A Framework for Probabilistic Analysis of Multiprocessor Scheduling Environments

This paper presents a novel probabilistic approach for the analysis of global performance issues of multiprocessor scheduling environments. It consists of an analytical framework to model scheduling situations where it is impossible, or inappropriate, to define task characteristics precisely. Central to the approach is the formation of a probabilistic picture of the tasks currently under execution on the basis of a probabilistic description of newly arriving tasks and assignment of processors for executing tasks. This enables the determination of performance measures such as successful completion rates of tasks, probability of successful execution of a given task and the number of processors required to guarantee a specified probability of success. These measures can be utilised for obtaining optimal schedules and in guiding run–time scheduling decisions of a scheduler. When dealing with individual tasks, the approach takes into account issues such as the combinatorial possibilities of different patterns of task execution and the effect of competition among tasks for a finite number of available processors.

[1]  P. Nash,et al.  Dominant Strategies in Stochastic Allocation and Scheduling Problems , 1982 .

[2]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.

[3]  Azer Bestavros,et al.  Statistical rate monotonic scheduling , 1998, Proceedings 19th IEEE Real-Time Systems Symposium (Cat. No.98CB36279).

[4]  Nimal Nissanke.  Realtime systems , 1997, Prentice Hall series in computer science.

[5]  Azer Bestavros,et al.  Probabilistic job scheduling for distributed real-time applications , 1993, [1993] Proceedings of the IEEE Workshop on Real-Time Applications.

[6]  David Wright,et al.  Probabilistic scheduling guarantees for fault-tolerant real-time systems , 1999, Dependable Computing for Critical Applications 7.

[7]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[8]  Jun Sun,et al.  Probabilistic performance guarantee for real-time tasks with varying computation times , 1995, Proceedings Real-Time Technology and Applications Symposium.

[9]  Azer Bestavros,et al.  Design and implementation of statistical rate monotonic scheduling in KURT Linux , 1999, Proceedings 20th IEEE Real-Time Systems Symposium (Cat. No.99CB37054).

[10]  Carey Williamson,et al.  Current techniques for measuring and modeling ATM traffic , 1996 .

[11]  John P. Lehoczky.  Scheduling communication networks carrying real-time traffic , 1998, Proceedings 19th IEEE Real-Time Systems Symposium (Cat. No.98CB36279).

[12]  Aloysius K. Mok,et al.  Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks , 1989, IEEE Trans. Software Eng..