Size-limited batch movement in product-form closed discrete-time queueing networks

Authors:
Michael E. Woodward
Affiliations:
Department of Electronic and Electrical Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, England, UK
Venue:
SIGMETRICS '97 Proceedings of the 1997 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Year:
1997

Citing 3
Cited 3

Modelling of computer and communication systems

Modelling of computer and communication systems
Closed queueing networks with batch services

Queueing Systems: Theory and Applications
Product form in networks of queues with batch arrivals and batch services

Queueing Systems: Theory and Applications

Queueing network analysis: concepts, terminology, and methods

Journal of Systems and Software
Discrete time queueing networks with product form steady state. Availability and performance analysis in an integrated model

Queueing Systems: Theory and Applications
Invited Towards the accurate modelling of high-speed communication networks with product-form discrete-time networks of queues

Computer Communications

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Abstract

Existing models for product-form closed discrete-time queueing networks with batch movement of customers implicitly assume that batch sizes are unrestricted. In many practical modelling situations however, it is necessary to impose restrictions on the batch sizes, and this paper examines the repercushions of such restrictions on the product-form properties of the networks. It is shown that when batch sizes are restricted independently then, in general, the resulting networks cannot have a product-form equilibrium distribution. Sufficient conditions to retain a product-form are derived in the cases when batch sizes are either correlated or depend on the state of the network. Examples of applying the results to obtain product-form networks with both correlated and state dependent batch movement are given.