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

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.

scholarly journals Resource Allocation in One-dimensional Distributed Service Networks with Applications

2020 ◽  
Vol 142 ◽  
pp. 102110
Author(s):  
Nitish K. Panigrahy ◽  
Prithwish Basu ◽  
Philippe Nain ◽  
Don Towsley ◽  
Ananthram Swami ◽  
...  
Keyword(s):  
Resource Allocation ◽  
Service Networks ◽  
One Dimensional ◽  
Distributed Service

scholarly journals Spatial birth-death processes with multiple changes and applications to batch service networks and clustering processes

1990 ◽  
Vol 22 (2) ◽  
pp. 433-455 ◽  
Author(s):  
Richard J. Boucherie ◽  
Nico M. Van Dijk
Keyword(s):  
Form Solution ◽  
Product Form ◽  
Symmetry Condition ◽  
Batch Service ◽  
Transition Rates ◽  
Service Networks ◽  
Batch Services ◽  
Concentration Equation ◽  
Networks Of Queues ◽  
Birth Death

Reversible spatial birth-death processes are studied with simultaneous jumps of multi-components. A relationship is established between (i) a product-form solution, (ii) a partial symmetry condition on the jump rates and (iii) a solution of a deterministic concentration equation. Applications studied are reversible networks of queues with batch services and blocking and clustering processes such as those found in polymerization chemistry. As illustrated by examples, known results are hereby unified and extended. An expectation interpretation of the transition rates is included.

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.

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