Phase-type distributions and their applications to the vehicle routing problem with stochastic travel and service times

International audienceThe vehicle routing problem with stochastic travel and service times (VRPSTT) consists in designing routes of minimal expected cost over a network where travel and service times are represented by random variables. Most of the existing approaches for VRPSTT are conceived to exploit the properties of the distributions assumed for the random variables. Therefore, these methods are tied to a given family of distributions and subject to strong modeling assumptions. We propose an alternative way to model travel and service times in VRPSTT while making few assumptions regarding such distributions. To illustrate our approach, we embed it into a state-of-the-art routing engine and use it to conduct experiments on instances with dierent travel and service time distributions

A Markov regime-switching framework to forecast El Niño Southern Oscillation patterns

International audienceThe El Niño-Southern Oscillation (ENSO) is an ocean-atmosphere phenomenon involving sustained sea surface temperature fluctuations in the Pacific Ocean, causing disruptions in the behavior of the ocean and atmosphere. We develop a Markov switching autoregressive model to describe the Southern Oscillation Index (SOI), a variable that explains ENSO, using two autoregressive processes to describe the time evolution of SOI, each of which associated with a specific phase of ENSO. The switching between these two models is governed by a discrete time Markov chain (DTMC), with time-varying transition probabilities. Then, we extend the model using sinusoidal functions to forecast future values of SOI. The results can be used as a decision-making tool in the process of risk mitigation against weather and climate related disasters

A decade of air quality in Bogotá: a descriptive analysis

In this work we apply a rigorous and reproducible data analytics process for validation and analysis of the historical data from Bogotá (Colombia) air quality monitoring network since 1998. The reasons for addressing this research study stem from the lack of a consistent approach for cleaning, validating and reporting air quality data. By analyzing the whole dataset, we are aiming at providing citizens and the city authorities with a clear view of the current situation of air quality and of its historical evolution. Without any loss of generality, we focus our analysis on both respirable and fine particulate matter (PM10 and PM2.5) concentrations, which in Bogotá and worldwide are source of concern for their negative impacts on human health. We develop a reproducible and flexible data cleaning methodology for particulate matter concentration data reported by the local authorities, which allows customizing and applying configurable validation rules. Then, we present statistical descriptive analyses by providing intuitive data visualizations, characterizing historical and spatial change of air pollutant levels. Results raise concerns for the high percentage of invalid data, as well as the high levels of PM2.5 and PM10 ambient concentrations as observed in the valid portion of the available data, which frequently exceed national and international air quality standards. The data exhibit encouraging signs of air quality improvement, particularly for PM10. However, the analyses indicate that significant differences exist across Bogotá, and particularly in the south-west zone of the city annual concentrations of particulate matter are up to three or four times the WHO recommendations. We are confident on the methodology and results from our analysis are useful both for local environmental authority and the general public to help in obtaining consistent conclusions from the available data

aiRe - a web-based R application for simple, accessible and repeatable analysis of urban air quality data

Recent technological advances in collecting data on emission sources, meteorological conditions and concentration of air pollutants in urban areas, offer invaluable opportunities for the better understanding of air quality problems. However, processing large sets of data to extract statistically valid evidence poses many challenges from both the conceptual and technical viewpoints. Air quality data acquisition, cleaning and authentication are necessary and crucial preliminary phases to support descriptive, predictive and prescriptive models and to ensure that aggregated and high-quality information is delivered to the central and local governments, decision makers and citizens. Automated software tools can facilitate drawing conclusions based on the information contained in the data, limiting subjective judgment and providing repeatability. However, the costly state-of-the-art software applications developed by major vendors are inaccessible to many cities and townships in the developing world. Moreover, their usage creates dependency on proprietary solutions, which can hinder the possibility of evolving the data processing and analysis protocols. We present an open-source web application for air quality data analysis and visualization, called aiRe, based on the R statistical framework and Shiny web package. aiRe has been developed in collaboration with the Colombian environmental authorities, and implements best practices validated by experts in air quality. We believe that the process of developing aiRe was extremely valuable with the ultimate purpose of supporting cities in air quality management, while strengthening local capabilities to improve urban air pollution. This open-access tool simplifies and makes air quality data analysis and visualization accessible, with the desirable effect of removing ownership costs, fostering appropriation by non-expert users and ultimately promoting informed decision-making for the general public and the local government authorities. We present the performance of this tool over a series of examples of open data collected by the air quality monitoring network of Bogota, Colombia

On the shortest alpha-reliable path problem

In this variant of the constrained shortest path problem, the time of traversing an arc is given by a non-negative continuous random variable. The problem is to find a minimum cost path from an origin to a destination, ensuring that the probability of reaching the destination within a time limit meets a certain reliability threshold. To solve this problem, we extend the pulse algorithm, a solution framework for short- est path problems with side constraints. To allow arbitrary non-negative continuous travel-time distributions, we model the random variables of the travel times using Phase-type distributions and Monte Carlo simulation. We conducted a set of experi- ments over small- and medium-size stochastic transportation networks with and without spatially-correlated travel times. As an alternative to handling correlations, we present a scenario-based approach in which the distributions of the arc travel times are conditioned to a given scenario (e.g., variable weather conditions). Our methodology and experiments highlight the relevance of considering on-time arrival probabilities and correlations when solving shortest path problems over stochastic transportation networks

Estimating the parameters of mixed shifted negative binomial distributions via an EM algorithm

Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show it

Classification and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions

Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have received less attention in the literature. In this paper, we present the definition, properties, characteristics and PH representations of ADPH distributions and their subclasses with finite state space. Based on the definitions of geometric and shifted geometric distributions, we propose a distinct classification for the ADPH subclasses analogous to ACPH family. We develop the PH representation for each ADPH subclass and prove them through their closure properties. The advantage of our proposed classifications is in applying precise representations of each subclass and preventing miscalculation of the probability mass function, by computing the ADPH family based on geometric and shifted geometric distributions

Personalized cotesting policies for cervical cancer screening: a POMDP approach

Screening for cervical cancer is a critical policy that requires clinical and managerial vigilance because of its serious health consequences. Recently the practice of conducting simultaneous tests of cytology and Human Papillomavirus (HPV)-DNA testing (known as cotesting) has been included in the public health policies and guidelines with a fixed frequency. On the other hand, personalizing medical interventions by incorporating patient characteristics into the decision making process has gained considerable attention in recent years. We develop a personalized partially observable Markov decision process (POMDP) model for cervical cancer screening decisions by cotesting. In addition to the merits offered by the guidelines, by availing the possibility of including patient-specific risks and other attributes, our POMDP model provides a patient-tailored screening plan. Our results show that the policy generated by the POMDP model outperforms the static guidelines in terms of quality-adjusted life years (QALY) gain, while performing comparatively equal in lifetime risk reduction

Results on a Binding Neuron Model and Their Implications for Modified Hourglass Model for Neuronal Network

The classical models of single neuron like Hodgkin-Huxley point neuron or leaky integrate and fire neuron assume the influence of postsynaptic potentials to last till the neuron fires. Vidybida (2008) in a refreshing departure has proposed models for binding neurons in which the trace of an input is remembered only for a finite fixed period of time after which it is forgotten. The binding neurons conform to the behaviour of real neurons and are applicable in constructing fast recurrent networks for computer modeling. This paper develops explicitly several useful results for a binding neuron like the firing time distribution and other statistical characteristics. We also discuss the applicability of the developed results in constructing a modified hourglass network model in which there are interconnected neurons with excitatory as well as inhibitory inputs. Limited simulation results of the hourglass network are presented

Copula autoregressive methodology for the simulation of wind speed and direction time series

In this paper we present a methodology for synthetic generation of wind speed and direction bivariate time series based on copula functions to represent the temporal and cross-dependence structure. We explore the advantages of using this nonlinear time series method over more traditional approaches that use a transformation to normal distributions as an intermediate step. The use of copulas gives some flexibility to represent the serial variability of the real data on the simulation, besides allowing more control on the desired properties of the data. Empirical Bernstein copulas were used to consider the circular nature of wind direction. Experimental analysis and real data application prove the usability and convenience of the proposed methodology