Dynamic search for a moving target

1994 ◽  
Vol 31 (02) ◽  
pp. 438-457
Author(s):  
David Assaf ◽  
Ariela Sharlin-Bilitzky
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Continuous Time ◽  
Search Costs ◽  
Cost Structure ◽  
Moving Target ◽  
Expected Cost ◽  
Bounded Controls ◽  
Dynamic Search ◽  
The Cost

An object is hidden in one of two boxes and occasionally moves between the boxes in accordance with some specified continuous-time Markov process. The objective is to find the object with a minimal expected cost. In this paper it is assumed that search efforts are unlimited. In addition to the search costs, the ‘real time' until the object is found is also taken into account in the cost structure. Our main results are that the optimal policy may consist of five regions and that the controls applied should be of the extreme 0 or ∞ type. The resulting expected cost compares favorably with that of the expected cost with bounded controls studied previously in the search literature.

Dynamic search for a moving target

1994 ◽  
Vol 31 (2) ◽  
pp. 438-457 ◽  
Author(s):  
David Assaf ◽  
Ariela Sharlin-Bilitzky
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Continuous Time ◽  
Search Costs ◽  
Cost Structure ◽  
Moving Target ◽  
Expected Cost ◽  
Bounded Controls ◽  
Dynamic Search ◽  
The Cost

An object is hidden in one of two boxes and occasionally moves between the boxes in accordance with some specified continuous-time Markov process. The objective is to find the object with a minimal expected cost. In this paper it is assumed that search efforts are unlimited. In addition to the search costs, the ‘real time' until the object is found is also taken into account in the cost structure. Our main results are that the optimal policy may consist of five regions and that the controls applied should be of the extreme 0 or ∞ type. The resulting expected cost compares favorably with that of the expected cost with bounded controls studied previously in the search literature.

Optimal search for a randomly moving object

1986 ◽  
Vol 23 (3) ◽  
pp. 708-717 ◽  
Author(s):  
R. R. Weber
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Moving Object ◽  
The Other ◽  
Optimal Search ◽  
Expected Cost

It is desired to minimize the expected cost of finding an object which moves back and forth between two locations according to an unobservable Markov process. When the object is in location i (i = 1, 2) it resides there for a time which is exponentially distributed with parameter λ1 and then moves to the other location. The location of the object is not known and at each instant until it is found exactly one of the two locations must be searched. Searching location i for time δ costs ciδ and conditional on the object being in location i there is a probability αiδ + o(δ) that this search will find it. The probability that the object starts in location 1 is known to bé p1(0). The location to be searched at time t is to be chosen on the basis of the value of p1(t), the probability that the object is in location 1, given that it has not yet been discovered. We prove that there exists a threshold Π such that the optimal policy may be described as: search location 1 if and only if the probability that the object is in location 1 is greater than Π. Expressions for the threshold Π are given in terms of the parameters of the model.

Scheduling jobs on non-identical IFR processors to minimize general cost functions

1991 ◽  
Vol 23 (04) ◽  
pp. 909-924 ◽  
Author(s):  
Rhonda Righter ◽  
Susan H. Xu
Keyword(s):  
Cost Function ◽  
Optimal Policy ◽  
Expected Number ◽  
Expected Cost ◽  
Processing Times ◽  
Special Cases ◽  
The Cost ◽  
General Cost Functions ◽  
Tardy Jobs ◽  
Completion Times

We consider the problem of scheduling n jobs non-preemptively on m parallel, non-identical processors to minimize a weighted expected cost function of job completion times, where the weights are associated with the jobs. The cost function is assumed to be increasing and concave but otherwise arbitrary. Processing times are IFR with different distributions for different processors. Jobs may be processed on any processor and there are no precedences. We show that the optimal policy orders the jobs in decreasing order of their weights and then uses the individually optimal policy for each job. In other words, processors are offered to jobs in order, and each job considers its own expected cost function for its completion time to decide whether to accept or reject a processor. Therefore, the optimal policy does not depend on the weights of the jobs except through their order. Special cases of our objective function are weighted expected flowtime, weighted discounted expected flowtime, and weighted expected number of tardy jobs.

An optimal inspection and replacement policy for a deteriorating system

1986 ◽  
Vol 23 (04) ◽  
pp. 973-988 ◽  
Author(s):  
Masamitsu Ohnishi ◽  
Hajime Kawai ◽  
Hisashi Mine
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Continuous Time ◽  
Average Cost ◽  
Control Limit ◽  
Replacement Policy ◽  
Optimal Time ◽  
Time Interval ◽  
Long Run ◽  
Monotonic Properties

This paper investigates a system whose deterioration is expressed as a continuous-time Markov process. It is assumed that the state of the system cannot be identified without inspection. This paper derives an optimal policy minimizing the expected total long-run average cost per unit time. It gives the optimal time interval between successive inspections and determines the states at which the system is to be replaced. Furthermore, under some reasonable assumptions reflecting the practical meaning of the deterioration, it is shown that the optimal policy has monotonic properties. A control limit rule holds for replacement, and the time interval between successive inspections decreases as the degree of deterioration increases.

Scheduling jobs on non-identical IFR processors to minimize general cost functions

1991 ◽  
Vol 23 (4) ◽  
pp. 909-924 ◽  
Author(s):  
Rhonda Righter ◽  
Susan H. Xu
Keyword(s):  
Cost Function ◽  
Optimal Policy ◽  
Expected Number ◽  
Expected Cost ◽  
Processing Times ◽  
Special Cases ◽  
The Cost ◽  
General Cost Functions ◽  
Tardy Jobs ◽  
Completion Times

We consider the problem of scheduling n jobs non-preemptively on m parallel, non-identical processors to minimize a weighted expected cost function of job completion times, where the weights are associated with the jobs. The cost function is assumed to be increasing and concave but otherwise arbitrary. Processing times are IFR with different distributions for different processors. Jobs may be processed on any processor and there are no precedences. We show that the optimal policy orders the jobs in decreasing order of their weights and then uses the individually optimal policy for each job. In other words, processors are offered to jobs in order, and each job considers its own expected cost function for its completion time to decide whether to accept or reject a processor. Therefore, the optimal policy does not depend on the weights of the jobs except through their order. Special cases of our objective function are weighted expected flowtime, weighted discounted expected flowtime, and weighted expected number of tardy jobs.

Optimal search for a randomly moving object

1986 ◽  
Vol 23 (03) ◽  
pp. 708-717 ◽  
Author(s):  
R. R. Weber
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Moving Object ◽  
The Other ◽  
Optimal Search ◽  
Expected Cost

It is desired to minimize the expected cost of finding an object which moves back and forth between two locations according to an unobservable Markov process. When the object is in location i (i = 1, 2) it resides there for a time which is exponentially distributed with parameter λ1 and then moves to the other location. The location of the object is not known and at each instant until it is found exactly one of the two locations must be searched. Searching location i for time δ costs ciδ and conditional on the object being in location i there is a probability α i δ + o(δ) that this search will find it. The probability that the object starts in location 1 is known to bé p 1(0). The location to be searched at time t is to be chosen on the basis of the value of p 1(t), the probability that the object is in location 1, given that it has not yet been discovered. We prove that there exists a threshold Π such that the optimal policy may be described as: search location 1 if and only if the probability that the object is in location 1 is greater than Π. Expressions for the threshold Π are given in terms of the parameters of the model.

An optimal inspection and replacement policy for a deteriorating system

1986 ◽  
Vol 23 (4) ◽  
pp. 973-988 ◽  
Author(s):  
Masamitsu Ohnishi ◽  
Hajime Kawai ◽  
Hisashi Mine
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Continuous Time ◽  
Average Cost ◽  
Control Limit ◽  
Replacement Policy ◽  
Optimal Time ◽  
Time Interval ◽  
Long Run ◽  
Monotonic Properties

This paper investigates a system whose deterioration is expressed as a continuous-time Markov process. It is assumed that the state of the system cannot be identified without inspection. This paper derives an optimal policy minimizing the expected total long-run average cost per unit time. It gives the optimal time interval between successive inspections and determines the states at which the system is to be replaced. Furthermore, under some reasonable assumptions reflecting the practical meaning of the deterioration, it is shown that the optimal policy has monotonic properties. A control limit rule holds for replacement, and the time interval between successive inspections decreases as the degree of deterioration increases.

An optimal inspection and replacement policy for a deteriorating system

1986 ◽  
Vol 23 (04) ◽  
pp. 973-988 ◽  
Author(s):  
Masamitsu Ohnishi ◽  
Hajime Kawai ◽  
Hisashi Mine
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Continuous Time ◽  
Average Cost ◽  
Control Limit ◽  
Replacement Policy ◽  
Optimal Time ◽  
Time Interval ◽  
Long Run ◽  
Monotonic Properties

This paper investigates a system whose deterioration is expressed as a continuous-time Markov process. It is assumed that the state of the system cannot be identified without inspection. This paper derives an optimal policy minimizing the expected total long-run average cost per unit time. It gives the optimal time interval between successive inspections and determines the states at which the system is to be replaced. Furthermore, under some reasonable assumptions reflecting the practical meaning of the deterioration, it is shown that the optimal policy has monotonic properties. A control limit rule holds for replacement, and the time interval between successive inspections decreases as the degree of deterioration increases.

MANAGEMENT OF THE SUCCESS OF STUDENT’S LEARNING BASED ON THE MARKOV MODEL

2018 ◽  
pp. 4-11
Author(s):  
M. V. Noskov ◽  
M. V. Somova ◽  
I. M. Fedotova
Keyword(s):  
Information System ◽  
Markov Process ◽  
Continuous Time ◽  
Information Technologies ◽  
Educational Process ◽  
Automated Information System ◽  
The Subject ◽  
The University ◽  
Independent Work ◽  
Near Future

The article proposes a model for forecasting the success of student’s learning. The model is a Markov process with continuous time, such as the process of “death and reproduction”. As the parameters of the process, the intensities of the processes of obtaining and assimilating information are offered, and the intensity of the process of assimilating information takes into account the attitude of the student to the subject being studied. As a result of applying the model, it is possible for each student to determine the probability of a given formation of ownership of the material being studied in the near future. Thus, in the presence of an automated information system of the university, the implementation of the model is an element of the decision support system by all participants in the educational process. The examples given in the article are the results of an experiment conducted at the Institute of Space and Information Technologies of Siberian Federal University under conditions of blended learning, that is, under conditions when classroom work is accompanied by independent work with electronic resources.

scholarly journals Comparison of LPWAN Technologies: Cost Structure and Scalability

2021 ◽  
Author(s):  
Mohammad Istiak Hossain ◽  
Jan I. Markendahl
Keyword(s):  
Communication Technology ◽  
Service Providers ◽  
Communication Technologies ◽  
Cost Structure ◽  
Small Scale ◽  
Area Network ◽  
Wide Area Network ◽  
Generic Framework ◽  
Cost Efficient ◽  
The Cost

AbstractSmall-scale commercial rollouts of Cellular-IoT (C-IoT) networks have started globally since last year. However, among the plethora of low power wide area network (LPWAN) technologies, the cost-effectiveness of C-IoT is not certain for IoT service providers, small and greenfield operators. Today, there is no known public framework for the feasibility analysis of IoT communication technologies. Hence, this paper first presents a generic framework to assess the cost structure of cellular and non-cellular LPWAN technologies. Then, we applied the framework in eight deployment scenarios to analyze the prospect of LPWAN technologies like Sigfox, LoRaWAN, NB-IoT, LTE-M, and EC-GSM. We consider the inter-technology interference impact on LoRaWAN and Sigfox scalability. Our results validate that a large rollout with a single technology is not cost-efficient. Also, our analysis suggests the rollout possibility of an IoT communication Technology may not be linear to cost-efficiency.

Sign in / Sign up

Export Citation Format

Share Document