Topics in Stochastic Networks Performance Scaling and Algorithmic Challenges

Instructor: Yuan Zhong; Class: Mudd 627, MW 2:40 – 3:55pm Office hour: Fri 4 – 6pm; Mudd 344 (or by appointment) Class homepage: 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 capacity Leave after being processed Network!

Call operator assignment English, etc Investment Chinese Spanish Savings Overview

Examples abound – Manufacturing: wafer fabrication, production – Services: call centers, cloud computing, healthcare – Communications: wireless networks, routers, Internet 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 operations and 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 operations and 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 operations and controls Good performance Simple design, easy control

Overview Important questions to address Good performance Simple design, easy control Achieve jointly?

Non-empty Queue 1 Simple Teaser O(n) memory

Random Queue 1 Simple Teaser Zero memory

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 “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

Appreciation of good modeling – an “art” Asking good research questions Good use of elementary and simple tools Takeaways from the class