Performance Analysis of Contention Based Medium Access Control Protocols

Sharma, Gaurav; Ganesh, Ayalvadi; Key, Peter

doi:10.1109/tit.2008.2009608

Cited by 69 publications

(74 citation statements)

References 18 publications

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“…Among these papers, it is worth mentioning [13], where the authors investigated the existence of a global attractor for the meanfield system and provided sufficient conditions for its existence, deducing the validity of Bianchi's assumption. Further papers which deserve to be mentioned are [7,32], where the authors exploited mean-field theory so as to obtain approximations for key performance measures of large systems. In particular, [7] focuses on the characterization of the stability region, while [32] examines the throughput performance of the system.…”

Section: Background and Related Workmentioning

confidence: 99%

“…Further papers which deserve to be mentioned are [7,32], where the authors exploited mean-field theory so as to obtain approximations for key performance measures of large systems. In particular, [7] focuses on the characterization of the stability region, while [32] examines the throughput performance of the system. None of the above-mentioned papers considered scenarios with unsaturated buffers, with the exception of [7], which however dealt with systems evolving in discrete time and did not consider performance metrics like packet delays.…”

Section: Background and Related Workmentioning

confidence: 99%

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Mean-field limits for multi-hop random-access networks

Cecchi

Ven

Shneer³

2018

SIGMETRICS Perform. Eval. Rev.

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We establish mean-field limits for large-scale random-access networks with buffer dynamics and arbitrary interference graphs. While saturated-buffer scenarios have been widely investigated and yield useful throughput estimates for persistent sessions, they fail to capture the fluctuations in buffer contents over time, and provide no insight in the delay performance of flows with intermittent packet arrivals. Motivated by that issue, we explore in the present paper random-access networks with buffer dynamics, where flows with empty buffers refrain from competition for the medium. The occurrence of empty buffers thus results in a complex dynamic interaction between activity states and buffer contents, which severely complicates the performance analysis. Hence we focus on a many-sources regime where the total number of nodes grows large, which not only offers mathematical tractability but is also highly relevant with the densification of wireless networks as the Internet of Things emerges. We exploit time scale separation properties to prove that the properly scaled buffer occupancy process converges to the solution of a deterministic initial-value problem, and establish the existence and uniqueness of the associated fixed point. This approach simplifies the performance analysis of networks with huge numbers of nodes to a low-dimensional fixed-point calculation. For the case of a complete interference graph, we demonstrate asymptotic stability, provide a simple closed-form expression for the fixed point, and prove interchange of the mean-field and steady-state limits. This yields asymptotically exact approximations for key performance metrics, in particular the stationary buffer content and packet delay distributions.

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Section: Background and Related Workmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

Mean-field limits for multi-hop random-access networks

Cecchi

Ven

Shneer³

2018

SIGMETRICS Perform. Eval. Rev.

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“…Instead, we prove both facts formally by applying the following strategy. First, we use Kurtz's result to show that the underlying rescaled stochastic process converges in probability to an ODE system of size L(K + 1) 2 . In this respect, we justify approximation E[ f (X(t))] ≈ f (E[X(t)]) as being asymptotically true in the limit of infinite populations.…”

Section: Related Workmentioning

confidence: 99%

“…Essentially, M (x,y) l (·) gives the diffusive dynamics of the system, i.e., the contribution to the vector field due to the movement of type-l nodes in each region (x, y); L (x,y) l (·), instead, encodes the reactive dynamics, by considering the effects on each variable of the local interactions f j . The latter essentially corresponds to the vector field of the corresponding stationary reaction network, i.e., compare L (x,y) l (·) with L l (·) in (2). For instance, the ODEs of…”

Section: Absorbing Boundary Conditionsmentioning

confidence: 99%

Spatial fluid limits for stochastic mobile networks

Tschaikowski

Tribastone

2017

Performance Evaluation

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We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial differential equations (PDEs) whose size depends neither on the lattice size nor on the population of nodes. This provides a macroscopic view of the model which approximates discrete stochastic movements with continuous deterministic diffusions. We illustrate the practical applicability of this result by modeling a network of mobile nodes with on/off behavior performing file transfers with connectivity to 802.11 access points. By means of an empirical validation against discrete-event simulation we show high quality of the PDE approximation even for low populations and coarse lattices. In addition, we confirm the computational advantage in using the PDE limit over a traditional ordinary differential equation limit where the lattice is modelled discretely, yielding speed-ups of up to two orders of magnitude.

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“…The theory gives conditions which define a family of such models called density-dependent population processes, and finds their deterministic approximations by a theorem which is generally called the law of large numbers for standard Poisson processes [15].The mean field theory of Markov processes is increasingly being applied in the fields of computer science and communication engineering. In the field of communication engineering and starting with Bianchi's analysis of the IEEE 802.11 DCF protocol [4,5], much research has focused on discussing the validity of the so-called decoupling assumption in this analysis [7,33,29,11]. Several general frameworks have also been proposed which target the analysis of computer and communication systems [2,25].…”

mentioning

confidence: 99%

The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

Talebi

Groote

Linnartz

2017

Analytical and Stochastic Modelling Techniques and Applications

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The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering applications one faces the problem of analysing middle-sized systems in which the number of agents is bounded. In this paper we build on previous work in this area and introduce the mean drift. We present the concept of population processes and the conditions under which the approximation theorems apply, and then show how the mean drift is derived through a systematic application of the propagation of chaos. We then use the mean drift to construct a new set of ordinary differential equations which address the analysis of population processes with an arbitrary size.Population processes are stochastic models of systems which consist of a number of similar agents (or particles) [23]. When the impact of each agent on the behaviour of the system is similar to other agents, it is said that the population process is a mean field interaction model [2]. It is possible to apply a symmetric reduction on the state space of these types of processes and gain some efficiency in their analysis. Mean field approximation refers to the continuous, deterministic approximations of the behaviour of such processes in their first moment, when the number of agents grows very large. These approximations were first proposed for several concrete cases in various areas of study e.g., from as early as the 18th century in population biology, where models such as the predator-prey equations and the SIR equations are used to describe the balance of species in an ecosystem and the dynamics of epidemics respectively [3,13].Since then, general theorems have been proven which show the convergence of the behaviour of population processes to solutions of differential equations. The proofs follow roughly the same steps which generally rely on Grönwall's lemma and martingale inequalities [12]. One of the first generalized approximation theorems was given by Kurtz [21]. The theory gives conditions which define a family of such models called density-dependent population processes, and finds their deterministic approximations by a theorem which is generally called the law of large numbers for standard Poisson processes [15].The mean field theory of Markov processes is increasingly being applied in the fields of computer science and communication engineering. In the field of communication engineering and starting with Bianchi's analysis of the IEEE 802.11 DCF protocol [4,5], much research has focused on discussing the validity of the so-called decoupling assumption in this analysis [7,33,29,11]. Several general frameworks have also been proposed which target the analysis of computer and communication systems [2,25]. In the field of computer science the initial application of the approximations was intuitively motivated by methods such as fluid and diffusion approximations of queueing networks [19]. These have resulted in the de...

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Performance Analysis of Contention Based Medium Access Control Protocols

Cited by 69 publications

References 18 publications

Mean-field limits for multi-hop random-access networks

Mean-field limits for multi-hop random-access networks

Spatial fluid limits for stochastic mobile networks

The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

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