Optimal control of batch service queues with compound Poisson arrivals and finite service capacity

1998 ◽  
Vol 48 (3) ◽  
pp. 317-335 ◽  
Author(s):  
Samuli Aalto
Keyword(s):  
Optimal Control ◽  
Batch Service ◽  
Service Capacity ◽  
Compound Poisson ◽  
Poisson Arrivals ◽  
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.

scholarly journals Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times

2019 ◽  
Vol 135 ◽  
pp. 102012 ◽  
Author(s):  
Jens Baetens ◽  
Bart Steyaert ◽  
Dieter Claeys ◽  
Herwig Bruneel
Keyword(s):  
Batch Service ◽  
Service Capacity ◽  
Service Times

scholarly journals On pseudo-conservation laws for the cyclic server system with compound Poisson arrivals

1991 ◽  
Vol 10 (8) ◽  
pp. 453-459 ◽  
Author(s):  
Jhitti Chiarawongse ◽  
Mandyam M Srinivasan
Keyword(s):  
Conservation Laws ◽  
Compound Poisson ◽  
Poisson Arrivals ◽  
Server System

A renewal input single and batch service queues with accessibility to batches

2011 ◽  
Vol 6 (5) ◽  
pp. 366-373 ◽  
Author(s):  
V. Goswami ◽  
P. Vijaya Laxmi
Keyword(s):  
Batch Service ◽  
Batch Service Queues

Optimal dispatching of an infinite capacity shuttle with compound poisson arrivals: Control at a single terminal

1994 ◽  
Vol 21 (1) ◽  
pp. 67-78 ◽  
Author(s):  
Hyo-Seong Lee ◽  
Sang Kuk Kim
Keyword(s):  
Compound Poisson ◽  
Poisson Arrivals

scholarly journals Insensitive Bounds for the Moments of the Sojourn Times in M/GI Systems Under State-Dependent Processor Sharing

2010 ◽  
Vol 42 (01) ◽  
pp. 246-267 ◽  
Author(s):  
Andreas Brandt ◽  
Manfred Brandt
Keyword(s):  
Waiting Times ◽  
The State ◽  
Single Server ◽  
Processor Sharing ◽  
Actual Number ◽  
Service Capacity ◽  
State Dependent ◽  
Poisson Arrivals ◽  
Service Times ◽  
The Given

We consider a system with Poisson arrivals and independent and identically distributed service times, where requests in the system are served according to the state-dependent (Cohen's generalized) processor-sharing discipline, where each request receives a service capacity that depends on the actual number of requests in the system. For this system, we derive expressions as well as tight insensitive upper bounds for the moments of the conditional sojourn time of a request with given required service time. The bounds generalize and extend corresponding results, recently given for the single-server processor-sharing system in Cheung et al. (2006) and for the state-dependent processor-sharing system with exponential service times by the authors (2008). Analogous results hold for the waiting times. Numerical examples for the M/M/m-PS and M/D/m-PS systems illustrate the given bounds.

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