1779:
1778:
1773:
1771:
1770:
1769:
1756:
1755:
1754:
1731:
1729:
1728:
1723:
1721:
1720:
1719:
1702:
1700:
1699:
1694:
1692:
1691:
1690:
1667:
1665:
1664:
1659:
1657:
1656:
1655:
1587:
1582:
1578:
1560:
1541:ceiling priority
1513:chained blocking
1495:
1485:
1481:
1445:Resource sharing
1440:
1429:
1427:
1426:
1421:
1404:
1403:
1390:
1385:
1357:Hyperbolic bound
1343:
1341:
1340:
1335:
1333:
1328:
1323:
1311:
1309:
1308:
1303:
1301:
1296:
1291:
1279:
1272:
1270:
1269:
1264:
1253:
1252:
1248:
1239:
1224:
1222:
1221:
1212:
1211:
1202:
1199:
1194:
1159:
1147:
1145:
1144:
1139:
1104:
1103:
1102:
1089:
1088:
1087:
1074:
1073:
1072:
1059:
1058:
1057:
1033:
1031:
1030:
1025:
1023:
1022:
1021:
1004:
1002:
1001:
996:
994:
993:
992:
975:
973:
972:
967:
965:
964:
963:
946:
944:
943:
938:
911:
909:
908:
903:
901:
900:
899:
889:
884:
883:
882:
865:
863:
862:
857:
855:
854:
853:
836:
834:
833:
828:
826:
825:
824:
796:
794:
793:
788:
786:
785:
773:
771:
770:
761:
760:
751:
746:
744:
743:
734:
733:
724:
719:
718:
699:
684:
682:
681:
676:
674:
672:
671:
659:
654:
653:
631:
629:
628:
623:
621:
619:
618:
606:
601:
600:
577:
566:
547:
545:
544:
539:
537:
536:
535:
518:
516:
515:
510:
508:
507:
506:
489:
487:
486:
481:
479:
478:
477:
454:
450:
446:
442:
440:
439:
434:
432:
424:
409:
407:
406:
401:
369:
367:
359:
350:
321:
317:
313:
309:
302:
298:
291:
284:
282:
281:
276:
265:
264:
260:
251:
236:
234:
233:
224:
223:
214:
211:
206:
188:
187:
186:
175:
170:
135:
21:computer science
4300:
4299:
4295:
4294:
4293:
4291:
4290:
4289:
4270:
4269:
4268:
4263:
4242:
4213:Completely Fair
4196:
4075:
4070:
4020:
4003:10.1109/2.55469
3988:
3965:
3952:
3947:
3934:
3924:
3921:
3919:Further reading
3916:
3907:
3905:
3896:
3895:
3891:
3882:
3881:
3877:
3867:
3866:
3862:
3840:
3839:
3835:
3826:
3824:
3819:
3818:
3814:
3804:
3803:
3799:
3756:
3755:
3751:
3720:
3719:
3715:
3700:
3679:
3678:
3674:
3659:
3638:
3637:
3633:
3627:
3614:
3613:
3609:
3587:
3586:
3582:
3576:Wayback Machine
3561:
3560:
3556:
3513:
3512:
3508:
3504:
3491:Queueing theory
3455:
3425:
3424:
3380:
3347:
3294:
3288:
3287:
3280:
3276:
3253:
3234:
3228:
3227:
3224:
3188:
3187:
3073:
3044:
3043:
3037:
3001:
2990:
2989:
2921:
2920:
2873:
2847:
2841:
2840:
2817:
2816:
2813:
2753:Release period
2739:
2610:
2581:
2580:
2574:
2538:
2527:
2526:
2458:
2457:
2410:
2384:
2378:
2377:
2354:
2353:
2350:
2290:Release period
2276:
2244:
2233:
2232:
2188:
2162:
2156:
2155:
2132:
2131:
2063:
2062:
2056:
1996:Release period
1982:
1977:
1917:
1916:
1865:
1864:
1836:
1813:
1790:
1784:
1783:
1761:
1740:
1734:
1733:
1711:
1705:
1704:
1676:
1670:
1669:
1641:
1635:
1634:
1630:
1618:
1610:Mars Pathfinder
1585:
1580:
1576:
1524:Wayback Machine
1517:real-time patch
1503:
1493:
1483:
1479:
1475:
1447:
1439:
1435:
1395:
1366:
1365:
1359:
1350:
1314:
1313:
1282:
1281:
1277:
1234:
1213:
1203:
1169:
1168:
1162:harmonic chains
1157:
1154:
1094:
1079:
1064:
1049:
1040:
1039:
1013:
1007:
1006:
984:
978:
977:
955:
949:
948:
914:
913:
891:
874:
868:
867:
845:
839:
838:
816:
810:
809:
806:
777:
762:
752:
735:
725:
710:
705:
704:
698:
694:
663:
645:
640:
639:
610:
592:
587:
586:
576:
572:
565:
561:
558:queueing theory
554:
527:
521:
520:
498:
492:
491:
466:
460:
459:
452:
448:
444:
415:
414:
331:
330:
319:
315:
311:
308:
304:
300:
297:
293:
289:
246:
225:
215:
178:
145:
144:
133:
127:
122:
105:
48:
17:
12:
11:
5:
4298:
4296:
4288:
4287:
4282:
4272:
4271:
4265:
4264:
4262:
4261:
4256:
4250:
4248:
4244:
4243:
4241:
4240:
4235:
4230:
4228:SCHED DEADLINE
4225:
4220:
4215:
4210:
4204:
4202:
4198:
4197:
4195:
4194:
4189:
4184:
4179:
4174:
4169:
4164:
4159:
4154:
4152:Rate-monotonic
4149:
4144:
4139:
4134:
4129:
4124:
4119:
4114:
4109:
4104:
4099:
4094:
4089:
4083:
4081:
4077:
4076:
4071:
4069:
4068:
4061:
4054:
4046:
4040:
4039:
4033:
4027:
4019:
4018:External links
4016:
4015:
4014:
3986:
3974:(5): 390–395,
3963:
3954:Liu, Jane W.S.
3950:
3945:
3932:
3920:
3917:
3915:
3914:
3889:
3875:
3860:
3833:
3812:
3797:
3775:10.1.1.46.7240
3768:(2): 105–117,
3758:Lampson, B. W.
3749:
3729:(7): 933–942,
3713:
3698:
3672:
3657:
3631:
3625:
3607:
3596:(4): 237–250,
3580:
3554:
3532:10.1.1.36.8216
3505:
3503:
3500:
3499:
3498:
3493:
3488:
3483:
3477:
3472:
3467:
3461:
3454:
3451:
3438:
3435:
3432:
3421:
3420:
3409:
3406:
3403:
3400:
3397:
3391:
3388:
3383:
3379:
3376:
3373:
3370:
3367:
3364:
3358:
3355:
3350:
3346:
3343:
3340:
3334:
3331:
3328:
3325:
3322:
3319:
3316:
3313:
3310:
3307:
3304:
3301:
3297:
3260:
3256:
3251:
3247:
3241:
3237:
3223:
3220:
3203:
3199:
3195:
3184:
3183:
3172:
3169:
3166:
3163:
3160:
3155:
3152:
3147:
3144:
3141:
3138:
3135:
3130:
3127:
3122:
3119:
3116:
3113:
3110:
3105:
3102:
3097:
3094:
3091:
3088:
3085:
3080:
3076:
3072:
3067:
3062:
3059:
3056:
3052:
3036:
3033:
3014:
3011:
3008:
3004:
3000:
2997:
2986:
2985:
2973:
2970:
2965:
2962:
2957:
2952:
2949:
2944:
2939:
2936:
2931:
2928:
2914:
2913:
2902:
2899:
2896:
2893:
2890:
2884:
2881:
2876:
2872:
2869:
2866:
2860:
2857:
2854:
2850:
2824:
2812:
2809:
2803:
2802:
2799:
2796:
2793:
2789:
2788:
2785:
2782:
2779:
2775:
2774:
2771:
2768:
2765:
2761:
2760:
2757:
2751:
2745:
2738:
2735:
2727:
2726:
2715:
2712:
2709:
2706:
2703:
2700:
2697:
2692:
2689:
2684:
2681:
2678:
2675:
2672:
2667:
2664:
2659:
2656:
2653:
2650:
2647:
2642:
2639:
