Optimal stopping in the parking problem with U-turn

1988 ◽  
Vol 25 (2) ◽  
pp. 363-374 ◽  
Author(s):  
Mitsushi Tamaki
Keyword(s):  
Optimal Stopping ◽  
Optimal Policy ◽  
Relative Speed ◽  
Time Duration ◽  
Expected Time ◽  
Parking Problem

A motorist drives his car toward his destination along a street and looks for a motor pool. Motor pools are assumed to occur independently, with probability p. Observing whether there exists a motor pool or not, the driver decides either to stop (i.e., return to the latest motor pool observed so far and park there) or continue driving. Once the driver stops, he walks the remaining distance to his destination. Let r, 0 < r < 1, be the relative speed of driving a car compared with that on foot. Then the time duration required to reach the destination is measured by r · (distance driven) + (distance on foot) and the objective of the driver is to find a parking policy which minimizes the expected time duration. It is shown that, under an optimal policy, a U-turn never occurs before the destination, but may occur beyond the destination. Moreover, the expected time is computed and some comparisons are made between our problem and the classical parking problem.

Optimal stopping in the parking problem with U-turn

1988 ◽  
Vol 25 (02) ◽  
pp. 363-374 ◽  
Author(s):  
Mitsushi Tamaki
Keyword(s):  
Optimal Stopping ◽  
Optimal Policy ◽  
Relative Speed ◽  
Time Duration ◽  
Expected Time ◽  
Parking Problem

A motorist drives his car toward his destination along a street and looks for a motor pool. Motor pools are assumed to occur independently, with probability p. Observing whether there exists a motor pool or not, the driver decides either to stop (i.e., return to the latest motor pool observed so far and park there) or continue driving. Once the driver stops, he walks the remaining distance to his destination. Let r, 0 &lt; r &lt; 1, be the relative speed of driving a car compared with that on foot. Then the time duration required to reach the destination is measured by r · (distance driven) + (distance on foot) and the objective of the driver is to find a parking policy which minimizes the expected time duration. It is shown that, under an optimal policy, a U-turn never occurs before the destination, but may occur beyond the destination. Moreover, the expected time is computed and some comparisons are made between our problem and the classical parking problem.

On the Kesten–Spitzer algorithm for minimal hitting time in controlled Markov chains

1980 ◽  
Vol 17 (03) ◽  
pp. 716-725
Author(s):  
Manish C. Bhattacharjee ◽  
Sujit K. Basu
Keyword(s):  
Markov Chain ◽  
Optimal Policy ◽  
Similar Condition ◽  
Control Policy ◽  
Hitting Time ◽  
Sufficient Condition ◽  
Expected Time ◽  
Fixed State ◽  
Necessary And Sufficient ◽  
Modified Algorithm

For a Markov chain with optional transitions, except for those to an arbitrary fixed state accessible from all others, Kesten and Spitzer proved the existence of a control policy which minimized the expected time to reach the fixed state and for constructing an optimal policy, proposed an algorithm which works in certain cases. For the algorithm to work they gave a sufficient condition which breaks down if there are countably many states and the minimal hitting time is bounded. We propose a modified algorithm which is shown to work under a weaker sufficient condition. In the bounded case with countably many states, the proposed sufficient condition is not necessary but a similar condition is. In the unbounded case as well as when the state space is finite, the proposed condition is shown to be both necessary and sufficient for the original Kesten–Spitzer algorithm to work. A new iterative algorithm which can be used in all cases is given.

scholarly journals Discrete Analysis of Portfolio Selection with Optimal Stopping Time

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Jianfeng Liang
Keyword(s):  
Linear Programming ◽  
Portfolio Selection ◽  
Integer Linear Programming ◽  
Optimal Stopping ◽  
Programming Model ◽  
Stopping Time ◽  
Integer Linear Programming Model ◽  
Numerical Example ◽  
Expected Time ◽  
Selection Policy

Most of the investments in practice are carried out without certain horizons. There are many factors to drive investment to a stop. In this paper, we consider a portfolio selection policy with market-related stopping time. Particularly, we assume that the investor exits the market once his wealth reaches a given investment target or falls below a bankruptcy threshold. Our objective is to minimize the expected time when the investment target is obtained, at the same time, we guarantee the probability that bankruptcy happens is no larger than a given level. We formulate the problem as a mix integer linear programming model and make analysis of the model by using a numerical example.

Optimal stopping in a partially observable binary-valued markov chain with costly perfect information

1982 ◽  
Vol 19 (1) ◽  
pp. 72-81 ◽  
Author(s):  
George E. Monahan
Keyword(s):  
Markov Chain ◽  
Optimal Stopping ◽  
Optimal Policy ◽  
Value Function ◽  
Structural Information ◽  
State Information ◽  
Mild Conditions ◽  
Optimal Value ◽  
Markov Decision ◽  
Partially Observable

The problem of optimal stopping in a Markov chain when there is imperfect state information is formulated as a partially observable Markov decision process. Properties of the optimal value function are developed. It is shown that under mild conditions the optimal policy is well structured. An efficient algorithm, which uses the structural information in the computation of the optimal policy, is presented.

