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Future Internet 2017, 9(3), 34; doi:10.3390/fi9030034

G-Networks with Adders

1
Laboratoire DAVID, Université de Versailles-Saint-Quentin, 78000 Versailles, France
2
Intelligent Systems & Networks Group, Imperial College, London SW7 2AZ, UK
*
Author to whom correspondence should be addressed.
Received: 17 May 2017 / Revised: 3 July 2017 / Accepted: 4 July 2017 / Published: 10 July 2017
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Abstract

Abstract: Queueing networks are used to model the performance of the Internet, of manufacturing and job-shop systems, supply chains, and other networked systems in transportation or emergency management. Composed of service stations where customers receive service, and then move to another service station till they leave the network, queueing networks are based on probabilistic assumptions concerning service times and customer movement that represent the variability of system workloads. Subject to restrictive assumptions regarding external arrivals, Markovian movement of customers, and service time distributions, such networks can be solved efficiently with “product form solutions” that reduce the need for software simulators requiring lengthy computations. G-networks generalise these models to include the effect of “signals” that re-route customer traffic, or negative customers that reject service requests, and also have a convenient product form solution. This paper extends G-networks by including a new type of signal, that we call an “Adder”, which probabilistically changes the queue length at the service center that it visits, acting as a load regulator. We show that this generalisation of G-networks has a product form solution. View Full-Text
Keywords: G-networks; internet; computer and network performance; queueing networks; transportation tetworks; product form solutions G-networks; internet; computer and network performance; queueing networks; transportation tetworks; product form solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Fourneau, J.-M.; Gelenbe, E. G-Networks with Adders. Future Internet 2017, 9, 34.

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