scholarly journals Non-Parametric Stochastic Sequential Assignment With Random Arrival Times

2021 ◽  
Author(s):  
Danial Dervovic ◽  
Parisa Hassanzadeh ◽  
Samuel Assefa ◽  
Prashant Reddy
Keyword(s):  
Decision Maker ◽  
Synthetic Data ◽  
Arrival Process ◽  
Sequential Assignment ◽  
Arrival Times ◽  
Reference Time ◽  
Time Period ◽  
Sequential Allocation ◽  
Random Times ◽  
Non Parametric

We consider a problem wherein jobs arrive at random times and assume random values. Upon each job arrival, the decision-maker must decide immediately whether or not to accept the job and gain the value on offer as a reward, with the constraint that they may only accept at most n jobs over some reference time period. The decision-maker only has access to M independent realisations of the job arrival process. We propose an algorithm, Non-Parametric Sequential Allocation (NPSA), for solving this problem. Moreover, we prove that the expected reward returned by the NPSA algorithm converges in probability to optimality as M grows large. We demonstrate the effectiveness of the algorithm empirically on synthetic data and on public fraud-detection datasets, from where the motivation for this work is derived.

Expectations and variances of stopping variables in sequential selection processes

1973 ◽  
Vol 10 (04) ◽  
pp. 786-806
Author(s):  
M. Henke
Keyword(s):  
Decision Maker ◽  
Decision Process ◽  
Random Variables ◽  
Independent Random Variables ◽  
Selection Processes ◽  
Time Period ◽  
Sequential Selection ◽  
Random Times

A sequential stochastic decision process with independent random variables is considered in which the decision maker selects a chance with a certain probability at each time period or at random times. If the decision maker has selected m chances, the process has to be stopped. The expectation and the variance of the stopping variable are determined for a finite and an infinite decision horizon.

Expectations and variances of stopping variables in sequential selection processes

1973 ◽  
Vol 10 (4) ◽  
pp. 786-806 ◽  
Author(s):  
M. Henke
Keyword(s):  
Decision Maker ◽  
Decision Process ◽  
Random Variables ◽  
Independent Random Variables ◽  
Selection Processes ◽  
Time Period ◽  
Sequential Selection ◽  
Random Times

A sequential stochastic decision process with independent random variables is considered in which the decision maker selects a chance with a certain probability at each time period or at random times. If the decision maker has selected m chances, the process has to be stopped. The expectation and the variance of the stopping variable are determined for a finite and an infinite decision horizon.

scholarly journals On the saturation rule for the stability of queues

1995 ◽  
Vol 32 (02) ◽  
pp. 494-507 ◽  
Author(s):  
François Baccelli ◽  
Serguei Foss
Keyword(s):  
Queueing Networks ◽  
Stability Region ◽  
Queueing Systems ◽  
Main Tool ◽  
Stationary Regime ◽  
Arrival Process ◽  
State Variables ◽  
Arrival Times ◽  
Harris Recurrence ◽  
The Stability

This paper focuses on the stability of open queueing systems under stationary ergodic assumptions. It defines a set of conditions, the monotone separable framework, ensuring that the stability region is given by the following saturation rule: ‘saturate' the queues which are fed by the external arrival stream; look at the ‘intensity' μ of the departure stream in this saturated system; then stability holds whenever the intensity of the arrival process, say λ satisfies the condition λ < μ, whereas the network is unstable if λ > μ. Whenever the stability condition is satisfied, it is also shown that certain state variables associated with the network admit a finite stationary regime which is constructed pathwise using a Loynes-type backward argument. This framework involves two main pathwise properties, external monotonicity and separability, which are satisfied by several classical queueing networks. The main tool for the proof of this rule is subadditive ergodic theory. It is shown that, for various problems, the proposed method provides an alternative to the methods based on Harris recurrence and regeneration; this is particularly true in the Markov case, where we show that the distributional assumptions commonly made on service or arrival times so as to ensure Harris recurrence can in fact be relaxed.