2634:
2631:
2628:
2625:
2622:
2617:
2613:
2609:
2604:
2599:
2596:
2593:
2589:
2573:
2570:
2551:
2548:
2545:
2541:
2537:
2534:
2523:
2522:
2510:
2507:
2502:
2499:
2494:
2489:
2486:
2481:
2476:
2473:
2468:
2465:
2451:
2450:
2439:
2436:
2433:
2430:
2427:
2421:
2418:
2413:
2409:
2406:
2403:
2397:
2394:
2391:
2387:
2361:
2349:
2346:
2340:
2339:
2336:
2333:
2330:
2326:
2325:
2322:
2319:
2316:
2312:
2311:
2308:
2305:
2302:
2298:
2297:
2294:
2288:
2282:
2275:
2272:
2257:
2254:
2251:
2247:
2243:
2240:
2229:
2228:
2217:
2214:
2211:
2208:
2205:
2199:
2196:
2191:
2187:
2184:
2181:
2175:
2172:
2169:
2165:
2139:
2128:
2127:
2115:
2112:
2107:
2104:
2099:
2094:
2091:
2086:
2081:
2078:
2073:
2070:
2055:
2052:
2046:
2045:
2042:
2039:
2036:
2032:
2031:
2028:
2025:
2022:
2018:
2017:
2014:
2011:
2008:
2004:
2003:
2000:
1994:
1988:
1981:
1978:
1976:
1973:
1956:
1952:
1947:
1944:
1941:
1936:
1931:
1928:
1925:
1904:
1900:
1895:
1892:
1889:
1884:
1879:
1876:
1873:
1849:
1846:
1843:
1839:
1833:
1826:
1823:
1820:
1816:
1810:
1803:
1800:
1797:
1793:
1768:
1764:
1759:
1753:
1750:
1747:
1743:
1718:
1714:
1689:
1686:
1683:
1679:
1654:
1651:
1648:
1644:
1629:
1626:
1617:
1614:
1600:
1599:
1596:
1594:
1590:
1589:
1583:
1574:
1570:
1569:
1566:
1563:
1554:
1553:
1532:
1531:
1502:
1499:
1498:
1497:
1490:
1474:
1471:
1446:
1443:
1437:
1432:
1431:
1419:
1416:
1413:
1410:
1407:
1402:
1398:
1394:
1389:
1384:
1381:
1378:
1374:
1358:
1355:
1349:
1346:
1332:
1327:
1322:
1300:
1295:
1290:
1274:
1273:
1262:
1259:
1256:
1251:
1247:
1243:
1238:
1233:
1230:
1227:
1220:
1216:
1210:
1206:
1198:
1193:
1190:
1187:
1183:
1179:
1176:
1153:
1150:
1137:
1134:
1131:
1128:
1125:
1122:
1119:
1116:
1113:
1110:
1107:
1101:
1097:
1092:
1086:
1082:
1077:
1071:
1067:
1062:
1056:
1052:
1047:
1020:
1016:
991:
987:
962:
958:
936:
933:
930:
927:
924:
921:
898:
894:
888:
881:
877:
852:
848:
823:
819:
805:
802:
798:
797:
784:
780:
776:
769:
765:
759:
755:
749:
742:
738:
732:
728:
722:
717:
713:
696:
691:
690:
670:
666:
662:
657:
652:
648:
637:
617:
613:
609:
604:
599:
595:
578:is called the
574:
567:is called the
563:
553:
550:
534:
530:
505:
501:
476:
473:
469:
431:
427:
423:
411:
410:
399:
396:
393:
390:
387:
384:
381:
378:
375:
372:
366:
362:
357:
354:
349:
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343:
339:
306:
295:
286:
285:
274:
271:
268:
263:
259:
255:
250:
245:
242:
239:
232:
228:
222:
218:
210:
205:
202:
199:
195:
191:
185:
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174:
169:
166:
163:
159:
155:
152:
126:
123:
121:
118:
104:
101:
88:
87:
84:
81:rate monotonic
77:
74:
71:
47:
44:
15:
13:
10:
9:
6:
4:
3:
2:
4297:
4286:
4283:
4281:
4278:
4277:
4275:
4260:
4257:
4255:
4252:
4251:
4249:
4245:
4239:
4236:
4234:
4231:
4229:
4226:
4224:
4221:
4219:
4216:
4214:
4211:
4209:
4206:
4205:
4203:
4199:
4193:
4192:YDS algorithm
4190:
4188:
4185:
4183:
4180:
4178:
4175:
4173:
4170:
4168:
4165:
4163:
4160:
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4150:
4148:
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4140:
4138:
4135:
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4120:
4118:
4115:
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4110:
4108:
4105:
4103:
4100:
4098:
4095:
4093:
4090:
4088:
4085:
4084:
4082:
4078:
4074:
4067:
4062:
4060:
4055:
4053:
4048:
4047:
4044:
4036:
4034:
4031:
4028:
4025:
4022:
4021:
4017:
4012:
4008:
4004:
4000:
3996:
3992:
3991:IEEE Computer
3987:
3982:
3977:
3973:
3969:
3964:
3959:
3955:
3951:
3948:
3942:
3938:
3933:
3928:
3923:
3922:
3918:
3904:on 2011-10-05
3903:
3899:
3893:
3890:
3885:
3879:
3876:
3871:
3864:
3861:
3856:
3852:
3848:
3844:
3837:
3834:
3822:
3816:
3813:
3808:
3801:
3798:
3793:
3789:
3785:
3781:
3776:
3771:
3767:
3763:
3759:
3753:
3750:
3745:
3740:
3736:
3732:
3728:
3724:
3717:
3714:
3709:
3705:
3701:
3695:
3691:
3687:
3683:
3676:
3673:
3668:
3664:
3660:
3658:0-8186-2450-7
3654:
3650:
3646:
3642:
3635:
3632:
3628:
3622:
3618:
3611:
3608:
3603:
3599:
3595:
3591:
3584:
3581:
3577:
3573:
3570:
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3558:
3555:
3550:
3546:
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3533:
3528:
3524:
3520:
3516:
3510:
3507:
3501:
3497:
3494:
3492:
3489:
3487:
3484:
3481:
3478:
3476:
3473:
3471:
3468:
3465:
3462:
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3457:
3456:
3452:
3450:
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3433:
3430:
3407:
3404:
3398:
3395:
3389:
3386:
3381:
3374:
3371:
3365:
3362:
3356:
3353:
3348:
3341:
3338:
3332:
3329:
3326:
3323:
3320:
3317:
3314:
3311:
3308:
3305:
3302:
3299:
3295:
3286:
3285:
3284:
3258:
3254:
3249:
3245:
3239:
3235:
3221:
3219:
3217:
3201:
3197:
3193:
3170:
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3150:
3142:
3136:
3133:
3128:
3125:
3117:
3111:
3108:
3103:
3100:
3092:
3086:
3083:
3078:
3074:
3065:
3060:
3057:
3054:
3050:
3042:
3041:
3040:
3034:
3032:
3030:
3012:
3009:
3006:
3002:
2998:
2995:
2971:
2968:
2963:
2960:
2955:
2950:
2947:
2942:
2937:
2934:
2929:
2926:
2919:
2918:
2917:
2900:
2897:
2891:
2888:
2882:
2879:
2874:
2867:
2864:
2858:
2855:
2852:
2848:
2839:
2838:
2837:
2822:
2810:
2808:
2800:
2797:
2794:
2791:
2790:
2786:
2783:
2780:
2777:
2776:
2772:
2769:
2766:
2763:
2762:
2758:
2756:
2752:
2750:
2746:
2743:
2742:
2736:
2734:
2733:schedulable.
