[Paper Review] Near Optimal Control of a Ride-Hailing Platform via Mirror Backpressure

Yash Kanoria, Pengyu Qian|arXiv (Cornell University)|Mar 7, 2019

Transportation and Mobility Innovations14 citations

TL;DR

This paper proposes Mirror Backpressure (MBP) policies for near-optimal control of ride-hailing and similar platforms in closed queueing networks with finite supply units. By combining mirror descent and backpressure principles, MBP achieves near-optimal performance without requiring prior knowledge of demand arrival rates, losing at most $O(\frac{K}{T} + \frac{1}{K} + \sqrt{\eta K})$ payoff per customer relative to the optimal policy with full knowledge.

ABSTRACT

We study the problem of maximizing payoff generated over a period of time in a general class of closed queueing networks with a 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. The key challenge is to manage the distribution of supply in the network. We consider general controls including customer 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 and rich 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 (these rates are permitted to vary slowly in time). Under mild conditions, we propose MBP policies that are provably near optimal. Specifically, our policies lose at most $O(\frac{K}{T}+\frac{1}{K} + \sqrt{\eta K})$ payoff per customer relative to the optimal policy that knows the demand arrival rates, where $K$ is the number of supply units, $T$ is the total number of customers over the time horizon, and $\eta$ is the maximum change in demand arrival rates per period (i.e., per customer arrival). A natural model of a scrip system is a special case of our setup. An adaptation of MBP is found to perform well in a realistic ride-hailing environment.

Motivation & Objective

• To address the challenge of efficiently managing supply distribution in closed queueing networks with finite, circulating supply units.
• To design control policies that maximize long-term payoff in systems with stochastic, time-varying demand, such as ride-hailing platforms and scrip systems.
• To develop a control framework that operates without prior knowledge of demand arrival rates, which are allowed to change slowly over time.
• To achieve near-optimal performance with provable guarantees under mild assumptions.
• To provide a practical and scalable policy that integrates customer entry control, pricing, and assignment decisions.

Proposed method

• The paper introduces Mirror Backpressure (MBP) policies, a novel family of control policies inspired by mirror descent and backpressure principles.
• MBP uses a dual-optimization framework that dynamically adjusts supply allocation based on real-time network state and queue differentials.
• The policy operates without requiring statistical knowledge of demand rates, making it robust to time-varying and unknown arrival processes.
• It leverages a Lyapunov-based analysis to derive performance bounds, ensuring stability and near-optimality.
• The control law is derived from a mirror descent update on the dual variables associated with supply constraints.
• The framework supports general control actions including customer acceptance decisions, dynamic pricing, and assignment routing.

Experimental results

Research questions

• RQ1 Can a control policy be designed that achieves near-optimal payoff in a closed queueing network with finite supply and unknown demand rates?
• RQ2 How can mirror descent and backpressure principles be combined to create a practical, data-driven control policy for dynamic platforms?
• RQ3 What is the fundamental performance loss of a policy that does not know demand rates compared to the optimal policy with full knowledge?
• RQ4 Can the proposed policy handle slowly time-varying demand without re-estimation or adaptation?
• RQ5 Does the MBP policy generalize to real-world applications such as ride-hailing and scrip systems?

Key findings

• The MBP policy achieves a regret bound of $O(\frac{K}{T} + \frac{1}{K} + \sqrt{\eta K})$ per customer relative to the optimal policy with full knowledge of demand rates.
• The performance loss is minimized when the number of supply units $K$ is chosen appropriately, balancing the trade-off between $\frac{K}{T}$ and $\frac{1}{K}$.
• The policy remains effective even when demand arrival rates change slowly over time, with $\eta$ capturing the maximum rate of change per period.
• The framework naturally accommodates a wide range of control actions, including customer entry control, pricing, and assignment.
• An adaptation of MBP demonstrates strong performance in a realistic ride-hailing simulation environment.
• A special case of the model corresponds to scrip systems, showing the generality and applicability of the proposed framework.