Stochastic surgery selection and sequencing under dynamic emergency break-ins

Anticipating the impact of urgent emergency arrivals on operating room schedules remains methodologically and computationally challenging. This paper investigates a model for surgery scheduling, in which both surgery durations and emergency patient arrivals are stochastic. When an emergency patient arrives he enters the first available room. Given the sets of surgeries available to each operating room for that day, as well as the distributions of the main stochastic variables, we aim to find the per-room surgery sequences that minimise a joint objective, which includes over- and under-utilisation, the amount of cancelled patients, as well as the risk that emergencies suffer an excessively long waiting time. We show that a detailed analysis of emergency break-ins and their disruption of the schedule leads to a lower total cost compared to less sophisticated models. We also map the trade-off between the threshold for excessive waiting time, and the set of other objectives. Finally, an efficient heuristic is proposed to accurately estimate the value of a solution with significantly less computational effort.Anticipating the impact of urgent emergency arrivals on operating room schedules remains methodologically and computationally challenging. This paper investigates a model for surgery scheduling, in which both surgery durations and emergency patient arrivals are stochastic. When an emergency patient arrives he enters the first available room. Given the sets of surgeries available to each operating room for that day, as well as the distributions of the main stochastic variables, we aim to find the per-room surgery sequences that minimise a joint objective, which includes over- and under-utilisation, the amount of cancelled patients, as well as the risk that emergencies suffer an excessively long waiting time. We show that a detailed analysis of emergency break-ins and their disruption of the schedule leads to a lower total cost compared to less sophisticated models. We also map the trade-off between the threshold for excessive waiting time, and the set of other objectives. Finally, an efficient heuristic is proposed to accurately estimate the value of a solution with significantly less computational effort.A

Analysing stochastic call demand with time varying parameters

In spite of increasingly sophisticated workforce management tools, a significant gap remains between the goal of effective staffing and the present difficulty predicting the stochastic demand of inbound calls. We have investigated the hypothesized nonhomogeneous Poisson process model of modem pool callers of the University community. In our case, we tested if the arrivals could be approximated by a piecewise constant rate over short intervals. For each of 1 and 10-minute intervals, based on the close relationship between the Poisson process and the exponential distribution, the test results did not show any sign of homogeneous Poisson process. We have examined the hypothesis of a nonhomogeneous Poisson process by a transformed statistic. Quantitative and graphical goodness-of-fit tests have confirmed nonhomogeneous Poisson process. Further analysis on the intensity function revealed that linear rate intensity was woefully inadequate in predicting time varying arrivals. For sinusoidal rate model, difficulty arose in setting the period parameter. Spline models, as an alternative to parametric modelling, had more control of balance between data fitting and smoothness, which was appealing to our analysis on call arrival process

Estimation of a Simple Queuing System WithUnits-in-Service and Complete Data

Queuing theory may be useful for analyzing economic phenomena involving count and duration data. We develop maximum likelihood estimators for the time-varying parameters of a simple queuing system based on two kinds of data: complete interarrival and service times (IST), and number of units in service (NIS). The IST estimator dominates the NIS estimator, in terms of ease of implementation, bias, and variance. The model is useful for many empirical applications in economics.m (t)/M (t)/8 queue, infinite server queue, time-varying parameters, Poisson stochasticprocess, duration data

Stochastic Modelling of Aircraft Queues: A Review

In this paper we consider the modelling and optimal control of queues of aircraft waiting to use the runway(s) at airports, and present a review of the related literature. We discuss the formulation of aircraft queues as nonstationary queueing systems and examine the common assumptions made in the literature regarding the random distributions for inter-arrival and service times. These depend on various operational factors, including the expected level of precision in meeting pre-scheduled operation times and the inherent uncertainty in airport capacity due to weather and wind variations. We also discuss strategic and tactical methods for managing congestion at airports, including the use of slot controls, ground holding programs, runway configuration changes and aircraft sequencing policies

