Inspired by ride-hailing and bike-sharing systems, we study the design of state-dependent controls for a closed queueing network model. We focus on the assignment policy, where the platform can choose which nearby vehicle to assign to an incoming customer; if no units are available nearby, the request is dropped. The vehicle becomes available at the destination after dropping the customer. We study how to minimize the proportion of dropped requests in steady state.We propose a family of simple state-dependent policies called Scaled MaxWeight (SMW) policies that dynamically manage the geographical distribution of supply. We prove that under the complete resource pooling (CRP) condition (analogous to the condition in Hall's marriage theorem), each SMW policy leads to exponential decay of demand-dropping probability as the number of supply units scales to infinity. Further, there is an SMW policy that achieves the optimal exponent among all assignment policies, and we analytically specify this policy in terms of the customer arrival rates for all source-destination pairs. The optimal SMW policy maintains high supply levels near structurally under-supplied locations. We also propose data-driven approaches for designing SMW policies and demonstrate excellent performance in simulations based on the NYC taxi dataset. * A preliminary version of this work appeared in ACM SIGMETRICS 2018(Banerjee et al. 2018. That publication is an extended abstract containing only a subset of the current theoretical results, proof sketches, and no simulation experiments.
We study the problem of maximizing payoff generated over a period of time in a general class of closed queueing networks with finite, fixed number of supply units which circulate in the system. Demand arrives stochastically, and serving a demand unit (customer) causes a supply unit to relocate from the "origin" to the "destination" of the customer. We consider general controls including entry control, pricing, and assignment. Motivating applications include shared transportation platforms and scrip systems.Inspired by the mirror descent algorithm for optimization and the backpressure policy for network control, we introduce a novel family of Mirror Backpressure (MBP) control policies.The MBP policies are simple and practical, and crucially do not need any statistical knowledge of the demand (customer) arrival rates.Under mild conditions, we show that MBP policies lose at most O( K T + 1 K ) payoff per customer relative to the optimal policy that knows the demand arrival rates, where K is the number of supply units and T is the total number of customers over the time horizon. The key technical challenge we overcome is that the number of supply units at any node can never be negative. Simulation results in a realistic ridehailing environment support our theoretical findings.
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