Search

A system manager makes dynamic pricing and dispatch control decisions in a queueing network model motivated by ride hailing applications. A novel feature of the model is that it incorporates travel times. Unfortunately, this renders the exact analysis of the problem intractable. Therefore, we study this problem in the heavy traffic regime. Under the assumptions of complete resource pooling and common travel time and routing distributions, we solve the problem in closed form by analyzing the corresponding Bellman equation. Using this solution, we propose a policy for the queueing system and illustrate its effectiveness in a simulation study. [ABSTRACT FROM AUTHOR]

This paper studies a diffusion control problem motivated by challenges faced by public health agencies who run clinics to serve the public. A key challenge for these agencies is to motivate individuals to participate in the services provided. They must manage the flow of (voluntary) participants so that the clinic capacity is highly utilized, but not overwhelmed. The organization can deploy costly promotion activities to increase the inflow of participants. Ideally, the system manager would like to have enough participants waiting in a queue to serve as many individuals as possible and efficiently use clinic capacity. However, if too many participants sign up, resulting in a long wait, participants may become irritated and hesitate to participate again in future. We develop a diffusion model of managing participant inflow mechanisms. Each mechanism corresponds to choosing a particular drift rate parameter for the diffusion model. The system manager seeks to balance three different costs optimally: (i) a linear holding cost that captures the congestion concerns, (ii) an idleness penalty corresponding to wasted clinic capacity and negative impact on public health, and (iii) costs of promotion activities. We show that a nested-threshold policy for deployment of participant inflow mechanisms is optimal under the long-run average cost criterion. In this policy, the system manager progressively deploys mechanisms in increasing order of cost, as the number of participants in the queue decreases. We derive explicit formulas for the queue length thresholds that trigger each promotion activity, providing the system manager with guidance on when to use each mechanism. [ABSTRACT FROM AUTHOR]

Motivated by applications in queueing theory, we consider a class of singular stochastic control problems whose state space is the d-dimensional positive orthant. The original problem is approximated by a drift control problem, to which we apply a recently developed computational method that is feasible for dimensions up to d=30\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d=30$$\end{document} or more. To show that nearly optimal solutions are obtainable using this method, we present computational results for a variety of examples, including queueing network examples that have appeared previously in the literature. [ABSTRACT FROM AUTHOR]

This paper studies a Geo/Geo/1 $$+GI$$ queue in which the abandonments are endogenous. One crucial feature of this model is that the abandonment behavior is affected by the system performance and vice versa. Our model captures this interaction by developing two closely related models: an abandonment model and a queueing model. In the abandonment model, customers take the virtual waiting time distribution as given. They receive a reward r from service and incur a cost c per period of waiting. Customers are forward-looking and maximize their expected discounted utilities by making wait or abandon decisions dynamically as they wait in the queue. The queueing model takes the customers' abandonment time distribution as an input and studies the resulting virtual waiting time distribution. In equilibrium, the customers' abandonment behavior and the system performance must be consistent across the two models. Therefore, combining the two models and imposing this consistency requirement, we show that there exists a unique equilibrium. Lastly, we provide a computational scheme to calculate the equilibrium numerically. [ABSTRACT FROM AUTHOR]