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Heavy Traffic Limit Theorems for Real-Time Computer Systems

Heavy Traffic Limit Theorems for Real-Time Computer Systems. Presented by: John Lehoczky Carnegie Mellon Co-authors: B.Doytchinov, J.Hansen, L.Kruk, R. Rajkumar, C.Yeung, and H.Zhu Presented at WORMS04 April 19, 2004. Background: 1.

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Heavy Traffic Limit Theorems for Real-Time Computer Systems

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  1. Heavy Traffic Limit Theorems for Real-Time Computer Systems Presented by: John Lehoczky Carnegie Mellon Co-authors: B.Doytchinov, J.Hansen, L.Kruk, R. Rajkumar, C.Yeung, and H.Zhu Presented at WORMS04 April 19, 2004

  2. Background: 1 • Real-time systems refer to computer and communication systems in which the applications/tasks/jobs/packets have explicit timing requirements (deadlines). • These arise in (e.g.): • voice and video transmission (e.g. video-conferencing) • control systems (e.g. automotive) • avionics systems

  3. Background: 2 • We often distinguish different types of real-time systems or tasks: • Hard real-time: any failure to meet a deadline is regarded as a system failure. (e.g. avionics or control systems) • Soft real-time: deadline misses or packet loss is acceptable as long as it doesn’t reduce the QoS below requirements (e.g. multi-media applications).

  4. For a given workload model we want: to predict the fraction of the workload that will miss its deadlines (end-to-end deadlines in the network case), to design workload scheduling and control policies that will ensure QoS guarantees (e.g. a suitably small fraction miss their deadlines), to investigate network design issues, e.g.: Number of priority bits needed Cost/benefit from flow tables Cost/benefit from keeping lead-time information Goals

  5. Formulation • In the hard real-time formulation where no deadlines misses are permitted, one must adopt a worst case formulation: • task arrivals occur as soon as possible, • task services take on their maximum values, • task deadlines are as short as possible. • One must bound the worst case utilization. • But it average case utilization is substantially less than worst case utilization, the system will, on average, be highly underutilized.

  6. Model • Multiple streams in a multi-node acyclic network. • Independent streams of jobs. • Jobs in a stream form a renewal process and have independent computational requirements at each node • For a given stream, each job has an i.i.d. deadline (different for different streams) • Node processing is EDF (Q-EDF), FIFO, PS, Fixed Priority.

  7. Processor Sharing – Exp. Deadlines

  8. Processor Sharing – Exp. Deadlines

  9. EDF Miss Rate Prediction EDF Deadline Miss Rate: =0.95 EDF scheduling Uniform(10,x) deadlines Internet Exponential : computed from the first two moments of task inter-arrival times and service times. : Mean Deadline Uniform

  10. Motivation/Payoff CPU 1 CPU 2 Server 1 Server 1.1 Server 4 Stream 1 FIFO FIFO FIFO Server 2 Server 5 Stream 2 FIFO FIFO Server 3 Server 6 Stream 3 Stream 4 FIFO FIFO

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