On Some Impulse Control Problems with Long Run Average Cost

1981 ◽  
Vol 19 (3) ◽  
pp. 333-358 ◽  
Author(s):  
Maurice Robin
Keyword(s):  
Average Cost ◽  
Impulse Control ◽  
Control Problems ◽  
Long Run

scholarly journals Optimal Control of a Stochastic Processing System Driven by a Fractional Brownian Motion Input

2010 ◽  
Vol 42 (01) ◽  
pp. 183-209 ◽  
Author(s):  
Arka P. Ghosh ◽  
Alexander Roitershtein ◽  
Ananda Weerasinghe
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stochastic Control ◽  
Average Cost ◽  
Infinite Horizon ◽  
Processing System ◽  
Control Problems ◽  
Value Functions ◽  
Discounted Cost ◽  
Long Run

We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an ON-OFF input process. We study stochastic control problems associated with the long-run average cost, the infinite-horizon discounted cost, and the finite-horizon cost. In addition, we find a solution to a constrained minimization problem as an application of our solution to the long-run average cost problem. We also establish Abelian limit relationships among the value functions of the above control problems.

scholarly journals Optimal Control of a Stochastic Processing System Driven by a Fractional Brownian Motion Input

2010 ◽  
Vol 42 (1) ◽  
pp. 183-209 ◽  
Author(s):  
Arka P. Ghosh ◽  
Alexander Roitershtein ◽  
Ananda Weerasinghe
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stochastic Control ◽  
Average Cost ◽  
Infinite Horizon ◽  
Processing System ◽  
Control Problems ◽  
Value Functions ◽  
Discounted Cost ◽  
Long Run

We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an ON-OFF input process. We study stochastic control problems associated with the long-run average cost, the infinite-horizon discounted cost, and the finite-horizon cost. In addition, we find a solution to a constrained minimization problem as an application of our solution to the long-run average cost problem. We also establish Abelian limit relationships among the value functions of the above control problems.

A bivariate optimal replacement policy for a repairable system

1994 ◽  
Vol 31 (4) ◽  
pp. 1123-1127 ◽  
Author(s):  
Yuan Lin Zhang
Keyword(s):  
Explicit Expression ◽  
Average Cost ◽  
Replacement Policy ◽  
Repairable System ◽  
Optimal Replacement ◽  
Long Run ◽  
Optimal Replacement Policy ◽  
Working Age ◽  
Better Than

In this paper, a repairable system consisting of one unit and a single repairman is studied. Assume that the system after repair is not as good as new. Under this assumption, a bivariate replacement policy (T, N), where T is the working age and N is the number of failures of the system is studied. The problem is to determine the optimal replacement policy (T, N)∗such that the long-run average cost per unit time is minimized. The explicit expression of the long-run average cost per unit time is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, under some conditions, we show that the policy (T, N)∗ is better than policies N∗ or T∗.

scholarly journals Childhood Reports of Food Neglect and Impulse Control Problems and Violence in Adulthood

2016 ◽  
Vol 13 (4) ◽  
pp. 389 ◽  
Author(s):  
Michael Vaughn ◽  
Christopher Salas-Wright ◽  
Sandra Naeger ◽  
Jin Huang ◽  
Alex Piquero
Keyword(s):  
Impulse Control ◽  
Control Problems

Optimal repair/replacement policy for a general repair model

2001 ◽  
Vol 33 (1) ◽  
pp. 206-222 ◽  
Author(s):  
Xiaoyue Jiang ◽  
Viliam Makis ◽  
Andrew K. S. Jardine
Keyword(s):  
Average Cost ◽  
Failure Time ◽  
Operating Time ◽  
Replacement Policy ◽  
Repair Cost ◽  
Virtual Age ◽  
Preventive Replacement ◽  
Long Run ◽  
Special Cases ◽  
Cost Limit

In this paper, we study a maintenance model with general repair and two types of replacement: failure and preventive replacement. When the system fails a decision is made whether to replace or repair it. The repair degree that affects the virtual age of the system is assumed to be a random function of the repair-cost and the virtual age at failure time. The system can be preventively replaced at any time before failure. The objective is to find the repair/replacement policy minimizing the long-run expected average cost per unit time. It is shown that a generalized repair-cost-limit policy is optimal and the preventive replacement time depends on the virtual age of the system and on the length of the operating time since the last repair. Computational procedures for finding the optimal repair-cost limit and the optimal average cost are developed. This model includes many well-known models as special cases and the approach provides a unified treatment of a wide class of maintenance models.

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