A Neurodynamic Approach for Real-Time Scheduling via Maximizing Piecewise Linear Utility

In this paper, we study a set of real-time scheduling problems whose objectives can be expressed as piecewise linear utility functions. This model has very wide applications in scheduling-related problems, such as mixed criticality, response time minimization, and tardiness analysis. Approximation schemes and matrix vectorization techniques are applied to transform scheduling problems into linear constraint optimization with a piecewise linear and concave objective; thus, a neural network-based optimization method can be adopted to solve such scheduling problems efficiently. This neural network model has a parallel structure, and can also be implemented on circuits, on which the converging time can be significantly limited to meet real-time requirements. Examples are provided to illustrate how to solve the optimization problem and to form a schedule. An approximation ratio bound of 0.5 is further provided. Experimental studies on a large number of randomly generated sets suggest that our algorithm is optimal when the set is nonoverloaded, and outperforms existing typical scheduling strategies when there is overload. Moreover, the number of steps for finding an approximate solution remains at the same level when the size of the problem (number of jobs within a set) increases.

[1]  Carlos Cardeira,et al.  Neural network versus max-flow algorithms for multiprocessor real-time scheduling , 1996, Proceedings of the Eighth Euromicro Workshop on Real-Time Systems.

[2]  Binoy Ravindran,et al.  Energy-efficient, utility accrual scheduling under resource constraints for mobile embedded systems , 2004, EMSOFT '04.

[3]  Qingshan Liu,et al.  Finite-Time Convergent Recurrent Neural Network With a Hard-Limiting Activation Function for Constrained Optimization With Piecewise-Linear Objective Functions , 2011, IEEE Transactions on Neural Networks.

[4]  Long Cheng,et al.  Recurrent Neural Network for Non-Smooth Convex Optimization Problems With Application to the Identification of Genetic Regulatory Networks , 2011, IEEE Transactions on Neural Networks.

[5]  Jacques Carlier,et al.  Handbook of Scheduling - Algorithms, Models, and Performance Analysis , 2004 .

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

[7]  Shengwei Zhang,et al.  Lagrange programming neural networks , 1992 .

[8]  Wei Bian,et al.  Subgradient-Based Neural Networks for Nonsmooth Nonconvex Optimization Problems , 2009, IEEE Transactions on Neural Networks.

[9]  Sanjoy K. Baruah,et al.  Mixed-Criticality Scheduling upon Varying-Speed Multiprocessors , 2014, 2014 IEEE 12th International Conference on Dependable, Autonomic and Secure Computing.

[10]  Zoubir Mammeri,et al.  Neural networks for multiprocessor real-time scheduling , 1994, Proceedings Sixth Euromicro Workshop on Real-Time Systems.

[11]  Qingshan Yang,et al.  A Neurodynamic Optimization Method for Recovery of Compressive Sensed Signals With Globally Converged Solution Approximating to $l_{0}$ Minimization , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Sanjoy K. Baruah,et al.  Implementing Mixed-criticality Systems Upon a Preemptive Varying-speed Processor , 2014, Leibniz Trans. Embed. Syst..

[13]  Jun Wang,et al.  A deterministic annealing neural network for convex programming , 1994, Neural Networks.

[14]  Yueh-Min Huang,et al.  Competitive neural network to solve scheduling problems , 2001, Neurocomputing.

[15]  Qingshan Liu,et al.  A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization , 2012, Neural Networks.

[16]  Sanjoy K. Baruah,et al.  Proportionate progress: a notion of fairness in resource allocation , 1993, STOC '93.

[17]  Z. Zeng,et al.  NEW PASSIVITY ANALYSIS OF CONTINUOUS-TIME RECURRENT NEURAL NETWORKS WITH MULTIPLE DISCRETE DELAYS , 2011 .

[18]  Zoubir Mammeri,et al.  Solving real-time scheduling problems with Hopfield-type neural networks , 1997, EUROMICRO 97. Proceedings of the 23rd EUROMICRO Conference: New Frontiers of Information Technology (Cat. No.97TB100167).

[19]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[20]  Sanjoy K. Baruah,et al.  On the competitiveness of on-line real-time task scheduling , 2004, Real-Time Systems.

[21]  Giorgio C. Buttazzo,et al.  HARD REAL-TIME COMPUTING SYSTEMS Predictable Scheduling Algorithms and Applications , 2007 .

[22]  Vincent W. S. Wong,et al.  Autonomous Demand-Side Management Based on Game-Theoretic Energy Consumption Scheduling for the Future Smart Grid , 2010, IEEE Transactions on Smart Grid.

[23]  Youshen Xia,et al.  A new neural network for solving linear and quadratic programming problems , 1996, IEEE Trans. Neural Networks.

[24]  G. C. Buttazzo,et al.  RE: Robust Earliest Deadline Scheduling , 1993 .

[25]  Hennadiy Leontyev,et al.  Compositional Analysis Techniques For Multiprocessor Soft Real-Time Scheduling , 2010 .

[26]  Robert I. Davis,et al.  Mixed Criticality Systems - A Review , 2015 .

[27]  Giorgio Buttazzo,et al.  Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications , 1997 .

[28]  Mauro Forti,et al.  Generalized neural network for nonsmooth nonlinear programming problems , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Qingshan Liu,et al.  A One-Layer Recurrent Neural Network for Pseudoconvex Optimization Subject to Linear Equality Constraints , 2011, IEEE Transactions on Neural Networks.

[30]  Xiaolin Hu,et al.  Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network , 2006, IEEE Transactions on Neural Networks.

[31]  Yueh-Min Huang,et al.  Scheduling multiprocessor job with resource and timing constraints using neural networks , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[32]  Jeremy P. Erickson.  Managing tardiness bounds and overload in soft real-time systems , 2014 .

[33]  Steve Vestal,et al.  Preemptive Scheduling of Multi-criticality Systems with Varying Degrees of Execution Time Assurance , 2007, 28th IEEE International Real-Time Systems Symposium (RTSS 2007).

[34]  Nuno Pereira,et al.  Static-Priority Scheduling over Wireless Networks with Multiple Broadcast Domains , 2007, RTSS 2007.

[35]  James H. Anderson,et al.  Soft real-time scheduling on multiprocessors , 2006 .

[36]  Dennis Shasha,et al.  D^over: An Optimal On-Line Scheduling Algorithm for Overloaded Uniprocessor Real-Time Systems , 1995, SIAM J. Comput..

[37]  Binoy Ravindran,et al.  On recent advances in time/utility function real-time scheduling and resource management , 2005, Eighth IEEE International Symposium on Object-Oriented Real-Time Distributed Computing (ISORC'05).

[38]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[39]  Sanjoy K. Baruah,et al.  Mixed-Criticality Scheduling upon Varying-Speed Processors , 2013, 2013 IEEE 34th Real-Time Systems Symposium.

[40]  Zhishan Guo,et al.  EDF Schedulability Analysis on Mixed-Criticality Systems with Permitted Failure Probability , 2015, 2015 IEEE 21st International Conference on Embedded and Real-Time Computing Systems and Applications.