A study on the arrival process of lift passengers in a multi-storey office building

2011 ◽  
Vol 33 (4) ◽  
pp. 437-449 ◽  
Author(s):  
J-M Kuusinen ◽  
J Sorsa ◽  
M-L Siikonen ◽  
H Ehtamo
Keyword(s):  
Poisson Process ◽  
Time Of Day ◽  
Office Building ◽  
Arrival Process ◽  
Batch Arrivals ◽  
Arrival Times ◽  
Piecewise Constant ◽  
Practical Applications ◽  
Video Recordings ◽  
Traffic Simulations

This article presents a study on the process of how passengers arrive at lift lobbies to travel to their destinations. Earlier studies suggest that passengers arrive at the lift lobbies individually with exponentially distributed inter-arrival times, that is, according to a Poisson process. This study was carried out in a multi-storey office building. The data was collected using a questionnaire, digital video recordings and the lift monitoring system. The results show that, in the studied building, passengers arrive in batches whose size varies with the time of day and the floor utilization. In addition, the batch arrivals follow a time-inhomogeneous Poisson process with piecewise constant arrival rates. Practical applications: This article contributes to the basic understanding of passenger behaviour, and how people move around in buildings and arrive at the lift lobbies. It is proposed that the model for the passenger arrival process should take into account that passengers do not always arrive individually but also in batches. The passenger arrival process affects the design of elevators. It will also affect the passenger generation in building traffic simulations.

The diminishing residual matrices method for surface-consistent statics — A review

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. V257-V274
Author(s):  
Necati Gülünay
Keyword(s):  
Synthetic Data ◽  
Reconstruction Technique ◽  
Data Set ◽  
Arrival Times ◽  
Long Wavelength ◽  
Iterative Reconstruction Technique ◽  
Land Survey ◽  
First Arrival ◽  
Waveform Distortions ◽  
The Individual

The diminishing residual matrices (DRM) method can be used to surface-consistently decompose individual trace statics into source and receiver components. The statics to be decomposed may either be first-arrival times after the application of linear moveout associated with a consistent refractor as used in refraction statics or residual statics obtained by crosscorrelating individual traces with corresponding model traces (known as pilot traces) at the same common-midpoint (CMP) location. The DRM method is an iterative process like the well-known Gauss-Seidel (GS) method, but it uses only source and receiver terms. The DRM method differs from the GS method in that half of the average common shot and receiver terms are subtracted simultaneously from the observations at each iteration. DRM makes the under-constrained statics problem a constrained one by implicitly adding a new constraint, the equality of the contribution of shots and receivers to the solution. The average of the shot statics and the average of the receiver statics are equal in the DRM solution. The solution has the smallest difference between shot and receiver statics profiles when the number of shots and the number of receivers in the data are equal. In this case, it is also the smallest norm solution. The DRM method can be derived from the well-known simultaneous iterative reconstruction technique. Simple numerical tests as well as results obtained with a synthetic data set containing only the field statics verify that the DRM solution is the same as the linear inverse theory solution. Both algorithms can solve for the long-wavelength component of the statics if the individual picks contain them. Yet DRM method is much faster. Application of the method to the normal moveout-corrected CMP gathers on a 3D land survey for residual statics calculation found that pick-decompose-apply-stack stages of the DRM method need to be iterated. These iterations are needed because of time and waveform distortions of the pilot traces due to the individual trace statics. The distortions lessen at every external DRM iteration.

scholarly journals Variational Inference for Sparse Gaussian Process Modulated Hawkes Process

2020 ◽  
Vol 34 (04) ◽  
pp. 6803-6810
Author(s):  
Rui Zhang ◽  
Christian Walder ◽  
Marian-Andrei Rizoiu
Keyword(s):  
Model Selection ◽  
Gaussian Process ◽  
Linear Time ◽  
Expectation Maximization Algorithm ◽  
Synthetic Data ◽  
Variational Inference ◽  
Hawkes Process ◽  
Prediction Confidence ◽  
Inference Schema ◽  
Non Parametric

The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the non-parametric Bayesian HP has been proposed. However, the inference of such models suffers from unscalability or slow convergence. In this paper, we aim to solve both problems. Specifically, first, we propose a new non-parametric Bayesian HP in which the triggering kernel is modeled as a squared sparse Gaussian process. Then, we propose a novel variational inference schema for model optimization. We employ the branching structure of the HP so that maximization of evidence lower bound (ELBO) is tractable by the expectation-maximization algorithm. We propose a tighter ELBO which improves the fitting performance. Further, we accelerate the novel variational inference schema to linear time complexity by leveraging the stationarity of the triggering kernel. Different from prior acceleration methods, ours enjoys higher efficiency. Finally, we exploit synthetic data and two large social media datasets to evaluate our method. We show that our approach outperforms state-of-the-art non-parametric frequentist and Bayesian methods. We validate the efficiency of our accelerated variational inference schema and practical utility of our tighter ELBO for model selection. We observe that the tighter ELBO exceeds the common one in model selection.

scholarly journals Deep Quality Assessment of a Solar Reflector Based on Synthetic Data: Detecting Surficial Defects from Manufacturing and Use Phase