2732:
2713:
2710:
2707:
2704:
2698:
2695:
2690:
2687:
2679:
2673:
2670:
2665:
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2640:
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2620:
2615:
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2508:
2505:
2500:
2497:
2492:
2487:
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2455:
2454:
2437:
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2300:
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2280:
2279:
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2255:
2252:
2249:
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2241:
2238:
2215:
2212:
2206:
2203:
2197:
2194:
2189:
2182:
2179:
2173:
2170:
2167:
2163:
2154:
2153:
2152:
2137:
2113:
2110:
2105:
2102:
2097:
2092:
2089:
2084:
2079:
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2068:
2061:
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2059:
2053:
2051:
2043:
2040:
2037:
2034:
2033:
2029:
2026:
2023:
2020:
2019:
2015:
2012:
2009:
2006:
2005:
2001:
1999:
1995:
1993:
1989:
1986:
1985:
1979:
1974:
1972:
1968:
1954:
1950:
1945:
1942:
1939:
1934:
1929:
1926:
1923:
1902:
1898:
1893:
1890:
1887:
1882:
1877:
1874:
1871:
1847:
1844:
1841:
1837:
1831:
1824:
1821:
1818:
1814:
1808:
1801:
1798:
1795:
1791:
1766:
1762:
1757:
1751:
1748:
1745:
1741:
1716:
1712:
1687:
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1681:
1677:
1652:
1649:
1646:
1642:
1627:
1625:
1623:
1615:
1613:
1611:
1606:
1597:
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1592:
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1567:
1564:
1562:
1561:
1558:
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1547:
1542:
1538:
1534:
1533:
1529:
1525:
1521:
1518:
1514:
1509:
1505:
1504:
1500:
1491:
1489:
1477:
1476:
1472:
1470:
1468:
1464:
1460:
1456:
1452:
1444:
1442:
1417:
1414:
1408:
1405:
1400:
1396:
1387:
1382:
1379:
1376:
1372:
1364:
1363:
1362:
1356:
1354:
1347:
1345:
1330:
1325:
1320:
1298:
1293:
1288:
1257:
1254:
1249:
1245:
1241:
1236:
1228:
1225:
1218:
1214:
1208:
1204:
1196:
1191:
1188:
1185:
1181:
1177:
1174:
1167:
1166:
1165:
1163:
1151:
1149:
1132:
1129:
1126:
1123:
1120:
1117:
1114:
1108:
1099:
1095:
1090:
1084:
1080:
1075:
1069:
1065:
1060:
1054:
1050:
1037:
1018:
1014:
989:
985:
960:
956:
934:
931:
928:
925:
922:
919:
896:
892:
886:
879:
875:
850:
846:
821:
817:
803:
801:
782:
778:
774:
767:
763:
757:
753:
747:
740:
736:
730:
726:
720:
715:
711:
703:
702:
701:
688:
668:
664:
660:
655:
650:
646:
638:
635:
615:
611:
607:
602:
597:
593:
585:
584:
583:
581:
570:
559:
551:
549:
532:
528:
503:
499:
474:
471:
467:
456:
429:
425:
421:
397:
394:
391:
388:
385:
382:
379:
373:
370:
364:
360:
352:
341:
329:
328:
327:
325:
269:
266:
261:
257:
253:
248:
240:
237:
230:
226:
220:
216:
208:
203:
200:
197:
193:
189:
183:
179:
172:
167:
164:
161:
157:
153:
150:
143:
142:
141:
139:
131:
124:
119:
117:
114:
110:
102:
100:
97:
93:
85:
82:
78:
75:
72:
69:
65:
61:
57:
53:
52:
51:
45:
43:
41:
36:
34:
30:
26:
22:
4238:SCHED NORMAL
4151:
3997:(4): 53–62,
3994:
3990:
3971:
3967:
3962:, Chapter 6.
3957:
3936:
3926:
3906:. Retrieved
3902:the original
3892:
3878:
3869:
3863:
3846:
3842:
3836:
3825:. Retrieved
3815:
3806:
3800:
3765:
3761:
3752:
3744:11382/200358
3726:
3722:
3716:
3681:
3675:
3640:
3634:
3616:
3610:
3593:
3589:
3583:
3563:
3557:
3525:(1): 46–61,
3522:
3518:
3509:
3422:
3225:
3215:
3185:
3038:
3028:
2987:
2915:
2814:
2806:
2754:
2748:
2730:
2728:
2575:
2565:
2524:
2452:
2351:
2343:
2291:
2285:
2230:
2129:
2057:
2049:
1997:
1991:
1969:
1631:
1619:
1607:
1603:
1565:pessimistic
1555:
1549:
1540:
1528:Linux kernel
1512:
1507:
1488:MicroC/OS-II
1450:
1448:
1433:
1360:
1351:
1275:
1161:
1155:
807:
799:
692:
687:service rate
686:
634:arrival rate
633:
580:service time
579:
568:
555:
457:
412:
287:
128:
108:
106:
96:time-sharing
89:
80:
55:
49:
46:Introduction
37:
28:
24:
18:
4157:Round-robin
1568:optimistic
700:, is then:
92:round-robin
4274:Categories
4259:Starvation
4233:SCHED FIFO
4208:Brain Fuck
4187:Windows NT
4102:Fair-share
4080:Algorithms
3908:2008-09-09
3827:2014-03-14
3515:Liu, C. L.
3502:References
1573:immediate
800:as above.