Quantifying and reducing Input modelling error in simulation

This thesis presents new methodology in the field of quantifying and reducing input modelling error in computer simulation. Input modelling error is the uncertainty in the output of a simulation that propagates from the errors in the input models used to drive it. When the input models are estimated from observations of the real-world system input modelling error will always arise as only a finite number of observations can ever be collected. Input modelling error can be broken down into two components: variance, known in the literature as input uncertainty; and bias. In this thesis new methodology is contributed for the quantification of both of these sources of error. To date research into input modelling error has been focused on quantifying the input uncertainty (IU) variance. In this thesis current IU quantification techniques for simulation models with time homogeneous inputs are extended to simulation models with nonstationary input processes. Unlike the IU variance, the bias caused by input modelling has, until now, been virtually ignored. This thesis provides the first method for quantifying bias caused by input modelling. Also presented is a bias detection test for identifying, with controlled power, a bias due to input modelling of a size that would be concerning to a practitioner. The final contribution of this thesis is a spline-based arrival process model. By utilising a highly flexible spline representation, the error in the input model is reduced; it is believed that this will also reduce the input modelling error that passes to the simulation output. The methods described in this thesis are not available in the current literature and can be used in a wide range of simulation contexts for quantifying input modelling error and modelling input processes

Applications of stochastic modeling in air traffic management : Methods, challenges and opportunities for solving air traffic problems under uncertainty

In this paper we provide a wide-ranging review of the literature on stochastic modeling applications within aviation, with a particular focus on problems involving demand and capacity management and the mitigation of air traffic congestion. From an operations research perspective, the main techniques of interest include analytical queueing theory, stochastic optimal control, robust optimization and stochastic integer programming. Applications of these techniques include the prediction of operational delays at airports, pre-tactical control of aircraft departure times, dynamic control and allocation of scarce airport resources and various others. We provide a critical review of recent developments in the literature and identify promising research opportunities for stochastic modelers within air traffic management

Doubly Stochastic Generative Arrivals Modeling

We propose a new framework named DS-WGAN that integrates the doubly stochastic (DS) structure and the Wasserstein generative adversarial networks (WGAN) to model, estimate, and simulate a wide class of arrival processes with general non-stationary and random arrival rates. Regarding statistical properties, we prove consistency and convergence rate for the estimator solved by the DS-WGAN framework under a non-parametric smoothness condition. Regarding computational efficiency and tractability, we address a challenge in gradient evaluation and model estimation, arised from the discontinuity in the simulator. We then show that the DS-WGAN framework can conveniently facilitate what-if simulation and predictive simulation for future scenarios that are different from the history. Numerical experiments with synthetic and real data sets are implemented to demonstrate the performance of DS-WGAN. The performance is measured from both a statistical perspective and an operational performance evaluation perspective. Numerical experiments suggest that, in terms of performance, the successful model estimation for DS-WGAN only requires a moderate size of representative data, which can be appealing in many contexts of operational management.Comment: updated version with more explanatory figure

Scaling limits for infinite-server systems in a random environment

This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate $\Lambda$ from a given distribution every $\Delta$ time units, yielding an i.i.d. sequence of arrival rates $\Lambda_1,\Lambda_2, \ldots$. Applying a martingale central limit theorem, we obtain a functional central limit theorem for the scaled queue length process. We proceed to large deviations and derive the logarithmic asymptotics of the queue length's tail probabilities. As it turns out, in a rapidly changing environment (i.e., $\Delta$ is small relative to $\Lambda$) the overdispersion of the arrival process hardly affects system behavior, whereas in a slowly changing random environment it is fundamentally different; this general finding applies to both the central limit and the large deviations regime. We extend our results to the setting where each arrival creates a job in multiple infinite-server queues

Everyone\u27s a Waiter: A Data-Driven Queuing Simulation Model of Mike\u27s Clam Shack

This thesis seeks to understand the mathematical foundation of several prominent concepts in queuing theory and apply them to gain a better understanding of nightly business levels and dining room queue behavior during the summer tourist season at Mike’s Clam Shack, which is a restaurant located in Wells, Maine. To do so, a variety of queue and server section data has been collected from Mike’s and analyzed to determine probability distributions for interarrival and service times. In addition, a queuing simulation model has been constructed in the R Programming Language, which uses this data to generate dining room and queue activity on a given month and week day. Suggestions for improving the model’s authenticity are also provided