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ENERGY PACKET NETWORKS WITH MULTIPLE ENERGY PACKET REQUIREMENTS

Published online by Cambridge University Press:  11 June 2019

Josu Doncel Open the ORCID record for Josu Doncel [Opens in a new window]  and
Jean-Michel Fourneau
Josu Doncel
Affiliation:
University of the Basque Country, UPV/EHU, Leioa, Spain E-mail: josu.doncel@ehu.eus
Jean-Michel Fourneau
Affiliation:
DAVID, UVSQ, Université Paris-Saclay, Versailles, France E-mail: jean-michel.fourneau@uvsq.fr
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Abstract

We analyze Energy Packet Networks (EPNs) in which the service centers consist of multiclass queues and the Data Packets (DPs) initiate the transfer (i.e., the arrival of a DP at the battery triggers the movement) with multiple energy packet requirements. In other words, a class-k DP in cell i is sent successfully to the next cell if there are $c_i^{(k)}$ energy packets and it is dropped otherwise. Besides, we consider that the queues handling DPs operate under one of the following disciplines: First-Input-First-Output (FIFO), Processor Sharing (PS), or Preemptive Last-Input-First-Output (LIFO-PR). This model is an extension of previously studied EPNs [6,16] where the steady-state distribution of the number of jobs in the queues has a product form. In our model, we show the existence of a product form of the steady-state stationary distribution, where the load of the servers is given by a fixed point expression. We study the existence of a solution to the derived fixed point problem and we provide sufficient conditions for the stability of our model. Finally, we show that, for feed forward EPNs, the load of all the queues can be fully characterized.

Keywords

probabilistic networksqueueing theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Special Issue 1: Learning, Optimization, and Theory of G-Networks , January 2021 , pp. 92 - 110
Copyright
Copyright © Cambridge University Press 2019

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