Dynamic Weighted Matching with Heterogeneous Arrival and Departure Rates

A strategic timing of arrivals to a linear slowdown processor sharing system

We consider a discrete population of users with homogeneous service demand who need to decide when to arrive to a system in which the service rate deteriorates linearly with the number of users in the system. The users have heterogeneous desired departure times from the system, and their goal is to minimize a weighted sum of the travel time and square deviation from the desired departure times. Users join the system sequentially, according to the order of their desired departure times. We model this scenario as a non-cooperative game in which each user selects his actual arrival time. We prese…

How to Hire Secretaries with Stochastic Departures

We study a generalization of the secretary problem, where decisions do not have to be made immediately upon candidates' arrivals. After arriving, each candidate stays in the system for some (random) amount of time and then leaves, whereupon the algorithm has to decide irrevocably whether to select this candidate or not. The goal is to maximize the probability of selecting the best candidate overall. We assume that the arrival and waiting times are drawn from known distributions. Our first main result is a characterization of the optimal policy for this setting. We show that when deciding wheth…

Dynamic Bipartite Matching Market with Arrivals and Departures

In this paper, we study a matching market model on a bipartite network where agents on each side arrive and depart stochastically by a Poisson process. For such a dynamic model, we design a mechanism that decides not only which agents to match, but also when to match them, to minimize the expected number of unmatched agents. The main contribution of this paper is to achieve theoretical bounds on the performance of local mechanisms with different timing properties. We show that an algorithm that waits to thicken the market, called the $\textit{Patient}$ algorithm, is exponentially better than t…

具有异质用户的出发时间选择均衡模型的新视角

A new look at departure time choice equilibrium models with heterogeneous users

本文提出基于最优传输理论和分解技术的系统方法，解析求解异质通勤者单瓶颈出发时间选择均衡问题，揭示了均衡排序模式的Monge性质条件，并扩展至多类异质性问题。

Maximizing Efficiency in Dynamic Matching Markets

We study the problem of matching agents who arrive at a marketplace over time and leave after d time periods. Agents can only be matched while they are present in the marketplace. Each pair of agents can yield a different match value, and the planner's goal is to maximize the total value over a finite time horizon. We study matching algorithms that perform well over any sequence of arrivals when there is no a priori information about the match values or arrival times. Our main contribution is a 1/4-competitive algorithm. The algorithm randomly selects a subset of agents who will wait until rig…

Online Algorithms for the Santa Claus Problem

The Santa Claus problem is a fundamental problem in fair division: the goal is to partition a set of heterogeneous items among heterogeneous agents so as to maximize the minimum value of items received by any agent. In this paper, we study the online version of this problem where the items are not known in advance and have to be assigned to agents as they arrive over time. If the arrival order of items is arbitrary, then no good assignment rule exists in the worst case. However, we show that, if the arrival order is random, then for $n$ agents and any $\varepsilon > 0$, we can obtain a competi…