On the Stability of Static Poisson Networks Under Random Access
Open Access
- 7 June 2016
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Communications
- Vol. 64 (7), 2985-2998
- https://doi.org/10.1109/tcomm.2016.2577678
Abstract
We investigate the stable packet arrival rate region of a discrete-time slotted random access network, where the sources are distributed as a Poisson point process. Each of the sources in the network has a destination at a given distance and a buffer of infinite capacity. The network is assumed to be random but static, i.e., the sources and the destinations are placed randomly and remain static during all the time slots. We employ tools from queueing theory as well as point process theory to study the stability of this system using the concept of dominance. The problem is an instance of the interacting queues problem, further complicated by the Poisson spatial distribution. We obtain sufficient conditions and necessary conditions for stability. Numerical results show that the gap between the sufficient conditions and the necessary conditions is small when the access probability, the density of transmitters, or the SINR threshold is small. The results also reveal that a slight change of the arrival rate may greatly affect the fraction of unstable queues in the network.Keywords
Funding Information
- National Basic Research Program of China (973 Program) (2012CB316004)
- National Natural Science Foundation of China (61379003)
- Fundamental Research Funds for the Central Universities (WK3500000003)
- U.S. National Science Foundation (CCF 1216407, CCF 1525904)
- A*STAR SERC (1224104048)
- MOE ARF Tier 2 (MOE2014-T2-2-002)
- MOE ARF Tier 2 (MOE2015-T2-2-104)
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