Classifications for batch service queues in production systems

2014 ◽  
Author(s):  
Kan Wu
Keyword(s):  
Production Systems ◽  
Batch Service ◽  
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.

ON TRUNCATION PROPERTIES OF FINITE-BUFFER QUEUES AND QUEUEING NETWORKS

2000 ◽  
Vol 14 (4) ◽  
pp. 409-423 ◽  
Author(s):  
Xiuli Chao ◽  
Masakiyo Miyazawa
Keyword(s):  
Stochastic Process ◽  
Continuous Time ◽  
Queueing Networks ◽  
Additional Condition ◽  
Queueing Systems ◽  
Batch Service ◽  
Single Server ◽  
Finite Buffer ◽  
Finite Buffers ◽  
Batch Service Queues

We show that several truncation properties of queueing systems are consequences of a simple property of censored stochastic processes. We first consider a discrete-time stochastic process and show that its censored process has a truncated stationary distribution. When the stochastic process has continuous time, we present a similar result under the additional condition that the process is locally balanced. We apply these results to single-server batch arrival batch service queues with finite buffers and queueing networks with finite buffers and batch movements, and extend the well-known results on truncation properties of the MX/G/1/k queues and queueing networks with jump-over blocking.

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.

scholarly journals One-dimensional service networks and batch service queues

2021 ◽  
Author(s):  
Philippe Nain ◽  
Nitish K. Panigrahy ◽  
Prithwish Basu ◽  
Don Towsley
Keyword(s):  
Batch Service ◽  
Service Networks ◽  
One Dimensional ◽  
Batch Service Queues
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