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Scheduling Algorithms for Real-Time Multiprocessor Systems

A real-time system is typically composed of several tasks with timing constraints. This timing

constraint of an operation is usually specified using a deadline, which corresponds to the time

by which that operation must complete. Thus a proper method is essential to ensure that all

activities are able to meet their timing constraints. Selecting appropriate methods for

scheduling activities is one of the important considerations in the design of a real-time system.

Scheduling of real-time systems has always assumed that the underlying hardware is a single

processor system. But current trends indicate that sophisticated real-time applications with

high computational demands are emerging. Examples of such systems include automatic

tracking systems and telepresence systems. These applications have timing constraints that are

used to ensure high system fidelity and responsiveness, and may also be crucial for correctness

in certain applications such as telesurgery. Also, the processing requirements of these systems

exceed the capacity of a single processor, and a multiprocessor may be necessary to achieve an

effective implementation. These observations underscore the growing importance of

multiprocessors in real-time systems.

The priority of the task to be scheduled may be fixed or dynamic. The rate-monotonic

scheduling (RMS) algorithm is an optimal fixed-priority scheduling algorithm. An optimal

dynamic-priority algorithm is the earliest-deadline first (EDF) algorithm. These scheduling

algorithms which are optimal in single processor systems will result in arbitrarily low processor

utilization in multiprocessor systems.

There are two approaches for scheduling on multiprocessors: partitioning and global

scheduling.

In partitioning, each task is assigned to a single processor. Each of these processors will execute

the jobs assigned to it. These processors are then scheduled independently. This reduces the

multiprocessor scheduling problem to a set of uniprocessor ones. We can then implement an

algorithm like the EDF or the RMS on the tasks. Unfortunately, finding an optimal assignment of

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tasks to processors is an NP-hard problem. Thus, tasks are usually partitioned using non-optimal

methods. Moreover, there exist task systems that are schedulable if and only if tasks are not

partitioned.

In global scheduling, all eligible tasks are stored in a single priority-ordered queue. The

scheduler selects the highest-priority tasks from this queue for execution. Thus a task is not

fixed to a processor and is allowed to migrate between processors. The issue with global

scheduling is that it can result in low processor utilization if used with the EDF or RMS

algorithms.

The algorithm that I discuss is called proportionate fair (Pfair) scheduling. The work of Baruah et

al. proved that periodic task systems could be optimally scheduled using global scheduling

algorithms based on Pfairness. Under Pfair scheduling, each task is required to execute at a

uniform rate by breaking it into a series of subtasks. Each task with weight w would receive w.L

units of processor time over interval L.

𝒘𝒊 =𝒆𝒊𝒑𝒊

Each task allocated resource for x.e time units in each interval. By breaking tasks into uniform-

sized subtasks, Pfair scheduling avoids the bin-packing issues of multiprocessor scheduling.

Indeed, Pfair scheduling is presently the only known approach for optimally scheduling periodic

tasks on multiprocessors.

The advantages of Pfair scheduling are that it is able to schedule periodic, sporadic or rate-

based task systems. Also it can handle dynamic events, such as tasks leaving and joining a

system.

However, the use of such a global scheduling algorithm results in degraded processor affinity.

Pfair scheduling algorithms can result in frequent preemptions and migrations resulting in

excessive overhead.

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In spite of these disadvantages, the Pfair scheduling is presently the only known approach for

optimally scheduling periodic tasks on multiprocessors.

References:

[1] K. Ramamritham, J.A. Stankovic, and P.F. Shiah, "Efficient Scheduling Algorithms for

Real-Time Multiprocessor Systems," IEEE Trans. Parallel and Distributed Systems, vol. 1,

no. 2, pp. 184- 194, Apr. 1990.

[2] J. Carpenter, S. Funk, et al. “A categorization of real-time multiprocessor scheduling

problems and algorithms," In J. Y. Leung, editor, Handbook on Scheduling Algorithms,

Methods, and Models, pp 30.130.19. Chapman Hall/CRC, Boca Raton, Florida, 2004.

[3] S. Baruah, N. Cohen, C. Plaxton and D. Varvel, "Proportionate Progress: A Notion of

Fairness in Resource Allocation", Algorithmica 15(6), pp. 600-625, 1996.

[4] M. Adler, P. Berenbrink, T. Friedetzy, L.A. Goldberg, P. Goldberg and M. Paterson, “A

proportionate fair scheduling rule with good worst-case performance,” Proceedings of

the fifteenth annual ACM symposium on Parallel algorithms and architectures, pp 101-

104, June 2003.

[5] O.U.P. Zapata and P. Meija-Alvarez, "Analysis of Real-Time Multiprocessors Scheduling

Algorithms, " Proceedings of the Real-Time Systems Symposium, Dec. 2003