Combinatorial Optimization in Real-Time Scheduling: Theory and Algorithms

Real-time computer systems are essential for many applications, such as robot control, avionics, medical instrumentation, manufacturing, etc. The correctness of the system depends on the temporal correctness as well as the functional correctness of the task executions. In order to assure temporal correctness it is necessary that the resources be scheduled to meet the temporal requirements of applications. When we consider the problem of nonpreemptive scheduling of a set of tasks in a processor for which no feasible solution exists, some tasks may have to be rejected so that a schedule can be generated for the rest. In this paper, we consider the problem of generating an optimal schedule such that the number of rejected tasks is minimized, and then the finish time is minimized for the accepted tasks. We propose to use an analytic approach to solve this problem. We first discuss the super sequence based technique which was originally proposed for reducing the search space in testing the feasibility of a task set. Then we show by the Conformation theorem that the super sequence constructed from the task set also provides a valid and reduced search space for the optimization problem. While the complexity of our scheduling algorithm in the worst case remains exponential, our simulation results show that the cost is reasonable for the average case.

[1]  Aloysius Ka-Lau Mok,et al.  Fundamental design problems of distributed systems for the hard-real-time environment , 1983 .

[2]  Lui Sha,et al.  Priority Inheritance Protocols: An Approach to Real-Time Synchronization , 1990, IEEE Trans. Computers.

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

[4]  John P. Lehoczky,et al.  Fixed priority scheduling of periodic task sets with arbitrary deadlines , 1990, [1990] Proceedings 11th Real-Time Systems Symposium.

[5]  Satish K. Tripathi,et al.  The MARUTI hard real-time operating system , 1989, [1989] Proceedings. The Fourth Israel Conference on Computer Systems and Software Engineering.

[6]  Shyh-In Hwang,et al.  Mission-oriented replication of periodic tasks in real-time distributed systems , 1994 .

[7]  Shyh-In Hwang,et al.  Optimization in non-preemptive scheduling for aperiodic tasks , 1994 .

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  Joseph Y.-T. Leung,et al.  On the complexity of fixed-priority scheduling of periodic, real-time tasks , 1982, Perform. Evaluation.

[10]  Kishor S. Trivedi,et al.  Transient overloads in fault-tolerant real-time systems , 1989, [1989] Proceedings. Real-Time Systems Symposium.

[11]  J. Erschler,et al.  A New Dominance Concept in Scheduling n Jobs on a Single Machine with Ready Times and Due Dates , 1983, Oper. Res..

[12]  M. Saksena,et al.  Temporal analysis for hard real-time scheduling , 1993, Proceedings of Phoenix Conference on Computers and Communications.

[13]  Hermann Kopetz,et al.  Distributed fault-tolerant real-time systems: the Mars approach , 1989, IEEE Micro.

[14]  Michael L. Dertouzos,et al.  Control Robotics: The Procedural Control of Physical Processes , 1974, IFIP Congress.

[15]  Shyh-In Hwang,et al.  Scheduling an overloaded real-time system , 1996, Conference Proceedings of the 1996 IEEE Fifteenth Annual International Phoenix Conference on Computers and Communications.