Bayesian estimators of Weibull distributions applied to a model of waiting lines G/G/s

Se ha estudiado en la literatura la aproximación de los modelos G/G/s a partir de modelos markovianos M/M/s. Un estudio de un modelo de colas se presenta en el presente artículo usando tiempos de llegadas y servicios Weibull distribuidos cuya estimación de parámetros se realizó con el método Bayesiano cadena de Markov Monte Carlo, específicamente el muestreador de Gibbs. La aproximación de este modelo de líneas de espera es evaluada mediante simulación. Esta metodología se aplicó al caso de repartición de refrigerios en la Universidad del Magdalena en Santa Marta, Colombia. Los resultados muestran la utilidad y potencia para calcular indicadores de un sistema de colas cuando los tiempos entre llegadas y de atención se distribuyen como una Weibull.The approximation of G/G/s models from Markov models M/M/s has been studied in the literature. The study of a queue model is detailed in the present article, using times of arrivals and time service distributed by Weibull whose estimation of parameters was performed with the Bayesian method Monte Carlo Markov chain, specifically the Gibbs sampler. The approximations of this model of waiting lines is evaluated by simulation. This methodology was applied to the case of delivery of refreshments to students of the University of Magdalena in Santa Marta, Colombia. The results show the utility and power to calculate indicators of a queue system when both, the arrival and attention times, are distributed as a Weibull.Universidad Pablo de Olavid

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