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Robust Dynamic Pricing and Admission Control with Fairness Guarantees

Yingqing Chen, Anni Li, Christos G. Cassandras, Homayoun Hamedmoghadam, Fabian Wirth, Robert Shorten

Abstract

Dynamic pricing is commonly used to regulate congestion in shared service systems. This paper is motivated by the fact that when heterogeneaous user groups (in terms of price responsiveness) are present, conventional monotonic pricing can lead to unfair outcomes by disproportionately excluding price-elastic users, particularly under high or uncertain demand. The paper's contributions are twofold. First, we show that when fairness is imposed as a hard state constraint, the optimal (revenue maximizing) pricing policy is generally non-monotonic in demand. This structural result departs fundamentally from standard surge pricing rules and reveals that price reduction under heavy load may be necessary to maintain equitable access. Second, we address the problem that price elasticity among heterogeneous users is unobservable. To solve it, we develop a robust dynamic pricing and admission control framework that enforces resource capacity and fairness constraints for all user type distributions consistent with aggregate measurements. By integrating integral High Order Control Barrier Functions (iHOCBFs) with a worst case robust optimization framework, we obtain a controller that guarantees forward invariance of safety and fairness constraints while optimizing revenue. Numerical experiments demonstrate improved fairness and revenue performance relative to monotonic surge pricing policies.

Robust Dynamic Pricing and Admission Control with Fairness Guarantees

Abstract

Dynamic pricing is commonly used to regulate congestion in shared service systems. This paper is motivated by the fact that when heterogeneaous user groups (in terms of price responsiveness) are present, conventional monotonic pricing can lead to unfair outcomes by disproportionately excluding price-elastic users, particularly under high or uncertain demand. The paper's contributions are twofold. First, we show that when fairness is imposed as a hard state constraint, the optimal (revenue maximizing) pricing policy is generally non-monotonic in demand. This structural result departs fundamentally from standard surge pricing rules and reveals that price reduction under heavy load may be necessary to maintain equitable access. Second, we address the problem that price elasticity among heterogeneous users is unobservable. To solve it, we develop a robust dynamic pricing and admission control framework that enforces resource capacity and fairness constraints for all user type distributions consistent with aggregate measurements. By integrating integral High Order Control Barrier Functions (iHOCBFs) with a worst case robust optimization framework, we obtain a controller that guarantees forward invariance of safety and fairness constraints while optimizing revenue. Numerical experiments demonstrate improved fairness and revenue performance relative to monotonic surge pricing policies.
Paper Structure (17 sections, 1 theorem, 31 equations, 7 figures)

This paper contains 17 sections, 1 theorem, 31 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Fairness Level
  4. Optimal Control Problem
  5. Robust Dynamic Pricing Control with iHOCBF
  6. CBF-Based Enforcement of Service Queue Capacity Constraints
  7. Extended State Space
  8. iHOCBF Formulation
  9. Robust Pricing Control Framework
  10. Simulation Results
  11. Light Demand Scenario
  12. Heavy Demand Scenario
  13. Dynamic Stochastic Demand
  14. Performance across Different Unfairness thresholds ($\theta_d$)
  15. Performance across Different Demand
  16. ...and 2 more sections

Key Result

Proposition 1

Consider the system with state defined in eqn: extended state vector and dynamics given in eqn: dynamics of new states. Let $\mathcal{W}(t;p)$ denote the set of user-type distributions consistent with the observable aggregate measurements at time $t$ under price $p$. Assume that the initial state sa

Figures (7)

  • Figure 1: Two-stage queueing model with heterogeneous demand sources. Each group $i$ ($i = 1, \ldots, N$) maintains a demand buffer $x_i$, driven by exogenous arrivals $K_i(t)$ and price-dependent dropout $f_i(p)x_i$. A fraction $\alpha(t)$ of demand is admitted to the shared service queue $q$, which serves at rate $\mu(t)$.
  • Figure 2: Trajectories Comparison under Light Stochastic Gaussian Demand
  • Figure 3: Trajectories Comparison under Heavy Stochastic Gaussian Demand
  • Figure 4: Trajectories Comparison under Time-varying Gaussian Demand
  • Figure 5: Trajectories Comparison under different $I$ threshold ($\theta_d$)
  • ...and 2 more figures

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Remark 3
  • Proposition 1: Robust fairness and capacity guarantees
  • proof