Self-Selecting Priority Queues with Burr Distributed Waiting Costs

Service providers, in the presence of congestion and heterogeneity of customer waiting costs, often introduce a fee-based premier option using which the customers self-segment themselves. Examples of this practice are found in health care, amusement parks, government (consular services), and transportation. Using a single-server queuing system with customer waiting costs modeled as a Burr Distribution, we perform a detailed analysis to (i) determine the conditions (fees, cost structure, etc.) under which this strategy is profitable for the service provider, (ii) quantify the benefits accrued by the premier customers; and (iii) evaluate the resulting impact on the other customers. We show that such self-selecting priority systems can be pareto-improving in the sense that they are beneficial to everyone. These benefits are larger when the variance in the customer waiting costs is high and the system utilization is high. We use income data from the poorest and richest areas (identified by zipcode) in the United States along with the countrywide income distribution to illustrate our results. Numerical results indicate that planning for a 20–40% enrollment in the high-priority option is robust in ensuring that all the stakeholders benefit from the proposed strategy

Recent Advances in Accumulating Priority Queues

This thesis extends the theory underlying the Accumulating Priority Queue (APQ) in three directions. In the first, we present a multi-class multi-server accumulating priority queue with Poisson arrivals and heterogeneous services. The waiting time distributions for different classes have been derived. A conservation law for systems with heterogeneous servers has been studied. We also investigate an optimization problem to find the optimal level of heterogeneity in the multi-server system. Numerical investigations through simulation are carried out to validate the model. We next focus on a queueing system with Poisson arrivals, generally distributed service times and nonlinear priority accumulation functions. We start with an extension of the power-law APQ in Kleinrock and Finkelstein (1967), and use a general argument to show that there is a linear system of the form discussed in Stanford, Taylor, and Ziedins (2014) which has the same priority ordering of all customers present at any given instant in time, for any sample path. Beyond the power-law case, we subsequently characterize the class of nonlinear accumulating priority queues for which an equivalent linear APQ can be found, in the sense that the waiting time distributions for each of the classes are identical in both the linear and nonlinear systems. Many operational queuing systems must adhere to waiting time targets known as Key Performance Indicators (KPIs), particularly in health care applications. In the last aspect, we address an optimization problem to minimize the weighted average of the expected excess waiting time (WAE), so as to achieve the optimal performance of a system operating under KPIs. We then find that the Accumulating Priority queuing discipline is well suited to systems with KPIs, in that each class of customers progresses fairly towards timely access by its own waiting time limit. Due to the difficulties in minimizing the WAE, we introduce a surrogate objective function, the integrated weighted average excess (IWAE), which provides a useful proxy for WAE. Finally, we propose a rule of thumb in which patients in the various classes accumulate priority credit at a rate that is inversely proportional to their time limits

The dynamic user equilibrium on a transport network: mathematical properties and economic applications

This thesis is focused on dynamic user equilibrium models and their applications to traffic assignment. It aims at providing a mathematically rigorous and general formulation for the dynamic user equilibrium. Particular attention is paid to the representation of transport demand and more specifically to trip scheduling and users with heterogeneous preferences. This is achieved by expressing the dynamic user equilibrium as a Nash game with a continuum of players. This allows for a precise, concise and microeconomically consistent description. This thesis also deals with computational techniques. We solve analytically equilibrium on small networks to get a general intuition of the complex linkage between the demand and supply of transport in dynamic frameworks. The intuition acquired from the resolution is used to elaborate efficient numerical solving methods that can be applied to large size, real life, transport networks. Along the thesis several economic applications are proposed. All of them are dealing with the assessment of congestion pricing policies where are likely to reschedule their trips. In particular, a pricing scheme designed to ease congestion during holiday departure periods is tested. In this scheme a toll varying within the day and from day to day is set on the french motorway network. This form to toll is especially appealing as it enables the operator to influence the departure day as well as the departure time. Indeed it is shown that even moderate variations of the toll with time might have strong impacts on an highly congested interurban network.Cette thèse porte sur les modèles d'équilibres dynamiques sur un réseau de transport et leurs applications à l'affectation de trafic. Elle tente d'en propose une formulation à la fois générale et mathématiquement rigoureuse. Une attention particulière est accordée à la représentation de la demande de transport. Plus spécifiquement, la modélisation de l'hétérogénéité dans les préférences des usagers d'un réseau de transport, ainsi que des stratégies de choix d'horaire dans les déplacements, occupe une place importante dans notre approche. Une caractéristique de ce travail est son fort recours au formalisme mathématique; cela nous permet d'obtenir une formulation concise et micro-économiquement cohérente des réseaux de transport et de la demande de transport dans un contexte dynamique. Cette thèse traite aussi de méthodes de résolution en lien avec les modèles d'équilibres dynamiques. Nous établissons analytiquement des équilibres sur des réseaux de petites tailles afin d'améliorer la connaissance qualitative de l'interaction entre offre et demande dans ce contexte. L'intuition retirée de ces exercices nous permet de concevoir des méthodes numériques de calculs qui peuvent être appliquées à des réseaux de transport de grande taille. Tout au long de la thèse plusieurs applications économiques de ces travaux sont explorées. Toutes traitent des politiques de tarification de la congestion et de leurs évaluation, notamment lorsque les automobilistes sont susceptibles d'ajuster leurs horaires de départ. En particulier une politique tarifaire conçue pour limiter la congestion lors des grands départs de vacances est testée. Elle consiste à mettre en place un péage sur le réseau autoroutier variant selon l'heure de la journée mais aussi de jour en jour. Ce type de péage est particulièrement intéressant pour les exploitants car il leur permet d'influencer à la fois sur l'heure et le jour de départ des vacanciers. Les méthodes développées dans cette thèse permettent d'établir que les gains en termes de réduction de la congestion sont substantiels