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5481
Author(s):  
Alexios Papacharalampopoulos ◽  
Konstantinos Tzimanis ◽  
Kyriakos Sabatakakis ◽  
Panagiotis Stavropoulos
Keyword(s):  
Quality Assessment ◽  
Computer Aided Design ◽  
Synthetic Data ◽  
Small Time ◽  
Self Monitoring ◽  
Time Period ◽  
Surface Irregularities ◽  
Reflector Surface ◽  
Aided Design ◽  
Full Utilization

Vision technologies are used in both industrial and smart city applications in order to provide advanced value products due to embedded self-monitoring and assessment services. In addition, for the full utilization of the obtained data, deep learning is now suggested for use. To this end, the current work presents the implementation of image recognition techniques alongside the original the quality assessment of a Parabolic Trough Collector (PTC) reflector surface to locate and identify surface irregularities by classifying images as either acceptable or non-acceptable. The method consists of a three-step solution that promotes an affordable implementation in a relatively small time period. More specifically, a 3D Computer Aided Design (CAD) of the PTC was used for the pre-training of neural networks, while an aluminum reflector surface was used to verify algorithm performance. The results are promising, as this method proved applicable in cases where the actual part was manufactured in small batches or under the concept of customized manufacturing. Consequently, the algorithm is capable of being trained with a limited number of data.

Improving crosshole radar velocity tomograms: A new approach to incorporating high-angle traveltime data

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. J31-J41 ◽  
Author(s):  
James D. Irving ◽  
Michael D. Knoll ◽  
Rosemary J. Knight
Keyword(s):  
Synthetic Data ◽  
High Angle ◽  
Data Set ◽  
Tomographic Images ◽  
Arrival Times ◽  
Angle Data ◽  
Automatic Picking ◽  
Velocity Images ◽  
First Arrival ◽  
Ground Penetrating

To obtain the highest-resolution ray-based tomographic images from crosshole ground-penetrating radar (GPR) data, wide angular ray coverage of the region between the two boreholes is required. Unfortunately, at borehole spacings on the order of a few meters, high-angle traveltime data (i.e., traveltime data corresponding to transmitter-receiver angles greater than approximately 50° from the horizontal) are notoriously difficult to incorporate into crosshole GPR inversions. This is because (1) low signal-to-noise ratios make the accurate picking of first-arrival times at high angles extremely difficult, and (2) significant tomographic artifacts commonly appear when high- and low-angle ray data are inverted together. We address and overcome thesetwo issues for a crosshole GPR data example collected at the Boise Hydrogeophysical Research Site (BHRS). To estimate first-arrival times on noisy, high-angle gathers, we develop a robust and automatic picking strategy based on crosscorrelations, where reference waveforms are determined from the data through the stacking of common-ray-angle gathers. To overcome incompatibility issues between high- and low-angle data, we modify the standard tomographic inversion strategy to estimate, in addition to subsurface velocities, parameters that describe a traveltime ‘correction curve’ as a function of angle. Application of our modified inversion strategy, to both synthetic data and the BHRS data set, shows that it allows the successful incorporation of all available traveltime data to obtain significantly improved subsurface velocity images.

scholarly journals Estimation of the Relative Arrival Time of Microseismic Events Based on Phase-Only Correlation

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2527 ◽  
Author(s):  
Peng Wang ◽  
Xu Chang ◽  
Xiyan Zhou
Keyword(s):  
Arrival Time ◽  
Linear Equations ◽  
Time Lag ◽  
Synthetic Data ◽  
Information Criterion ◽  
Peak Position ◽  
Arrival Times ◽  
Time Frequency ◽  
Microseismic Events ◽  
Microseismic Event

The arrival time of a microseismic event is an important piece of information for microseismic monitoring. The accuracy and efficiency of arrival time identification is affected by many factors, such as the low signal-to-noise ratio (SNR) of the records, the vast amount of real-time monitoring records, and the abnormal situations of monitoring equipment. In order to eliminate the interference of these factors, we propose a method based on phase-only correlation (POC) to estimate the relative arrival times of microseismic events. The proposed method includes three main steps: (1) The SNR of the records is improved via time-frequency transform, which is used to obtain the time-frequency representation of each trace of a microseismic event. (2) The POC functions of all pairs of time-frequency representations are calculated. The peak value of the POC function indicates the similarity of the traces, and the peak position in the time lag axis indicates the relative arrival times between the traces. (3) Using the peak values as weighting coefficients of the linear equations, consistency processing is used to exclude any abnormal situations and obtain the optimal relative arrival times. We used synthetic data and field data to validate the proposed method. Comparing with Akaike information criterion (AIC) and cross-correlation, the proposed method is more robust at estimating the relative arrival time and excluding the influence of abnormal situations.

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