On a quickest detection problem with variable monitoring

1976 ◽  
Vol 13 (4) ◽  
pp. 760-767
Author(s):  
D. W. Balmer
Keyword(s):  
Optimal Stopping ◽  
Optimal Policy ◽  
Necessary Conditions ◽  
Fast Mode ◽  
Optimal Stopping Problem ◽  
Detection Problem ◽  
Quickest Detection ◽  
Necessary Conditions Of Optimality ◽  
And Control ◽  
Monitoring Facility

The problem of detecting the arrival of a ‘disorder' in a process observed through a monitoring facility which may operate in ‘slow’ or ‘fast’ mode, is formulated as an optimal stopping problem. It is shown that in all circumstances where there may exist an optimal policy specifying the mode of observation and the time of stopping there is a unique policy satisfying certain necessary conditions of optimality; the various circumstances and control policies are specified.

Optimal stopping in a partially observable binary-valued markov chain with costly perfect information

1982 ◽  
Vol 19 (01) ◽  
pp. 72-81 ◽  
Author(s):  
George E. Monahan
Keyword(s):  
Markov Chain ◽  
Optimal Stopping ◽  
Optimal Policy ◽  
Value Function ◽  
Structural Information ◽  
State Information ◽  
Mild Conditions ◽  
Optimal Value ◽  
Markov Decision ◽  
Partially Observable

The problem of optimal stopping in a Markov chain when there is imperfect state information is formulated as a partially observable Markov decision process. Properties of the optimal value function are developed. It is shown that under mild conditions the optimal policy is well structured. An efficient algorithm, which uses the structural information in the computation of the optimal policy, is presented.

On the Kesten–Spitzer algorithm for minimal hitting time in controlled Markov chains

1980 ◽  
Vol 17 (3) ◽  
pp. 716-725
Author(s):  
Manish C. Bhattacharjee ◽  
Sujit K. Basu
Keyword(s):  
Markov Chain ◽  
Optimal Policy ◽  
Similar Condition ◽  
Control Policy ◽  
Hitting Time ◽  
Sufficient Condition ◽  
Expected Time ◽  
Fixed State ◽  
Necessary And Sufficient ◽  
Modified Algorithm

For a Markov chain with optional transitions, except for those to an arbitrary fixed state accessible from all others, Kesten and Spitzer proved the existence of a control policy which minimized the expected time to reach the fixed state and for constructing an optimal policy, proposed an algorithm which works in certain cases. For the algorithm to work they gave a sufficient condition which breaks down if there are countably many states and the minimal hitting time is bounded. We propose a modified algorithm which is shown to work under a weaker sufficient condition. In the bounded case with countably many states, the proposed sufficient condition is not necessary but a similar condition is. In the unbounded case as well as when the state space is finite, the proposed condition is shown to be both necessary and sufficient for the original Kesten–Spitzer algorithm to work. A new iterative algorithm which can be used in all cases is given.

scholarly journals Brute force algorithm implementation for traveljoy travelling recommendation system

2019 ◽  
Vol 16 (2) ◽  
pp. 1042
Author(s):  
K.A.F.A. Samah ◽  
N. Sabri ◽  
R. Hamzah ◽  
R. Roslan ◽  
N.A. Mangshor ◽  
...  
Keyword(s):  
Recommendation System ◽  
Traveling Salesman ◽  
The Internet ◽  
Reliability Testing ◽  
Brute Force ◽  
Time Duration ◽  
Application System ◽  
Expected Time ◽  
Algorithm Implementation ◽  
Test Result

<span>This paper presents the Brute Force algorithm implementation for TravelJoy Travelling Recommendation System.  Due to overwhelmed information in the internet, travelers faced difficulties in finding and comparing which places in Melaka that worth to visit. Melaka is a well-known place as one of the most popular tourist spots in Malaysia, famous with historical places. All the mentioned problems were time-consuming and required lots of efforts for manual comparison between places and planning the trip itinerary. An efficient application system is needed to assist travelers in planning their trip itinerary by providing details of interesting place in Melaka, budget estimating and recommendation of sequence places which to visit. The TravelJoy application applied Traveling Salesman Problem (TSP) concept using Brute Force algorithm in determining the least time duration for the selected places and adapting Expected Time Arrival (ETA). It was found through Brute Force algorithm adaptation; the recommendation system is reliable based on the functional and reliability testing with t-test result of 0.00067, indicates the system is accepted.</span>

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