scholarly journals Optimal control of batch service queues with finite service capacity and linear holding costs

2000 ◽  
Vol 51 (2) ◽  
pp. 263-285 ◽  
Author(s):  
Samuli Aalto
Keyword(s):  
Optimal Control ◽  
Batch Service ◽  
Service Capacity ◽  
Holding Costs ◽  
Batch Service Queues

Optimal control of batch service queues

1973 ◽  
Vol 5 (2) ◽  
pp. 340-361 ◽  
Author(s):  
Rajat K. Deb ◽  
Richard F. Serfozo
Keyword(s):  
Decision Process ◽  
Time Horizon ◽  
Optimal Level ◽  
Batch Size ◽  
Batch Service ◽  
Service Capacity ◽  
Infinite Time ◽  
Discounted Cost ◽  
Markov Decision ◽  
Batch Service Queues

A batch service queue is considered where each batch size and its time of service is subject to control. Costs are incurred for serving the customers and for holding them in the system. Viewing the system as a Markov decision process (i.e., dynamic program) with unbounded costs, we show that policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the form: at a review point when x customers are waiting, serve min {x, Q} customers (Q being the, possibly infinite, service capacity) if and only if x exceeds a certain optimal level M. Methods of computing M for both the discounted and average cost contexts are presented.

Optimal control of batch service queues

1973 ◽  
Vol 5 (02) ◽  
pp. 340-361 ◽  
Author(s):  
Rajat K. Deb ◽  
Richard F. Serfozo
Keyword(s):  
Decision Process ◽  
Time Horizon ◽  
Optimal Level ◽  
Batch Size ◽  
Batch Service ◽  
Service Capacity ◽  
Infinite Time ◽  
Discounted Cost ◽  
Markov Decision ◽  
Batch Service Queues

A batch service queue is considered where each batch size and its time of service is subject to control. Costs are incurred for serving the customers and for holding them in the system. Viewing the system as a Markov decision process (i.e., dynamic program) with unbounded costs, we show that policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the form: at a review point when x customers are waiting, serve min {x, Q} customers (Q being the, possibly infinite, service capacity) if and only if x exceeds a certain optimal level M. Methods of computing M for both the discounted and average cost contexts are presented.

Optimal control of batch service queues with switching costs

1976 ◽  
Vol 8 (1) ◽  
pp. 177-194 ◽  
Author(s):  
Rajat K. Deb
Keyword(s):  
Optimal Level ◽  
Fixed Number ◽  
Batch Size ◽  
Batch Service ◽  
Service Capacity ◽  
Discounted Cost ◽  
Markov Decision ◽  
Batch Sizes ◽  
Batch Service Queues ◽  
Number Of Customers

We consider a batch service queue which is controlled by switching the server on and off, and by controlling the batch size and timing of services. These batch sizes cannot exceed a fixed number Q, which we call the service capacity. Costs are charged for switching the server on and off, for serving customers and for holding them in the system. Viewing the system as a semi-Markov decision process, we show that the policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the following form: at a review point if the server is off, leave the server off until the number of customers x reaches an optimal level M, then turn the server on and serve min (x, Q) customers; and when the server is on, serve customers in batches of size min(x, Q) until the number of customers falls below an optimal level m(m ≦ M) and then turn the server off. An example for computing these optimal levels is also presented.

Optimal control of batch service queues with switching costs

1976 ◽  
Vol 8 (01) ◽  
pp. 177-194 ◽  
Author(s):  
Rajat K. Deb
Keyword(s):  
Optimal Level ◽  
Fixed Number ◽  
Batch Size ◽  
Batch Service ◽  
Service Capacity ◽  
Discounted Cost ◽  
Markov Decision ◽  
Batch Sizes ◽  
Batch Service Queues ◽  
Number Of Customers

We consider a batch service queue which is controlled by switching the server on and off, and by controlling the batch size and timing of services. These batch sizes cannot exceed a fixed number Q, which we call the service capacity. Costs are charged for switching the server on and off, for serving customers and for holding them in the system. Viewing the system as a semi-Markov decision process, we show that the policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the following form: at a review point if the server is off, leave the server off until the number of customers x reaches an optimal level M, then turn the server on and serve min (x, Q) customers; and when the server is on, serve customers in batches of size min(x, Q) until the number of customers falls below an optimal level m(m ≦ M) and then turn the server off. An example for computing these optimal levels is also presented.

OPTIMAL CONTROL OF FLEXIBLE SERVERS IN TWO TANDEM QUEUES WITH OPERATING COSTS

2007 ◽  
Vol 22 (1) ◽  
pp. 107-131 ◽  
Author(s):  
Dimitrios G. Pandelis
Keyword(s):  
Optimal Control ◽  
Optimal Policy ◽  
Optimal Allocation ◽  
Operating Costs ◽  
Queuing Systems ◽  
Tandem Queues ◽  
Holding Costs ◽  
Flexible Servers ◽  
Tandem Queuing ◽  
Dedicated Servers

We consider two-stage tandem queuing systems with dedicated servers in each station and flexible servers that can serve in both stations. We assume exponential service times, linear holding costs, and operating costs incurred by the servers at rates proportional to their speeds. Under conditions that ensure the optimality of nonidling policies, we show that the optimal allocation of flexible servers is determined by a transition-monotone policy. Moreover, we present conditions under which the optimal policy can be explicitly determined.

THE N-NETWORK MODEL WITH UPGRADES

2010 ◽  
Vol 24 (2) ◽  
pp. 171-200 ◽  
Author(s):  
Douglas G. Down ◽  
Mark E. Lewis
Keyword(s):  
Optimal Control ◽  
Numerical Study ◽  
Waiting Times ◽  
Control Policy ◽  
Wait Times ◽  
Threshold Policy ◽  
Holding Costs ◽  
Class 1 ◽  
Service Rates ◽  
Flexible Server

In this article we introduce a new method of mitigating the problem of long wait times for low-priority customers in a two-class queuing system. To this end, we allow class 1 customers to be upgraded to class 2 after they have been in queue for some time. We assume that there are ci servers at station i, i=1, 2. The servers at station 1 are flexible in the sense that they can work at either station, whereas the servers at station 2 are dedicated. Holding costs at rate hi are accrued per customer per unit time at station i, i=1, 2. This study yields several surprising results. First, we show that stability analysis requires a condition on the order of the service rates. This is unexpected since no such condition is required when the system does not have upgrades. This condition continues to play a role when control is considered. We provide structural results that include a c-μ rule when an inequality holds and a threshold policy when the inequality is reversed. A numerical study verifies that the optimal control policy significantly reduces holding costs over the policy that assigns the flexible server to station 1. At the same time, in most cases the optimal control policy reduces waiting times of both customer classes.

Sign in / Sign up

Export Citation Format

Share Document