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We study the problem of maximizing payoff generated over a period of time ina general class of closed queueing networks with a finite, fixed number ofsupply units which circulate in the system. Demand arrives stochastically, andserving a demand unit (customer) causes a supply unit to relocate from the``origin'' to the ``destination'' of the customer. The key challenge is tomanage the distribution of supply in the network. We consider general controlsincluding customer entry control, pricing, and assignment. Motivatingapplications include shared transportation platforms and scrip systems.  Inspired by the mirror descent algorithm for optimization and thebackpressure policy for network control, we introduce a rich family of\emph{Mirror Backpressure} (MBP) control policies. The MBP policies are simpleand practical, and crucially do not need any statistical knowledge of thedemand (customer) arrival rates (these rates are permitted to vary in time).Under mild conditions, we propose MBP policies that are provably near optimal.Specifically, our policies lose at most $O(\frac{K}{T}+\frac{1}{K} + \sqrt{\etaK})$ payoff per customer relative to the optimal policy that knows the demandarrival rates, where $K$ is the number of supply units, $T$ is the total numberof customers over the time horizon, and $\eta$ is the demand process' averagerate of change per customer arrival. An adaptation of MBP is found to performwell in numerical experiments based on data from ride-hailing.

Blind Dynamic Resource Allocation in Closed Networks via Mirror Backpressure