An Optimal Threshold Policy in Applications of a Two-State Markov Process

2013 ◽  
pp. 203-219
Author(s):  
Eugene Khmelnitsky
Keyword(s):  
Markov Process ◽  
Optimal Threshold ◽  
Threshold Policy

scholarly journals A Threshold Policy for Dispatching Vehicles in Demand-responsive Transit Systems

2019 ◽  
Vol 31 (4) ◽  
pp. 387-395
Author(s):  
Nikola Marković ◽  
Myungseob (Edward) Kim ◽  
Eungcheol Kim ◽  
Sanjin Milinković
Keyword(s):  
Optimal Threshold ◽  
Time Varying ◽  
Threshold Policy ◽  
Transit System ◽  
Travel Mode ◽  
Transit Systems ◽  
Fleet Size ◽  
Vehicle Dispatching ◽  
Simulation Based ◽  
Demand Responsive Transit

This paper considers vehicle dispatching for a flexible transit system providing doorstep services from a terminal. The problem is tackled with an easy-to-implement threshold policy, where an available vehicle is dispatched when the number of boarded passengers reaches or exceeds a certain threshold. A simulation-based approach is applied to find the threshold that minimizes the expected system-wide cost. Results show that the optimal threshold is a function of demand, which is commonly stochastic and time-varying. Consequently, the dispatching threshold should be adjusted for different times of the day. In addition, the simulation-based approach is used to simultaneously adjust dispatching threshold and fleet size. The proposed approach is the first work to analyse threshold dispatching policy. It could be used to help improve efficiency of flexible transit systems, and thereby make this sustainable travel mode more economical and appealing to users.

THE OPTIMAL ADMISSION THRESHOLD IN OBSERVABLE QUEUES WITH STATE DEPENDENT PRICING

2013 ◽  
Vol 28 (1) ◽  
pp. 101-119 ◽  
Author(s):  
Christian Borgs ◽  
Jennifer T. Chayes ◽  
Sherwin Doroudi ◽  
Mor Harchol-Balter ◽  
Kuang Xu
Keyword(s):  
Social Welfare ◽  
Optimal Threshold ◽  
Single Class ◽  
Threshold Policy ◽  
Delay Sensitive ◽  
State Dependent ◽  
Multiple Servers ◽  
The Social ◽  
State Dependent Pricing ◽  
Welfare Model

We consider the social welfare model of Naor [20] and revenue-maximization model of Chen and Frank [7], where a single class of delay-sensitive customers seek service from a server with an observable queue, under state dependent pricing. It is known that in this setting both revenue and social welfare can be maximized by a threshold policy, whereby customers are barred from entry once the queue length reaches a certain threshold. However, no explicit expression for this threshold has been found. This paper presents the first derivation of the optimal threshold in closed form, and a surprisingly simple formula for the (maximum) revenue under this optimal threshold. Utilizing properties of the Lambert W function, we also provide explicit scaling results of the optimal threshold as the customer valuation grows. Finally, we present a generalization of our results, allowing for settings with multiple servers.

Optimal Threshold Policy for In-Home Smart Grid with Renewable Generation Integration

2015 ◽  
Vol 26 (4) ◽  
pp. 1096-1105 ◽  
Author(s):  
Gi-Ren Liu ◽  
Phone Lin ◽  
Yuguang Fang ◽  
Yi-Bing Lin
Keyword(s):  
Smart Grid ◽  
Optimal Threshold ◽  
Renewable Generation ◽  
Threshold Policy

scholarly journals Optimal Threshold Policy for Sequential Weapon Target Assignment

2016 ◽  
Vol 49 (17) ◽  
pp. 7-10 ◽  
Author(s):  
Krishnamoorthy Kalyanam ◽  
Sivakumar Rathinam ◽  
David Casbeer ◽  
Meir Pachter
Keyword(s):  
Optimal Threshold ◽  
Threshold Policy ◽  
Target Assignment

scholarly journals Estimation of the Optimal Threshold Policy in a Queue with Heterogeneous Servers Using a Heuristic Solution and Artificial Neural Networks

