Toward Understanding of Metastability in Cellular Networks: Emergence and Implications for Performance

Genin, D. E.; Marbukh, Vladimir

doi:10.1109/glocom.2008.ecp.255

Cited by 1 publication

(6 citation statements)

References 3 publications

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“…Note that compared to wired networks and the works in [11]- [13], the mean-field limit approximation does not abstract the network (environment) as a single value that represents the network time-average state. Instead, it abstracts the network state as a density function, which represents the spatial distribution of users in the network.…”

Section: Summary Of Contributionsmentioning

confidence: 99%

“…Hence, γ p (x) is inversely proportional to the path loss function after inversion L(x) 1−l . By substituting (15) in (13), we get…”

Section: A Definitionmentioning

confidence: 99%

“…Another interesting line of work where metastability was observed is [11]- [13]. The basic underlying model for these works consists of a finite number of queues (BSs) with finite capacity with multiple classes of users arriving uniformly to these queues.…”

Section: Metastabilitymentioning

confidence: 99%

“…Users migrate from one queue to another according to some exponential time clock if the chosen queue has the capacity to accommodate them, and otherwise, they leave the network. It was shown in [11]- [13] that for some network parameters, the network also has two equilibrium points, where the network state remains at one of these points for a long time, then due to a rare event, the state switches to the other equilibrium point and stays there also for a long time. Hence, in this case, the metastability is different from the one we observe, where the network becomes unstable.…”

Section: Metastabilitymentioning

confidence: 99%

“…Hence, in this case, the metastability is different from the one we observe, where the network becomes unstable. Metastability in [11]- [13] is believed to be due to three ingredients: (i) mobility, (ii) multiple cells, and (iii) multiple classes of users. Interestingly, in our case, we have only a single cell without mobility.…”

Section: Metastabilitymentioning

confidence: 99%

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Stability and Metastability of Traffic Dynamics in Uplink Random Access Networks

AlAmmouri,

Andrews,

Baccelli

2019

Preprint

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We characterize the stability, metastability, and the stationary regime of traffic dynamics in a singlecell uplink wireless system. The traffic is represented in terms of spatial birth-death processes, in which users arrive as a Poisson point process in time and space, each with a file to transmit to the base station. The service rate of each user is based on its signal to interference plus noise ratio (SINR), where the interference is from other active users in the cell. Once the file is fully transmitted, the user leaves the cell. We derive the necessary and sufficient condition for network stability, which is independent of the specific path loss function as long as it satisfies mild boundedness conditions. A novel observation, shown through mean-field analysis and simulations, is that for a certain range of arrival rates, the network appears stable for possibly a long time, but can suddenly become unstable. This property is called metastability which is widely known in statistical physics but rarely observed in wireless communication. Finally, using mean-field analysis, we propose a heuristic characterization of the network steady-state regime when it exists, and demonstrate that it is tight for the whole range of arrival rates.have sporadic traffic to send. In such a scenario, devices enter the network without warning, wish to transmit some data quickly and without going through a lengthy acquisition and scheduling process, and then go back to sleep. The stability, latency, and scalability of such a random access scenario -despite considerable study, as explained below -is largely unknown, and very challenging to analyze. This paper takes a step forward in this direction by studying the dynamics of a single-cell uplink wireless system, along with its stability and metastability. Our approach and analysis rely on tools form mean-field theory along with queuing theory, and allows us to derive the exact stability condition of the system, along with some simple heuristics to describe the stationary regime when it exists. A. History and Motivation: Wired Random Access NetworksThe history of analyzing dynamics in communication networks goes back to wired data networks, where multiple nodes share a common wire to a common destination [2]. A benchmark random access protocol for these networks that has been extensively analyzed in the past three decades is slotted Aloha, where N nodes share the same resource to the destination, each has a packet arrival rate of λ i , and node i transmits at the beginning of each time slot with a probability p i if its queue is not empty. If more than one node transmit in the same time slot, then a collision is declared, and the packets are queued back at their sources. Although the slotted Aloha protocol is simple, its stability region for general N -which is the set of arrival ratesthat leads to stable queues -is a long-standing open problem [3]. In some special cases, the stability region is known. For example, if the arrivals follow a Bernoulli process, then the exact stability re...

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Section: Summary Of Contributionsmentioning

confidence: 99%

“…Hence, γ p (x) is inversely proportional to the path loss function after inversion L(x) 1−l . By substituting (15) in (13), we get…”

Section: A Definitionmentioning

confidence: 99%

Section: Metastabilitymentioning

confidence: 99%

Section: Metastabilitymentioning

confidence: 99%

Section: Metastabilitymentioning

confidence: 99%

See 3 more Smart Citations

Stability and Metastability of Traffic Dynamics in Uplink Random Access Networks

AlAmmouri,

Andrews,

Baccelli

2019

Preprint

View full text Add to dashboard Cite

show abstract

Toward Understanding of Metastability in Cellular Networks: Emergence and Implications for Performance

Cited by 1 publication

References 3 publications

Stability and Metastability of Traffic Dynamics in Uplink Random Access Networks

Stability and Metastability of Traffic Dynamics in Uplink Random Access Networks

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