103:Optimality
68:busy-waits
40:preemptive
4182:Two-level
3770:CiteSeerX
3708:206524469
3549:207669821
3527:CiteSeerX
3396:−
3363:−
3143:∗
3118:∗
3051:∏
2889:−
2759:Priority
2737:Example 3
2711:≤
2680:∗
2655:∗
2588:∏
2426:−
2296:Priority
2274:Example 2
2204:−
2002:Priority
1980:Example 1
1415:≤
1373:∏
1255:−
1226:≤
1182:∑
932:−
737:μ
727:λ
712:ρ
647:μ
594:λ
490:process,
426:≥
398:…
392:≈
386:
371:−
348:∞
345:→
267:−
238:≤
194:∑
158:∑
64:semaphore
4038:problem.
4011:12647942
3956:(2000),
3667:31127772
3572:Archived
3453:See also
3226:Because
2744:Process
2281:Process
2231:Because
1987:Process
1975:Examples
1520:Archived
1459:deadlock
395:0.693147
324:infinity
60:hardware
4132:Lottery
3792:1594544
3431:0.81875
2972:0.81875
2901:0.77976
2438:0.77976
2216:0.77976
1546:VxWorks
1526:to the
685:is the
632:is the
109:optimal
4177:Stride
4009:
3943:
3790:
3772:
3706:
3696:
3665:
3655:
3623:
3547:
3529:
3202:2.0475
3186:Since
3171:2.0475
2988:Since
2525:Since
2509:0.7875
1586:splx()
1552:(HLP).
1494:splx()
1434:where
866:where
695:ρ
571:, and
314:, and
288:where
4247:Other
4201:Linux
4007:S2CID
3788:S2CID
3704:S2CID
3663:S2CID
3545:S2CID
3480:RTEMS
3437:0.828
3408:0.828
3279:, is
2708:1.995
2114:0.725
1903:0.125
1593:lazy
636:, and
4223:O(n)
4218:O(1)
4117:Gang
3941:ISBN
3694:ISBN
3653:ISBN
3621:ISBN
3464:Deos
3434:<
3198:<
2999:>
2536:>
2242:<
1620:All
1535:The
1506:The
1492:The
1482:and
1478:The
1457:and
926:1...
912:and
887:>
94:and
56:e.g.
3999:doi
3976:doi
3851:doi
3780:doi
3739:hdl
3731:doi
3686:doi
3645:doi
3598:doi
3537:doi
3216:not
3194:2.0
3029:not
2798:10
2792:P3
2778:P2
2770:32
2764:P1
2566:not
2335:10
2329:P3
2315:P2
2307:16
2301:P1
2041:10
2035:P3
2021:P2
2007:P1
1955:0.5
1924:0.5
1915:to
1872:0.5
1451:RMS
556:In
338:lim
138:CPU
29:RMS
19:In
4276::
4005:,
3995:23
3993:,
3972:29
3970:,
3847:39
3845:,
3786:,
3778:,
3766:23
3764:,
3737:,
3727:52
3725:,
3702:,
3692:,
3661:.
3651:.
3592:,
3567:,
3543:,
3535:,
3523:20
3521:,
3283:.
3154:10
3104:32
2964:10
2938:32
2801:2
2795:2
2787:1
2784:5
2781:2
2773:3
2767:7
2731:is
2691:10
2641:16
2501:10
2475:16
2338:2
2332:2
2324:1
2321:5
2318:2
2310:3
2304:3
2106:10
2044:3
2038:2
2030:1
2027:5
2024:2
2016:2
2013:8
2010:1
1579:/
1133:12
947:,
837:,
560:,
430:10
383:ln
303:,
70:))
58:a
23:,
4065:e
4058:t
4051:v
4001::
3985:.
3978::
3931:.
3911:.
3886:.
3858:.
3853::
3830:.
3795:.
3782::
3741::
3733::
3711:.
3688::
3669:.
3647::
3605:.
3600::
3594:2
3578:.
3552:.
