Design a Win-Win Strategy That Is Fair to Both Service Providers and Tasks When Rejection Is Not an Option

TL;DR

The paper addresses online task assignment where tasks arrive dynamically to a fixed set of service providers, with a no-rejection constraint and the goal of fairness for both tasks and workers. It introduces two minimax fairness objectives, FAIR-T (minimize the maximum relative waiting time $\max_j \bar{w}_j$) and FAIR-S (minimize the maximum workload $\max_i \rho_i$), and demonstrates that the second can be exactly solved as a linear program, while the first can be closely approximated by it under mild conditions. The authors develop an LP-based algorithmic framework and two practical heuristics, and validate them through extensive simulations on teleoperation data from autonomous vehicles, showing favorable fairness-performance tradeoffs. The results provide actionable strategies for fair, no-rejection task allocations in dynamic online matching settings and offer insights into how fairness notions translate into real-world teleoperation and related applications. Overall, the work advances two-sided fairness guarantees in online allocation and delivers scalable methods with practical impact for dynamic task assignment contexts.

Abstract

Assigning tasks to service providers is a frequent procedure across various applications. Often the tasks arrive dynamically while the service providers remain static. Preventing task rejection caused by service provider overload is of utmost significance. To ensure a positive experience in relevant applications for both service providers and tasks, fairness must be considered. To address the issue, we model the problem as an online matching within a bipartite graph and tackle two minimax problems: one focuses on minimizing the highest waiting time of a task, while the other aims to minimize the highest workload of a service provider. We show that the second problem can be expressed as a linear program and thus solved efficiently while maintaining a reasonable approximation to the objective of the first problem. We developed novel methods that utilize the two minimax problems. We conducted extensive simulation experiments using real data and demonstrated that our novel heuristics, based on the linear program, performed remarkably well.

Figures (9)

• Figure 1: An example where $\overline{\operatorname{\textbf{PT}}\xspace}$ and $\overline{\operatorname{\textbf{PS}}\xspace}$ each have a unique optimal solution with non-uniform values of $\{\rho_i\}$ and $\{\bar{w}_j\}$, though $\eta_t({\boldsymbol \mu}\xspace,\mathbf{x}_s^*)=\eta^*_t$ since the programs share the same unique optimal solution.
• Figure 2: Y axis is the maximum waiting time(in seconds) for a task(a,c and e) and the max. worker workload(b,d and f). The X axis in (a,b) is the value of $\kappa$(x axis) and the task load is of 120000 tasks per day. In (c,d), the X axis is the task load and $\kappa$ is set to 1. In (e,f) the X axis is for different balances of arrival distribution: first bar is for equal distribution for each task type. In the second bar, the first type has probability of 70% and the others have 10%. the other bars are defined similarly for the second, third and forth task types (task load was 80000 tasks per day and $\kappa$ is set to 1). In the legend: SIM(PT) and SIM(PS) denote Algorithm \ref{['alg:pb']}'s results for $\operatorname{\textbf{PT}}$ and $\operatorname{\textbf{PS}}$ in simulation. SIM-F(PT) and SIM-F(PS) are Algorithm \ref{['alg:ha']}'s results (in which we assign to a free worker first) for $\operatorname{\textbf{PT}}\xspace$ and $\operatorname{\textbf{PS}}\xspace$ in simulation. $GTW$ and $GWU$ are the results of the greedy heuristics targeting task waiting time and worker workload in simulation. Error bars represent a confidence interval of 0.95.
• Figure 3: A toy example showing the objective function in Program $\operatorname{\textbf{PT}}$ can be neither convex nor concave even when $\kappa=1$.
• Figure 4: Maximum Task Waiting Time (left) and Maximum worker workload (right) under varying task arrival loads. The x-axis represents the expected number of arrivals per day. In these graphs, the arrival distributions of all tasks are equal.
• Figure 5: Task waiting time (left) and worker workload (right) for different arrival distributions: equal task arrival vs. one task type arriving seven times more than the others (task load was 60000 requests per day).

Theorems & Definitions (21)

• Lemma 1
• proof
• Lemma 2
• Theorem 1
• Lemma 3
• proof
• Example 1
• Lemma 4
• proof
• Lemma 5