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

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 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.

Discounted Cost Markov Decision Processes with a Constraint

1998 ◽  
Vol 12 (2) ◽  
pp. 177-187 ◽  
Author(s):  
Kazuyoshi Wakuta
Keyword(s):  
Markov Decision Process ◽  
Markov Decision Processes ◽  
Decision Process ◽  
Decision Processes ◽  
Discounted Cost ◽  
Markov Decision ◽  
Vector Valued

We consider a discounted cost Markov decision process with a constraint. Relating this to a vector-valued Markov decision process, we prove that there exists a constrained optimal randomized semistationary policy if there exists at least one policy satisfying a constraint. Moreover, we present an algorithm by which we can find the constrained optimal randomized semistationary policy, or we can discover that there exist no policies satisfying a given constraint.

Optimal admission control for a single-server loss queue

2004 ◽  
Vol 41 (02) ◽  
pp. 535-546 ◽  
Author(s):  
Kyle Y. Lin ◽  
Sheldon M. Ross
Keyword(s):  
Admission Control ◽  
Time Horizon ◽  
Queueing System ◽  
Single Server ◽  
Sufficient Condition ◽  
Infinite Time ◽  
Discounted Cost ◽  
Time Period ◽  
Service Distribution ◽  
General Service

This paper presents a single-server loss queueing system where customers arrive according to a Poisson process. Upon arrival, the customer presents itself to a gatekeeper who has to decide whether to admit the customer into the system without knowing the busy–idle status of the server. There is a cost if the gatekeeper blocks a customer, and a larger cost if an admitted customer finds the server busy and therefore has to leave the system. The goal of the gatekeeper is to minimize the total expected discounted cost on an infinite time horizon. In the case of an exponential service distribution, we show that a threshold-type policy—block for a time period following each admission and then admit the next customer—is optimal. For general service distributions, we show that a threshold-type policy need not be optimal; we then present a sufficient condition for the existence of an optimal threshold-type policy.

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