3539::
3405:=
3402:)
3399:1
3390:2
3387:1
3382:2
3378:(
3375:2
3372:=
3369:)
3366:1
3357:K
3354:1
3349:2
3345:(
3342:K
3339:=
3333:c
3330:i
3327:n
3324:o
3321:m
3318:r
3315:a
3312:h
3309:,
3306:b
3303:u
3300:l
3296:U
3281:2
3277:K
3259:2
3255:T
3250:2
3246:=
3240:3
3236:T
3168:=
3165:)
3162:1
3159:+
3151:2
3146:(
3140:)
3137:1
3134:+
3129:5
3126:2
3121:(
3115:)
3112:1
3109:+
3101:7
3096:(
3093:=
3090:)
3087:1
3084:+
3079:i
3075:U
3071:(
3066:n
3061:1
3058:=
3055:i
3013:b
3010:u
3007:l
3003:U
2996:U
2984:.
2969:=
2961:2
2956:+
2951:5
2948:2
2943:+
2935:7
2930:=
2927:U
2898:=
2895:)
2892:1
2883:3
2880:1
2875:2
2871:(
2868:3
2865:=
2859:b
2856:u
2853:l
2849:U
2823:3
2755:T
2749:C
2714:2
2705:=
2702:)
2699:1
2696:+
2688:2
2683:(
2677:)
2674:1
2671:+
2666:5
2663:2
2658:(
2652:)
2649:1
2646:+
2638:3
2633:(
2630:=
2627:)
2624:1
2621:+
2616:i
2612:U
2608:(
2603:n
2598:1
2595:=
2592:i
2550:b
2547:u
2544:l
2540:U
2533:U
2521:.
2506:=
2498:2
2493:+
2488:5
2485:2
2480:+
2472:3
2467:=
2464:U
2435:=
2432:)
2429:1
2420:3
2417:1
2412:2
2408:(
2405:3
2402:=
2396:b
2393:u
2390:l
2386:U
2360:3
2292:T
2286:C
2256:b
2253:u
2250:l
2246:U
2239:U
2213:=
2210:)
2207:1
2198:3
2195:1
2190:2
2186:(
2183:3
2180:=
2174:b
2171:u
2168:l
2164:U
2138:3
2126:.
2111:=
2103:2
2098:+
2093:5
2090:2
2085:+
2080:8
2077:1
2072:=
2069:U
1998:T
1992:C
1951:=
1946:s
1943:m
1940:1
1935:/
1930:s
1927:m
1899:=
1894:s
1891:m
1888:4
1883:/
1878:s
1875:m
1848:r
1845:s
1842:i
1838:T
1832:/
1825:r
1822:s
1819:i
1815:C
1809:=
1802:r
1799:s
1796:i
1792:U
1767:1
1763:T
1758:=
1752:r
1749:s
1746:i
1742:T
1717:1
1713:T
1688:r
1685:s
1682:i
1678:T
1653:r
1650:s
1647:i
1643:C
1438:i
1436:U
1430:,
1418:2
1412:)
1409:1
1406:+
1401:i
1397:U
1393:(
1388:n
1383:1
1380:=
1377:i
1331:1
1326:=
1321:K
1299:n
1294:=
1289:K
1278:n
1261:)
1258:1
1250:K
1246:/
1242:1
1237:2
1232:(
1229:K
1219:i
1215:T
1209:i
1205:C
1197:n
1192:1
1189:=
1186:i
1178:=
1175:U
1158:K
1136:]
1130:,
1127:6
1124:,
1121:3
1118:,
1115:1
1112:[
1109:=
1106:]
1100:4
1096:T
1091:,
1085:3
1081:T
1076:,
1070:2
1066:T
1061:,
1055:1
1051:T
1046:[
1019:1
1015:T
990:i
986:T
961:m
957:T
935:1
929:m
923:=
920:i
897:i
893:T
880:m
876:T
851:i
847:T
822:m
818:T
783:i
779:U
775:=
768:i
764:T
758:i
754:C
748:=
741:i
731:i
721:=
716:i
697:i
689:.
669:i
665:C
661:1
656:=
651:i
616:i
612:T
608:1
603:=
598:i
575:i
573:C
564:i
562:T
533:i
529:T
504:i
500:C
475:h
472:t
468:i
453:U
449:n
445:U
422:n
389:2
380:=
377:)
374:1
365:n
361:2
356:(
353:n
342:n
316:n
312:i
307:i
305:T
301:i
296:i
294:C
290:U
273:)
270:1
262:n
258:/
254:1
249:2
244:(
241:n
231:i
227:T
221:i
217:C
209:n
204:1
201:=
198:i
190:=
184:i
180:U
173:n
168:1
165:=
162:i
154:=
151:U
134:n
27:(
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