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Scheduling Processes with Release Times, Deadlines, Precedence and Exclusion Relations

Scheduling Processes with Release Times, Deadlines, Precedence and Exclusion Relations. J. Xu and D. L. Parnas IEEE Transactions on Software Engineering, March 1990 Presented by: Umamaheswaran Arumugam Amit Sahoo. Original paper. Periodic processes in real-time systems

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Scheduling Processes with Release Times, Deadlines, Precedence and Exclusion Relations

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  1. Scheduling Processes with Release Times, Deadlines, Precedence and Exclusion Relations J. Xu and D. L. Parnas IEEE Transactions on Software Engineering, March 1990 Presented by: Umamaheswaran Arumugam Amit Sahoo

  2. Original paper • Periodic processes in real-time systems • Pre-run time scheduling • Arbitrary release times, deadlines, precedence and exclusion relations • NP-Hard problem • Branch & bound approach used [Xu and Parnas, TSE 1990]

  3. Original paper contd. • Terms: • Segments • Lateness • Feasibility and Optimality • Adjusted release time • Eligibility [Xu and Parnas, TSE 1990]

  4. Algorithm • Initial solution using earliest-deadline first • Root of the search tree • Identify segment with maximum lateness • Z[j]: Set of segments that affect the lateness of the latest segment j • Calculate lowerbound at the root • Select a segment from Z[j] which when moved to the end will minimize the lateness [Xu and Parnas, TSE 1990]

  5. Algorithm (contd.) • G1: segments which can be preceded by j • G2: segments which can be preempted by j • Successor nodes created for all nodes in G1 and G2 • Appropriate relations are added to the schedule • Initial solution, lowerbound and lateness calculated at each child node • Branch and Bound until solution found [Xu and Parnas, TSE 1990]

  6. Impact • First paper to consider the most general case of precedence and exclusion relations • Acceptable performance for reasonably large problem sets • Used in Air Information Management System for Boeing 777 [Xu and Parnas, TSE 1990]

  7. Related paper 1Optimal Combined Task and Message Scheduling in Distributed Real-Time Systems • Pre-run time scheduling algorithm for distributed systems • Integrated strategy for scheduling both tasks and messages in distributed real-time systems • Algorithm: At the root • Initial schedule using EDF • Message are prioritized according to the sum of the laxity of the receiving processand the difference between the send and receive times [Abdelzaher and Shin, RTSS 1995]

  8. Related Paper 1 (contd.) • Task graph created at root node to calculate adjusted release times and deadlines • EDF scheduling done again to get complete schedule • Mi: latest module, Bi: Busy period before Mi (same as Z[j] in original paper) • Branching Functions • Set L: Exclusion relations between two modules in Bi replaced by precedence relations • Set M: Increment the priority of a message received by a module in Bi [Abdelzaher and Shin, RTSS 1995]

  9. Related Paper 1 (contd.) • Set N: Deadline of a remote predecessor of a module in Bi is reduced so that it has the same lateness as Mi • Lower bound on lateness is used to bound the search tree • Search ends when only one node, with a computed schedule, is left in the set of active vertices [Abdelzaher and Shin, RTSS 1995]

  10. Related Paper 2Scheduling Fault-Tolerant Distributed Real-Time Tasks Independently of Replication Strategies • Objective • Scheduling real-time tasks independently of replication strategies (active or passive replication). • Requirements 1. Tasks – synchronized using precedence relations. 2. Determinism – enforced using ordering constraints. • 1 and 2 should be satisfied for a scheduling algorithm to be independent of replication. [Chevochot and Puaut, RTCSA 1999]

  11. Related Paper 2 (contd.) • Ordering Constraints • Identical order (IO) relation between two couples of elementary units (segments) that execute in the same site. • Identical Order (eui, euj) IO (euk, eul) • E(REP, gr) • gr – granularity at which fault-tolerance is applied. • Represent the set of all groups of segments that leads to non-deterministic execution. [Chevochot and Puaut, RTCSA 1999]

  12. Related Paper 2 (contd.) • E/(si, sj, R); E - Union of E(REP, gr) • Set of all segments that use the replica R and are in site si and sj. • ((eui, euj), (euk, eul)) belongs to E/(si, sj, R) and exclusive request, then (eui, euj) IO (euk, eul) is added. • Extension to Xu and Parnas’ algorithm • Exclusion relation - segments in different sites. • Precedence relation - segments in different sites. • Ordering constraints. [Chevochot and Puaut, RTCSA 1999]

  13. Related Paper 3Hybrid Online/Offline Scheduling for Hard Real-Time Systems • Objective • To improve the utilization of the systems that require schedulability guarantees. • Offline Scheduling • Periodic tasks using a modified version of Xu and Parnas’ algorithm. • Online Scheduling • Priority based scheduling technique for sporadic tasks. [Young and Shu, RTMS 1996]

  14. Related Paper 3 (contd.) • Technical Overview • Rate monotonic task assignment – A periodic task should finish executing before its period. • Optimal allocation of idle times across different periodic tasks – using binary search algorithm • Algorithm • Find a schedule using Xu and Parnas’ algorithm. • If lateness > 0, no valid schedule. • Else distribute the idle time across task boundaries using binary search method. [Young and Shu, RTMS 1996]

  15. Related Paper 3 (contd.) • Advantages of this approach • Not all tasks are scheduled offline (compared to pure offline scheduling). • Reduces semaphores and context-switch overhead (compared to pure online scheduling). • Suggested improvements to Xu and Parnas’ algorithm • Observation – Partial initial schedule Vs Complete initial schedule. [Young and Shu, RTMS 1996]

  16. Uncited paperOptimal scheduling of cooperative tasks in a distributed system using an enumerative method • To minimize the system hazard (maximum normalized task response time) • Task graphs are used to describe precedence relations and message passing between modules • Sets of preceded/dependent modules: 0, 1 • Dominance properties (DPs) • Z • sp, , S • Used to generate immaterial sets (IM) of modules [Peng and Shin, TSE 1993]

  17. Uncited Paper (contd.) • Branch and bound approach used to schedule the dominant IM at all times • Search continues until a complete schedule is determined • Similarities/Extensions to original paper • Set of schedules generated at each node • Algorithm to compute lower bound similar to the one in the original paper • DPs take into account the aftereffects of scheduling a module, not just its deadline/response time [Peng and Shin, TSE 1993]

  18. References • T. F. Abdelzaher and K. G. Shin, "Optimal Combined Task and Message Scheduling in Distributed Real-Time Systems", in Proceedings. of the IEEE Real-Time Systems Symposium, Dec. 5-7, 1995, pp. 162-171 • P. Chevochot and I. Puaut, "Scheduling fault-tolerant distributed hard real-time tasks independently of the replication strategies", in Proceedings of the 6th International Conference on Real-Time Computing Systems and Applications , December 1999, pp. 356-363 • D. Peng and K. G. Shin, "Optimal scheduling of cooperative tasks in a distributed system using an enumerative method", IEEE Transactions on Software Engineering, vol. 19, no. 3, March 1993, pp. 253-267 • J. Xu and D. L. Parnas, "Scheduling Processes with Release Times, Deadlines, Precedence, and Exclusion Relations", IEEE Transactions on Software Engineering, vol. 16, March 1990, pp. 360-369 • Michal Young and Lih-Chyun Shu, "Hybrid Online/Offline Scheduling for Hard Real-Time Systems", in Proceedings of 2nd International Symposium on Real-Time and Media Systems, July 1996, pp. 231-240

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