1,067 research outputs found
A Spatio-Temporal Point Process Model for Ambulance Demand
Ambulance demand estimation at fine time and location scales is critical for
fleet management and dynamic deployment. We are motivated by the problem of
estimating the spatial distribution of ambulance demand in Toronto, Canada, as
it changes over discrete 2-hour intervals. This large-scale dataset is sparse
at the desired temporal resolutions and exhibits location-specific serial
dependence, daily and weekly seasonality. We address these challenges by
introducing a novel characterization of time-varying Gaussian mixture models.
We fix the mixture component distributions across all time periods to overcome
data sparsity and accurately describe Toronto's spatial structure, while
representing the complex spatio-temporal dynamics through time-varying mixture
weights. We constrain the mixture weights to capture weekly seasonality, and
apply a conditionally autoregressive prior on the mixture weights of each
component to represent location-specific short-term serial dependence and daily
seasonality. While estimation may be performed using a fixed number of mixture
components, we also extend to estimate the number of components using
birth-and-death Markov chain Monte Carlo. The proposed model is shown to give
higher statistical predictive accuracy and to reduce the error in predicting
EMS operational performance by as much as two-thirds compared to a typical
industry practice
Forecasting emergency medical service call arrival rates
We introduce a new method for forecasting emergency call arrival rates that
combines integer-valued time series models with a dynamic latent factor
structure. Covariate information is captured via simple constraints on the
factor loadings. We directly model the count-valued arrivals per hour, rather
than using an artificial assumption of normality. This is crucial for the
emergency medical service context, in which the volume of calls may be very
low. Smoothing splines are used in estimating the factor levels and loadings to
improve long-term forecasts. We impose time series structure at the hourly
level, rather than at the daily level, capturing the fine-scale dependence in
addition to the long-term structure. Our analysis considers all emergency
priority calls received by Toronto EMS between January 2007 and December 2008
for which an ambulance was dispatched. Empirical results demonstrate
significantly reduced error in forecasting call arrival volume. To quantify the
impact of reduced forecast errors, we design a queueing model simulation that
approximates the dynamics of an ambulance system. The results show better
performance as the forecasting method improves. This notion of quantifying the
operational impact of improved statistical procedures may be of independent
interest.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS442 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
IDENTIFYING EFFECTIVE POLICIES IN APPROXIMATE DYNAMIC PROGRAMMING: BEYOND REGRESSION
ABSTRACT Dynamic programming formulations may be used to solve for optimal policies in Markov decision processes. Due to computational complexity dynamic programs must often be solved approximately. We consider the case of a tunable approximation architecture used in lieu of computing true value functions. The standard methodology advocates tuning the approximation architecture via sample path information and regression to get a good fit to the true value function. We provide an example which shows that this approach may unnecessarily lead to poorly performing policies and suggest direct search methods to find better performing value function approximations. We illustrate this concept with an application from ambulance redeployment
Call Center Staffing with Simulation and Cutting Plane Methods
We present an iterative cutting plane method for minimizing staffing costs in a service system subject to satisfying acceptable service level requirements over multiple time periods. We assume that the service level cannot be easily computed, and instead is evaluated using simulation. The simulation uses the method of common random numbers, so that the same sequence of random phenomena is observed when evaluating different staffing plans. In other words, we solve a sample average approximation problem. We establish convergence of the cutting plane method on a given sample average approximation. We also establish both convergence, and the rate of convergence, of the solutions to the sample average approximation to solutions of the original problem as the sample size increases. The cutting plane method relies on the service level functions being concave in the number of servers. We show how to verify this requirement as our algorithm proceeds. A numerical example showcases the properties of our method, and sheds light on when the concavity requirement can be expected to hold.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44119/1/10479_2004_Article_5255891.pd
- …