Stability of adaptive feedback-based resource managers for systems with execution time variations

Today’s embedded systems are exposed to variations in load demand due to complex software applications, dynamic hardware platforms, and the impact of the run-time environment. When these variations are large, and efficiency is required, adaptive on-line resource managers may be deployed on the system to control its resource usage. An often neglected problem is whether these resource managers are stable, meaning that the resource usage is controlled under all possible scenarios. In this paper we develop mathematical models for real-time embedded systems and we derive conditions which, if satisfied, lead to stable systems. For the developed system models, we also determine bounds on the worst case response times of tasks. We also give an intuition of what stability means in a real-time context and we show how it can be applied for several resource managers. We also discuss how our results can be extended in various ways.

[1]  Xue Liu,et al.  Optimal multivariate control for differentiated services on a shared hosting platform , 2007, 2007 46th IEEE Conference on Decision and Control.

[2]  Petru Eles,et al.  Low Overhead Dynamic QoS Optimization under Variable Task Execution Times , 2010, 2010 IEEE 16th International Conference on Embedded and Real-Time Computing Systems and Applications.

[3]  Tommaso Cucinotta,et al.  QoS Control for Pipelines of Tasks Using Multiple Resources , 2010, IEEE Transactions on Computers.

[4]  Chung Laung Liu,et al.  Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment , 1989, JACM.

[5]  Daniel P. Siewiorek,et al.  On quality of service optimization with discrete QoS options , 1999, Proceedings of the Fifth IEEE Real-Time Technology and Applications Symposium.

[6]  Anton Cervin,et al.  The control server: a computational model for real-time control tasks , 2003, 15th Euromicro Conference on Real-Time Systems, 2003. Proceedings..

[7]  Xue Liu,et al.  Online adaptive utilization control for real-time embedded multiprocessor systems , 2010, J. Syst. Archit..

[8]  Joseph Sifakis,et al.  Symbolic quality control for multimedia applications , 2008, Real-Time Systems.

[9]  James W. Layland,et al.  Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment , 1989, JACM.

[10]  Giorgio C. Buttazzo,et al.  Elastic DVS Management in Processors With Discrete Voltage/Frequency Modes , 2007, IEEE Transactions on Industrial Informatics.

[11]  Giorgio C. Buttazzo,et al.  Managing quality-of-control performance under overload conditions , 2004, Proceedings. 16th Euromicro Conference on Real-Time Systems, 2004. ECRTS 2004..

[12]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[13]  Giorgio C. Buttazzo,et al.  Adaptive Workload Management through Elastic Scheduling , 2002, Real-Time Systems.

[14]  Tommaso Cucinotta,et al.  AQuoSA—adaptive quality of service architecture , 2009 .

[15]  Sang Hyuk Son,et al.  Feedback Control Real-Time Scheduling: Framework, Modeling, and Algorithms* , 2001, Real-Time Systems.

[16]  Alessandro Astolfi,et al.  Stability of Dynamical Systems - Continuous, Discontinuous, and Discrete Systems (by Michel, A.N. et al.; 2008) [Bookshelf] , 2007, IEEE Control Systems.

[17]  Sean P. Meyn,et al.  Stability of queueing networks and scheduling policies , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[18]  A. H. Siddiqi,et al.  Introduction to functional analysis with applications , 2006 .

[19]  Rafael Castro-Linares,et al.  Trajectory tracking for non-holonomic cars: A linear approach to controlled leader-follower formation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[20]  Chenyang Lu,et al.  Feedback performance control in software services , 2003 .

[21]  Giuseppe Lipari,et al.  Elastic task model for adaptive rate control , 1998, Proceedings 19th IEEE Real-Time Systems Symposium (Cat. No.98CB36279).

[22]  D. Down,et al.  Stability of Queueing Networks , 1994 .

[23]  Petru Eles,et al.  Stability Conditions of On-line Resource Managers for Systems with Execution Time Variations , 2011, 2011 23rd Euromicro Conference on Real-Time Systems.

[24]  Karl-Erik Årzén,et al.  Feedback–Feedforward Scheduling of Control Tasks , 2002, Real-Time Systems.

[25]  A. Michel,et al.  Stability of Dynamical Systems — Continuous , Discontinuous , and Discrete Systems , 2008 .