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1267
Author(s):  
Dmitry Efrosinin ◽  
Natalia Stepanova
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Optimal Allocation ◽  
Optimal Threshold ◽  
Iteration Algorithm ◽  
Heterogeneous Servers ◽  
Heuristic Solution ◽  
Threshold Policy ◽  
Optimal Thresholds ◽  
Artificial Neural

This paper deals with heterogeneous queues where servers differ not only in service rates but also in operating costs. The classical optimisation problem in queueing systems with heterogeneous servers consists in the optimal allocation of customers between the servers with the aim to minimise the long-run average costs of the system per unit of time. As it is known, under some assumptions the optimal allocation policy for this system is of threshold type, i.e., the policy depends on the queue length and the state of faster servers. The optimal thresholds can be calculated using a Markov decision process by implementing the policy-iteration algorithm. This algorithm may have certain limitations on obtaining a result for the entire range of system parameter values. However, the available data sets for evaluated optimal threshold levels and values of system parameters can be used to provide estimations for optimal thresholds through artificial neural networks. The obtained results are accompanied by a simple heuristic solution. Numerical examples illustrate the quality of estimations.

Threshold Management Policies for Exploited Populations

1990 ◽  
Vol 47 (10) ◽  
pp. 2016-2029 ◽  
Author(s):  
Terrance J. Quinn II ◽  
Robert Fagen ◽  
Jie Zheng
Keyword(s):  
Planning Horizon ◽  
Maximum Sustainable Yield ◽  
Management Policy ◽  
Optimal Threshold ◽  
Fishing Mortality ◽  
Average Yield ◽  
Threshold Policy ◽  
Threshold Levels ◽  
Age Structured ◽  
Stochastic Recruitment

Under a threshold management policy, harvesting occurs at a constant rate but ceases when a population drops below a threshold. A simulation model of an age-structured population with stochastic recruitment was constructed with such a harvest policy with several threshold levels. Other factors were fishing mortality, recruitment, and initial biomass. The objective function was a weighted function of average yield and standard deviation over a planning horizon. First, we determined the optimal threshold given fishing mortality. Secondly, we determined optimal threshold and fishing mortality, simultaneously. In application to eastern Bering Sea pollock, a threshold management policy always increased average yield over a non-threshold policy. For the first problem, optimal threshold levels ranged from 20 to 30% of pristine biomass. For the second problem, each scenario had a unique threshold and fishing mortality, with fishing mortality slightly above the maximum sustainable yield (MSY) level and a threshold range of 25–50%. These results were robust in regard to other factors. Benefits of the threshold policy were greater with a Ricker spawner-recruit model and with higher fishing mortality. The success of the threshold management policy is due to the relatively rapid rebuilding of a population to levels producing MSY.

Analysis of the Optimal Threshold Policy of the E-Tailer with Mixture Strategy in E-Fulfillment

2016 ◽  
Vol 9 (2) ◽  
pp. 21-34 ◽  
Author(s):  
Yuepeng Cheng ◽  
Bo Li ◽  
Zhenhong Li
Keyword(s):  
Lead Time ◽  
Profit Maximization ◽  
Optimal Threshold ◽  
The Internet ◽  
Threshold Policy ◽  
Limited Ability ◽  
Time Uncertainty ◽  
Operating Environments ◽  
Lead Time Uncertainty ◽  
Demand Variability

This study considers a supply chain consisting of a supplier and an e-tailer on the internet. The e-tailer replenishes products from the supplier for private inventory and sends drop shipping requests to him for delivering orders to customers when private inventory is insufficient or stock out, whereas the supplier provides drop shipping service with a limited ability for the e-tailer. This paper proposes an algorithm to simulate the scheduling sequences of the e-tailer with the optimal threshold policy and mixture strategy in every scheduling unit and obtains the optimal threshold of private inventory for the e-tailer to achieve average profit maximization. The impacts of mixture of demand and lead time uncertainty are examined. The influence of high priority demand variability on the optimal threshold policy in two complex scenarios are also considered in this study. These results have an important guiding significance for the e-tailer who adopts the mixture strategy in e-fulfillment under complex operating environments.

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