Stability and Learning in Strategic Queuing Systems Jason Gaitonde, - - PowerPoint PPT Presentation

Stability and Learning in Strategic Queuing Systems

Jason Gaitonde, Cornell University EC 2020 Joint work with Éva Tardos (Cornell)

Motivation: Learning in Repeated Games

• No-regret learning in repeated games has many attractive features
• Critical assumption: no carryover effect between rounds

Morning rush-hour traffic Second-by-second packet traffic

We study the quality of competitive, learning outcomes in a selfish queuing system with this carryover effect.

Strategic Queuing Systems: Results

• Selfish queues receive packets stochastically, compete to clear them

at servers à unprocessed packets returned to queues to be resent Main Results [G-Tardos ’20]

• Servers serve oldest packet first: no-regret learning helps coordinate

selfish queues with just twice service rate needed for centralized feasibility

• Servers serve packets uniformly at random: learning need not help

coordinate queues, unless prohibitively large service rates

• Proof techniques: coupling/deferred decisions, supermartingale

arguments, concentration to analyze highly dependent stochastic process

Proof Ideas & Details

• Use potential function argument to argue queue sizes remain

bounded in expectation

• Show that no-regret condition & slack factor of 2 together imply older

queues with priority must be using the best servers enough to decrease on average on long window

• Apply at all scales to prove potential decreases with high probability
• Use deferred decisions/coupling to study queue ages rather than sizes
• Apply concentration to show queue and server behavior is sufficiently

well-behaved