scholarly journals The optimal control in batch arrival queue with server vacations, startup and breakdowns

2004 ◽  
Vol 14 (1) ◽  
pp. 41-55 ◽  
Author(s):  
Jau-Chuan Ke
Keyword(s):  
Optimal Control ◽  
Poisson Process ◽  
Cost Function ◽  
Minimum Cost ◽  
Compound Poisson Process ◽  
General Distribution ◽  
Server Vacations ◽  
Startup Time ◽  
Number Of Customers ◽  
System Characteristics

This paper studies the N policy M[x]/G/1 queue with server vacations; startup and breakdowns, where arrivals form a compound Poisson process and service times are generally distributed. The server is turned off and takes a vacation whenever the system is empty. If the number of customers waiting in the system at the instant of a vacation completion is less than N, the server will take another vacation. If the server returns from a vacation and finds at least N customers in the system, he is immediately turned on and requires a startup time before providing the service until the system is empty again. It is assumed that the server breaks down according to a Poisson process whose repair time has a general distribution. The system characteristics of such a model are analyzed and the total expected cost function per unit time is developed to determine the optimal threshold of N at a minimum cost.

Optimal Policies for a K-Phase Service System with Bernoulli Vacation Schedule

2014 ◽  
Vol 590 ◽  
pp. 768-772
Author(s):  
Ching Chang Kuo ◽  
Jau Chuan Ke
Keyword(s):  
Poisson Process ◽  
Cost Function ◽  
Service System ◽  
Repair Time ◽  
General Distribution ◽  
Unreliable Server ◽  
Optimal Policies ◽  
The Cost ◽  
System Characteristics ◽  
Bernoulli Vacation

This paper studies Optimal NT policies for a k-phase service M/G/1 system with Bernoulli vacation schedule. The system contains an unreliable server with a breakdown period and delaying period. The server determines to start service by the policy: the server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the completion period. There are k phases of service in the system. After the completion of k phases service, the server may take a short vacation or may remain in the system to serve the next unit, which is defined by Bernoulli vacation schedule. Moreover, we assume the server fails according to a Poisson process whose repair time follows a general distribution. In final, we analyze the system characteristics for each scheme and obtained the optimal NT threshold to minimize the cost function.

A service model in which the server is required to search for customers

1984 ◽  
Vol 21 (1) ◽  
pp. 157-166 ◽  
Author(s):  
Marcel F. Neuts ◽  
M. F. Ramalhoto
Keyword(s):  
Poisson Process ◽  
Numerical Computation ◽  
Probability Distributions ◽  
General Distribution ◽  
Search Process ◽  
Single Server ◽  
Stationary Probability ◽  
Service Model ◽  
Service Times ◽  
Number Of Customers

Customers enter a pool according to a Poisson process and wait there to be found and processed by a single server. The service times of successive items are independent and have a common general distribution. Successive services are separated by seek phases during which the server searches for the next customer. The search process is Markovian and the probability of locating a customer in (t, t + dt) is proportional to the number of customers in the pool at time t. Various stationary probability distributions for this model are obtained in explicit forms well-suited for numerical computation.Under the assumption of exponential service times, corresponding results are obtained for the case where customers may escape from the pool.

A service model in which the server is required to search for customers

1984 ◽  
Vol 21 (01) ◽  
pp. 157-166 ◽  
Author(s):  
Marcel F. Neuts ◽  
M. F. Ramalhoto
Keyword(s):  
Poisson Process ◽  
Numerical Computation ◽  
Probability Distributions ◽  
General Distribution ◽  
Search Process ◽  
Single Server ◽  
Stationary Probability ◽  
Service Model ◽  
Service Times ◽  
Number Of Customers

Customers enter a pool according to a Poisson process and wait there to be found and processed by a single server. The service times of successive items are independent and have a common general distribution. Successive services are separated by seek phases during which the server searches for the next customer. The search process is Markovian and the probability of locating a customer in (t, t + dt) is proportional to the number of customers in the pool at time t. Various stationary probability distributions for this model are obtained in explicit forms well-suited for numerical computation. Under the assumption of exponential service times, corresponding results are obtained for the case where customers may escape from the pool.