Online Algorithms for Dynamic Resource Allocation Problems

Dynamic resource allocation problems are everywhere. Airlines reserve flight seats for those who purchase flight tickets. Healthcare facilities reserve appointment slots for patients who request them. Freight carriers such as motor carriers, railroad companies, and shipping companies pack containers with loads from specific origins to destinations. We focus on optimizing such allocation problems where resources need to be assigned to customers in real time. These problems are particularly difficult to solve because they depend on random external information that unfolds gradually over time, and the number of potential solutions is overwhelming to search through by conventional methods. In this dissertation, we propose viable allocation algorithms for industrial use, by fully leveraging data and technology to produce gains in efficiency, productivity, and usability of new systems. The first chapter presents a summary of major methodologies used in modeling and algorithm design, and how the methodologies are driven by the size of accessible data. Chapters 2 to 5 present genuine research results of resource allocation problems that are based on Wang and Truong (2017); Wang et al. (2015); Stein et al. (2017); Wang et al. (2016). The algorithms and models cover problems in multiple industries, from a small clinic that aims to better utilize its expensive medical devices, to a technology giant that needs a cost-effective, distributed resource-allocation algorithm in order to maintain the relevance of its advertisements to hundreds of millions of consumers

Essays on patient-flow in the emergency department

Emergency department (ED) overcrowding is a global concern. To help mitigate this issue, this thesis studies impediments to efficient patient flow in the ED caused by suboptimal worker behaviors and patient routing policies. I focus on three issues: (i) admission batching, (ii) hallway placement and (iii) under-triage behavior, and empirically demonstrate their impact on patient flow and quality of care. These studies are summarized as follows. Admissions batching: We study the behavior of admitting patients back-to-back (i.e., batching) by ED physicians. Using data from a large hospital, we show that the probability of batching admissions is increasing in the hour of an ED physician’s shift, and that batched patients experience a longer delay from hospital admission to receiving an inpatient bed. We further show that this effect is partially due to the increase in the coefficient of variation of inpatient bed-requests caused by batching. However, we also find that batching admissions is associated with a higher shift-level productivity. An important implication of our work is that workers may induce delays in downstream stages, caused by practices that increase their productivity. Hallway utilization: A common practice in busy EDs is to admit patients from the waiting area to hallway beds as the regular beds fill up. Using data from a large ED, we first perform a causal analysis to quantify the impact of hallway placement on wait times and quality of care – as defined by disposition time, room-to-departure (R2D) time and likelihood of adverse outcomes. We find that patients admitted to the hallway experience a significantly lower door-to-doctor time at the cost of longer disposition and R2D times. Hallway patients are also substantially more likely to experience an adverse outcome. Next, using a counterfactual analysis we show that a pooling policy, where hallway beds are used only if all regular beds are full, significantly reduces wait times, albeit at the cost of a slightly higher hallway utilization. Also, too little or too much wait tolerance for rooming patients may result in under- or over-utilization of the hallway space, both of which are detrimental to overall ED length of stay (LOS) and wait times. Under-triage behavior: Triaging ED patients upon arrival to the ED and assessing their urgency for treatment is crucial for timely service to all patients. Despite the standard patient classification algorithm by which all nurses are trained, we hypothesize, and show, that the ED’s workload impacts the perceived patient urgency, and subsequently, patient severity scores. We first use a predictive model to predict a patient’s true triage level using information collected at triage and define under-triage, accordingly. We find that under-triage is decreasing up to a certain point of workload but increasing after (U-shape). We also quantify the impact of under-triage on disposition time, room-to-departure time and risk of readmission. Collectively, this thesis demonstrates how patient-flow may be improved without the need to increase explicit physical capacity in the ED (e.g., beds). It offers practical solutions to managers and contributes to the operations management literature

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios