scholarly journals An optimized continuous fractional grey model for forecasting of the time dependent real world cases

2021 ◽  
pp. 1-19
Author(s):  
Zafer ÖZTÜRK ◽  
Halis BİLGİL ◽  
Ümmügülsüm ERDİNÇ
Keyword(s):  
Real World ◽  
Time Dependent ◽  
Grey Model

Performance Approximation for Time-Dependent Queues with Generally Distributed Abandonments

2021 ◽  
Author(s):  
Gregor Selinka ◽  
Raik Stolletz ◽  
Thomas I. Maindl
Keyword(s):  
Performance Measures ◽  
Real World ◽  
Queueing System ◽  
Time Dependent ◽  
Interval Length ◽  
Arrival Process ◽  
Real World Data ◽  
World Data ◽  
Extant Literature ◽  
Approximation Quality

Many stochastic systems face a time-dependent demand. Especially in stochastic service systems, for example, in call centers, customers may leave the queue if their waiting time exceeds their personal patience. As discussed in the extant literature, it can be useful to use general distributions to model such customer patience. This paper analyzes the time-dependent performance of a multiserver queue with a nonhomogeneous Poisson arrival process with a time-dependent arrival rate, exponentially distributed processing times, and generally distributed time to abandon. Fast and accurate performance approximations are essential for decision support in such queueing systems, but the extant literature lacks appropriate methods for the setting we consider. To approximate time-dependent performance measures for small- and medium-sized systems, we develop a new stationary backlog-carryover (SBC) approach that allows for the analysis of underloaded and overloaded systems. Abandonments are considered in two steps of the algorithm: (i) in the approximation of the utilization as a reduced arrival stream and (ii) in the approximation of waiting-based performance measures with a stationary model for general abandonments. To improve the approximation quality, we discuss an adjustment to the interval lengths. We present a limit result that indicates convergence of the method for stationary parameters. The numerical study compares the approximation quality of different adjustments to the interval length. The new SBC approach is effective for instances with small numbers of time-dependent servers and gamma-distributed abandonment times with different coefficients of variation and for an empirical distribution of the abandonment times from real-world data obtained from a call center. A discrete-event simulation benchmark confirms that the SBC algorithm approximates the performance of the queueing system with abandonments very well for different parameter configurations. Summary of Contribution: The paper presents a fast and accurate numerical method to approximate the performance measures of a time‐dependent queueing system with generally distributed abandonments. The presented stationary backlog carryover approach with abandonment combines algorithmic ideas with stationary queueing models for generally distributed abandonment times. The reliability of the method is analyzed for transient systems and numerically studied with real‐world data.

scholarly journals Antagonistic One-To-N Stochastic Duel Game

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1114 ◽  
Author(s):  
Song-Kyoo (Amang) Kim
Keyword(s):  
Real World ◽  
Payoff Function ◽  
Marketing Strategies ◽  
Time Dependent ◽  
Random Time ◽  
Game Model ◽  
Explicit Formulas ◽  
Entry Timing ◽  
The One ◽  
Person Game

This paper is dealing with a multiple person game model under the antagonistic duel type setup. The unique multiple person duel game with the one-shooting-to-kill-all condition is analytically solved and the explicit formulas are obtained to determine the time dependent duel game model by using the first exceed theory. The model could be directly applied into real-world situations and an analogue of the theory in the paper is designed for solving the best shooting time for hitting all other players at once which optimizes the payoff function under random time conditions. It also mathematically explains to build the marketing strategies for the entry timing for both blue and red ocean markets.

scholarly journals Generating spatial precipitation ensembles: impact of temporal correlation structure

2012 ◽  
Vol 16 (9) ◽  
pp. 3419-3434 ◽  
Author(s):  
O. Rakovec ◽  
P. Hazenberg ◽  
P. J. J. F. Torfs ◽  
A. H. Weerts ◽  
R. Uijlenhoet
Keyword(s):  
Sensitivity Analysis ◽  
Real World ◽  
Temporal Correlation ◽  
Rain Gauge ◽  
Time Dependent ◽  
Spatial And Temporal Variability ◽  
Conditional Simulations ◽  
Hilly Region ◽  
Spatially Distributed ◽  
Precipitation Estimates

Abstract. Sound spatially distributed rainfall fields including a proper spatial and temporal error structure are of key interest for hydrologists to force hydrological models and to identify uncertainties in the simulated and forecasted catchment response. The current paper presents a temporally coherent error identification method based on time-dependent multivariate spatial conditional simulations, which are conditioned on preceding simulations. A sensitivity analysis and real-world experiment are carried out within the hilly region of the Belgian Ardennes. Precipitation fields are simulated for pixels of 10 km × 10 km resolution. Uncertainty analyses in the simulated fields focus on (1) the number of previous simulation hours on which the new simulation is conditioned, (2) the advection speed of the rainfall event, (3) the size of the catchment considered, and (4) the rain gauge density within the catchment. The results for a sensitivity analysis show for typical advection speeds >20 km h−1, no uncertainty is added in terms of across ensemble spread when conditioned on more than one or two previous hourly simulations. However, for the real-world experiment, additional uncertainty can still be added when conditioning on a larger number of previous simulations. This is because for actual precipitation fields, the dynamics exhibit a larger spatial and temporal variability. Moreover, by thinning the observation network with 50%, the added uncertainty increases only slightly and the cross-validation shows that the simulations at the unobserved locations are unbiased. Finally, the first-order autocorrelation coefficients show clear temporal coherence in the time series of the areal precipitation using the time-dependent multivariate conditional simulations, which was not the case using the time-independent univariate conditional simulations. The presented work can be easily implemented within a hydrological calibration and data assimilation framework and can be used as an improvement over currently used simplistic approaches to perturb the interpolated point or spatially distributed precipitation estimates.

scholarly journals Generating spatial precipitation ensembles: impact of temporal correlation structure

2012 ◽  
Vol 9 (3) ◽  
pp. 3087-3127 ◽  
Author(s):  
O. Rakovec ◽  
P. Hazenberg ◽  
P. J. J. F. Torfs ◽  
A. H. Weerts ◽  
R. Uijlenhoet
Keyword(s):  
Real World ◽  
Temporal Correlation ◽  
Rain Gauge ◽  
Time Dependent ◽  
Spatial And Temporal Variability ◽  
Conditional Simulations ◽  
Observation Network ◽  
Hilly Region ◽  
Spatially Distributed ◽  
Added Uncertainty

Abstract. Sound spatially distributed rainfall fields including a proper spatial and temporal error structure are of key interest for hydrologists to force hydrological models and to identify uncertainties in the simulated and forecasted catchment response. The current paper presents a temporal coherent error identification method based on time-dependent multivariate spatial conditional simulations, which are made further conditional on preceding simulations. Synthetic and real world experiments are carried out within the hilly region of the Belgian Ardennes. Precipitation fields are simulated for pixels of 10 × 10 km2 resolution. Uncertainty analyses in the simulated fields focus on (1) the number of previous simulation hours on which the new simulation is conditioned, (2) the advection speed of the rainfall event, (3) the size of the catchment considered, and (4) the rain gauge density within the catchment. The results for a synthetic experiment show for typical advection speeds of >20 km h−1, no uncertainty is added in terms of across ensemble spread when conditioned on more than one or two previous simulations. However, for the real world experiment, additional uncertainty can be still added when conditioning on a higher number of previous simulations. This is, because for actual precipitation fields, the dynamics exhibit a larger spatial and temporal variability. Moreover, by thinning the observation network with 50%, the added uncertainty increases only slightly. Finally, the first order autocorrelation coefficients show clear temporal coherence in the time series of the areal precipitation using the time-dependent multivariate conditional simulations, which was not the case using the time-independent univariate conditional simulations.

scholarly journals Real-World Implications of a Rapidly Responsive COVID-19 Spread Model with Time-Dependent Parameters via Deep Learning: Model Development and Validation

10.2196/19907 ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. e19907 ◽  
Author(s):  
Se Young Jung ◽  
Hyeontae Jo ◽  
Hwijae Son ◽  
Hyung Ju Hwang
Keyword(s):  
Deep Learning ◽  
Real World ◽  
Influenza Pandemic ◽  
The United States ◽  
Sir Model ◽  
Time Dependent ◽  
Systems Science ◽  
Model Parameters ◽  
Viral Spread ◽  
Spread Model

Background The COVID-19 pandemic has caused major disruptions worldwide since March 2020. The experience of the 1918 influenza pandemic demonstrated that decreases in the infection rates of COVID-19 do not guarantee continuity of the trend. Objective The aim of this study was to develop a precise spread model of COVID-19 with time-dependent parameters via deep learning to respond promptly to the dynamic situation of the outbreak and proactively minimize damage. Methods In this study, we investigated a mathematical model with time-dependent parameters via deep learning based on forward-inverse problems. We used data from the Korea Centers for Disease Control and Prevention (KCDC) and the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University for Korea and the other countries, respectively. Because the data consist of confirmed, recovered, and deceased cases, we selected the susceptible-infected-recovered (SIR) model and found approximated solutions as well as model parameters. Specifically, we applied fully connected neural networks to the solutions and parameters and designed suitable loss functions. Results We developed an entirely new SIR model with time-dependent parameters via deep learning methods. Furthermore, we validated the model with the conventional Runge-Kutta fourth order model to confirm its convergent nature. In addition, we evaluated our model based on the real-world situation reported from the KCDC, the Korean government, and news media. We also crossvalidated our model using data from the CSSE for Italy, Sweden, and the United States. Conclusions The methodology and new model of this study could be employed for short-term prediction of COVID-19, which could help the government prepare for a new outbreak. In addition, from the perspective of measuring medical resources, our model has powerful strength because it assumes all the parameters as time-dependent, which reflects the exact status of viral spread.

scholarly journals Exact Time-Dependent Queue-Length Solution to a Discrete-Time Geo/D/1 Queue

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 717
Author(s):  
Jung Woo Baek ◽  
Yun Han Bae
Keyword(s):  
Closed Form ◽  
Discrete Time ◽  
Real World ◽  
Queue Length ◽  
Service Systems ◽  
Time Dependent ◽  
World Systems ◽  
Exact Time ◽  
Queuing Models

Time-dependent solutions to queuing models are beneficial for evaluating the performance of real-world systems such as communication, transportation, and service systems. However, restricted results have been reported due to mathematical complexity. In this study, we present a time-dependent queue-length formula for a discrete-time G e o / D / 1 queue starting with a positive number of initial customers. We derive the time-dependent formula in closed form.

Online Learning for Linear Programming with Time-Dependent Cost

2011 ◽  
Vol 230-232 ◽  
pp. 793-797
Author(s):  
Wei Li ◽  
Chong Yang Deng
Keyword(s):  
Machine Learning ◽  
Linear Programming ◽  
Online Learning ◽  
Real World ◽  
Time Dependent ◽  
Programming Models ◽  
Intelligent Optimization ◽  
Learning Parameter ◽  
Real World Problems

Machine learning and linear programming with time dependent cost are two popular intelligent optimization tools to handle uncertainty in real world problems. Thus, combining these two technologies is quite attractive. This paper proposed an effective framework to deal with uncertainty in practice, based on combing introducing learning parameter into linear programming models.

Cost-Optimal Time-dEpendent Routing with Time and Speed Constraints in Directed Acyclic Road Networks

2016 ◽  
Vol 15 (06) ◽  
pp. 1413-1450
Author(s):  
Yaqiong Liu ◽  
Hock Soon Seah ◽  
Guochu Shou
Keyword(s):  
Travel Time ◽  
Nonlinear Optimization ◽  
Fuel Consumption ◽  
Real World ◽  
Computer Games ◽  
Road Networks ◽  
Minimum Cost ◽  
Time Dependent ◽  
Optimal Time ◽  
Step Algorithm

Travel costs on road networks always change over time which implies road networks are time dependent. Most studies on time-dependent road networks simply find the shortest path with the least travel time without considering waiting at some nodes, or fuel consumption and toll fee. In real-world applications or computer games, waiting may be allowed at some nodes but disallowed at other nodes; a user can traverse an edge at different speeds; monetary travel cost contains fuel cost and toll fees; and users usually prefer the minimum-cost route under time and speed constraints. Therefore, we study Cost-Optimal Time-dEpendent Routing (COTER) problem with time and speed constraints. We utilize two fuel consumption models and compute the minimum fuel consumption with given travel time for highway edges via nonlinear optimization. We allow the toll fee function to be an arbitrary single-valued time-dependent function. We define an Optimal Cost (OC) function for each candidate node [Formula: see text], and derive the recurrence relation formula between [Formula: see text]’s incoming neighbors’ OC-functions and [Formula: see text]’s OC-functions. To solve COTER, we propose a five-step algorithm, namely, ALG-COTER, which uses Fibonacci-heap optimized Dijkstra, topological sorting, dynamic programming, binary min-heap optimization, nonlinear optimization, and backtracking algorithms. Experimental results on three real-world road networks of different sizes demonstrate that our algorithm finds the optimal route efficiently and is scalable to different parameters.

scholarly journals Using Congestion Zones for Solving the Time Dependent Vehicle Routing Problem

2020 ◽  
Vol 32 (1) ◽  
pp. 25-38 ◽  
Author(s):  
Tonči Carić ◽  
Juraj Fosin
Keyword(s):  
Vehicle Routing ◽  
Real World ◽  
Vehicle Routing Problem ◽  
Time Delays ◽  
Historical Data ◽  
Time Dependent ◽  
Routing Problem ◽  
Real World Problem ◽  
Independent Case ◽  
Real World Problems

This paper provides a framework for solving the Time Dependent Vehicle Routing Problem (TDVRP) by using historical data. The data are used to predict travel times during certain times of the day and derive zones of congestion that can be used by optimization algorithms. A combination of well-known algorithms was adapted to the time dependent setting and used to solve the real-world problems. The adapted algorithm outperforms the best-known results for TDVRP benchmarks. The proposed framework was applied to a real-world problem and results show a reduction in time delays in serving customers compared to the time independent case.

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