Optimal control of a dam using Pλ,τM policies and penalty cost when the input process is a compound Poisson process with positive drift

2000 ◽  
Vol 37 (2) ◽  
pp. 408-416 ◽  
Author(s):  
Mohamed Abdel-Hameed
Keyword(s):  
Optimal Control ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Input Process ◽  
Compound Poisson ◽  
Discounted Cost ◽  
Penalty Cost ◽  
Drift Term ◽  
Long Run ◽  
Negative Drift

In this paper we consider the optimal control of an infinite dam using policies assuming that the input process is a compound Poisson process with a non-negative drift term, and using the total discounted cost and long-run average cost criteria. The results of Lee and Ahn (1998) as well as other well-known results are shown to follow from our results.

scholarly journals The reserve of joint torque determines movement coordination

2021 ◽  
Author(s):  
Germain Faity ◽  
Denis Mottet ◽  
Simon Pla ◽  
Jérôme Froger
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Degrees Of Freedom ◽  
Minimum Cost ◽  
Joint Torque ◽  
Movement Coordination ◽  
Trunk Motion ◽  
Additional Load ◽  
The Cost ◽  
Healthy Participants

AbstractHumans coordinate biomechanical degrees of freedom to perform tasks at minimum cost. When reaching a target from a seated position, the trunk-arm-forearm coordination moves the hand to the well-defined spatial goal, while typically minimising hand jerk and trunk motion. However, due to fatigue or stroke, people visibly move the trunk more, and it is unclear what cost can account for this. Here we show that people recruit their trunk when the torque at the shoulder is too close to the maximum. We asked 26 healthy participants to reach a target while seated and we found that the trunk contribution to hand displacement increases from 11% to 27% when an additional load is handled. By flexing and rotating the trunk, participants spontaneously increase the reserve of anti-gravitational torque at the shoulder from 25% to 40% of maximal voluntary torque. Our findings provide hints on how to include the reserve of torque in the cost function of optimal control models of human coordination in healthy fatigued persons or in stroke victims.

Optimal control of a dam using P λ,τ M policies and penalty cost when the input process is a compound Poisson process with positive drift

2000 ◽  
Vol 37 (02) ◽  
pp. 408-416
Author(s):  
Mohamed Abdel-Hameed
Keyword(s):  
Optimal Control ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Input Process ◽  
Compound Poisson ◽  
Discounted Cost ◽  
Penalty Cost ◽  
Drift Term ◽  
Long Run ◽  
Negative Drift

In this paper we consider the optimal control of an infinite dam using policies assuming that the input process is a compound Poisson process with a non-negative drift term, and using the total discounted cost and long-run average cost criteria. The results of Lee and Ahn (1998) as well as other well-known results are shown to follow from our results.

scholarly journals OPP approach for multi degree of freedom robotic arm Based on Kinematics and Dynamics of Robot

2015 ◽  
Vol 4 (4) ◽  
pp. 284
Author(s):  
Praneet Dutta ◽  
Rashmi Ranjan Das ◽  
Rupali Mathur ◽  
Deepika Rani Sona
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Minimum Principle ◽  
Equations Of Motion ◽  
Optimal Path ◽  
Minimum Cost ◽  
Simulation Software ◽  
Degree Of Freedom ◽  
The Cost ◽  
Joint Velocity

This paper deals with the trajectory and path generation of the industrial manipulator. The trajectory is obtained using the equations of motion and also the optimal path planning (OPP) approach under kinodynamic constraints. The optimal control problem is defined for the minimum cost function and to obtain the necessary conditions. Here we have used pontrygain’s minimum principle to obtain the limiting value of joint angle and also  the joint velocity and torque. In this paper we have used the “Two degree of freedom (DOF) manipulator” for analysis and designing the optimal control for multi link and multi degree of freedom manipulator. For analysis purposes,  simulation software has been used to formulate the trajectory and minimize the cost function involved.

scholarly journals The reserve of joint torque determines movement coordination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Germain Faity ◽  
Denis Mottet ◽  
Simon Pla ◽  
Jérôme Froger
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Degrees Of Freedom ◽  
Minimum Cost ◽  
Joint Torque ◽  
Movement Coordination ◽  
Trunk Motion ◽  
Additional Load ◽  
The Cost ◽  
Healthy Participants

AbstractHumans coordinate biomechanical degrees of freedom to perform tasks at minimum cost. When reaching a target from a seated position, the trunk-arm-forearm coordination moves the hand to the well-defined spatial goal, while typically minimising hand jerk and trunk motion. However, due to fatigue or stroke, people visibly move the trunk more, and it is unclear what cost can account for this. Here we show that people recruit their trunk when the torque at the shoulder is too close to the maximum. We asked 26 healthy participants to reach a target while seated and we found that the trunk contribution to hand displacement increases from 11 to 27% when an additional load is handled. By flexing and rotating the trunk, participants spontaneously increase the reserve of anti-gravitational torque at the shoulder from 25 to 40% of maximal voluntary torque. Our findings provide hints on how to include the reserve of torque in the cost function of optimal control models of human coordination in healthy fatigued persons or in stroke victims.

Sign in / Sign up

Export Citation Format

Share Document