Topics in Stochastic Networks
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Transcript of Topics in Stochastic Networks
• Instructor: Yuan Zhong; [email protected]
• Class: Mudd 627, MW 2:40 – 3:55pm
• Office hour: Fri 4 – 6pm; Mudd 344 (or by appointment)
• Class homepage: http://www.columbia.edu/~yz2561/teaching.html
Logistics
• Grading policy:– 4 hw sets; 40% in total– Handout/return: L3/8, L8/13, L13/18, L18/23– Extensions will be allowed as per instructor’s permission– Project: 60%
• Project:– Critical survey of literature (2-3 papers) + suggestions for
future work. Possible topics and references coming soon.– Model formulation and analysis/simulations.– Presentation last week of classes; short paper before.– Final versions due Dec 10; proposals due Nov 9.
Logistics
• Stochastic networks: broadly speaking, systems of interacting components + stochasticity
• Some examples:– Ideal gas, Ising models– Social and economic networks – Epidemic networks– Etc…
• This course is about none of the above!
Overview
• Scope: processing networks
Overview
Diff. entities arrive to be processed
System that processes them
Leave after being processed
• Scope: processing networks
Overview
Diff. entities arrive to be processed
• Coupled processing activities
• Constrained capacityLeave after being processed
Network!
• Examples abound– Manufacturing: wafer fabrication, production– Services: call centers, cloud computing, healthcare– Communications: wireless networks, routers, Internet
Overview
Overview
• Loss system: lose entities if demands cannot be satisfied instantly
• Loss probability
• Queueing system: queue up entities if demands cannot be satisfied instantly
• Delay/queue size
Overview
• Important questions to address
• Also the pricing and economic aspect (not covered)
Performance: Loss prob, queueing delay,
etc
Long-term capacity management and planning
Day-to-day operationsand controls
Overview
• Important questions to address
• Also the pricing and economic aspect (not covered)
Call drops, time to download files,
etc
Design of networks: hiring of personnel,
Bandwidth capacity, etc
Routing and scheduling of customers/entities
Overview
• Important questions to address
Performance: Loss prob, queueing delay,
etc
Long-term capacity management and planning
Day-to-day operationsand controls
• Science: analysis of network and compute perf. metrics• ≈ More classical
• Engineering: design and optimize network• ≈ More modern
Overview
• Important questions to address
Performance: Loss prob, queueing delay,
etc
Long-term capacity management and planning
Day-to-day operationsand controls
• Good performance
• Simple design, easy control
Overview
• Important questions to address
• Good performance
• Simple design, easy control
Achieve jointly?
• Examples: telephone networks, workforce management, hotel room mgmt., etc; also abundant applications in communications
• Control-less system: loss probability computation
• Key insight: loss probabilities are hard to compute, but simple approximations work well– Limit theorems, Erlang’s fixed point approximation
• Tools: Markov processes, cvx opt, some analysis
• “Loss networks” by F. Kelly, AAP 1991. “Lecture notes on stochastic networks”, by Kelly and Yudovina
Part I(a): Loss Networks
• Mostly control-less systems: Jackson networks, Kelly networks, Whittle networks
• Manufacturing and production; communications
• Key insight: for a broad range of systems, queue-size distributions have product form– Product of independent components– Simple description; good for provisioning and optimization
• Main tool: Markov processes (time reversal)
• “Fundamentals of queueing networks” by H. Chen and D. D. Yao “Reversibility and stochastic networks” by Kelly for examples
Part I(b): Network of Queues
• Wireless networks, Internet routers, call centers
• Operation and control of networks– Queue size difficult to compute; focus on system stablity– Q: how can I keep queue size finite?
• Key insight: a simple, wide applicable class of control policies that ensure system stability– Q1: queue size bounds under these policies? – Q2: Low-complexity approximation of these policies?
• Tools: Markov chains, Lyapunov functions, graph theory, optimization, randomized algorithms
• No textbook, research papers
Part 2(a): Switched Networks
• Main application: congestion control in the Internet– a major achievement of stoc. net. over the last 10 – 20 years– Ideas found in operations management as well
• Main question: how to fairly and efficiently allocate resources?– A framework that successfully explains TCP of the Internet
• Tools: Markov processes, Lyapunov functions, convex optimization, (a little bit of econ)
• No textbook, research papers
• Also connections with product-form networks
Part 2(b): Flow-Level Networks
• Algorithmic in nature; perhaps of more interest to electrical engineers and computer scientists
• Main question: in a large-scale network, how to ensure good performance without a central coordinator/controller?
• Applications: road networks, the Internet, wireless networks
• Tools: convex optimization, mixing time of Markov chains, graph theory, Markov processes
• Very recent research results
Part 3: Decentralized Opt.
• Fluid models of queueing networks
• Mean-field analysis
• Heavy-traffic analysis; diffusion approximation
• Large-deviations analysis
• Simulation methods
Some Important Omissions