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Real-Time Queueing Theory. Presented by: John Lehoczky Carnegie Mellon SAMSI Workshop Congestion Control and Heavy Traffic. Background. Real-time systems refer to computer and communication systems in which the applications/tasks/jobs/packets have explicit timing requirements (deadlines). - PowerPoint PPT Presentation
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Real-Time Queueing TheoryReal-Time Queueing Theory
Presented by:
John Lehoczky
Carnegie Mellon
SAMSI Workshop
Congestion Control and Heavy Traffic
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BackgroundBackground
• 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. teleconferencing)
– control systems (e.g. automotive)
– avionics systems
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GoalsGoals
• For a given workload model we want:
– to predict the fraction of the workload that will meet its deadline (end-to-end in the network case),
– to design workload scheduling and control policies that will ensure service guarantees (e.g. a suitably small fraction miss their deadline),
– to investigate network design issues, e.g.:
• Number of priority bits needed
• Cost/benefit from flow tables
• Cost/benefit from keeping lead-time information
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ModelModel
• 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.
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Analysis: 1Analysis: 1
• In addition to tracking the workload at each node, we need to track the lead-time (= time until deadline elapses) for each task.
• The dimensionality becomes unbounded, and exact analysis is impossible.
• We resort to a heavy traffic analysis. This is appropriate for real-time problems. If we can analyze and control under heavy traffic, moderate traffic will be better.
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Analysis: 2Analysis: 2
• Heavy traffic analysis (traffic intensity on each node converges to 1)
• One node – workload converges to Brownian motion. Multiple nodes, workload may converge to RBM.
• Conditional on the workload, lead-time profile converges to a deterministic form depending upon – stream deadline distributions,– scheduling policy– traffic intensity
• Combining the lead-time profile with the equilibrium distribution of the workload process, we can determine the lateness fraction for each flow.
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Processor Sharing – Exp. DeadlinesProcessor Sharing – Exp. Deadlines
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Processor Sharing – Exp. DeadlinesProcessor Sharing – Exp. Deadlines
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Processor Sharing – Exp. DeadlinesProcessor Sharing – Exp. Deadlines
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Processor Sharing – Exp. DeadlinesProcessor Sharing – Exp. Deadlines
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Processor Sharing–Const. DeadlinesProcessor Sharing–Const. Deadlines
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Processor Sharing-Const. DeadlinesProcessor Sharing-Const. Deadlines
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Processor Sharing-Const. DeadlinesProcessor Sharing-Const. Deadlines
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EDF Miss Rate PredictionEDF Miss Rate Prediction=0.95EDF schedulingUniform(10,x) deadlines
EDF Deadline Miss Rate:
_
DEDF e Internet
Exponential
Uniform
: computed from the first two moments of task inter-arrival times and service times.
: Mean Deadline_
D