Queue-based Random-access Algorithms: Fluid Limits and Stability Issues

Abstract

We use fluid limits to explore the (in)stability properties of wireless networks with queue-based random-access algorithms. Queuebased random-access schemes are simple and inherently distributed in nature, yet provide the capability to match the optimal throughput performance of centralized scheduling mechanisms in a wide range of scenarios. Unfortunately, the type of activation rules for which throughput optimality has been established, may result in excessive queue lengths and delays. The use of more aggressive/persistent access schemes can improve the delay performance, but does not offer any universal maximum-stability guarantees.In order to gain qualitative insight and investigate the (in)stability properties of more aggressive/persistent activation rules, we examine fluid limits where the dynamics are scaled in space and time. In some situations, the fluid limits have smooth deterministic features and maximum stability is maintained, while in other scenarios they exhibit random oscillatory characteristics, giving rise to major technical challenges. In the latter regime, more aggressive access schemes continue to provide maximum stability in some networks, but may cause instability in others. In order to prove that, we focus on a particular network example and conduct a detailed analysis of the fluid limit process for the associated Markov chain. Specifically, we develop a novel approach based on stopping time sequences to deal with the switching probabilities governing the sample paths of the fluid limit process. Simulation experiments are conducted to illustrate and validate the analytical results.

Maximizing Broadcast Throughput Under Ultra-Low-Power Constraints

“…Additionally, there are protocols that often require some explicit coordination (e.g., slotting [14,43,46,59], or explicitly require exchange of parameters [42], which are not suitable for emerging ultra-low-power nodes. From the theoretical point of view, our approach is inspired by the prior work on network utility maximization (e.g., [13,30,35,36]), and queue-based CSMA literature (e.g., [18,19,25,33,40,58]). However, the problem considered in this paper is not a simple extension of the prior work for two reasons.…”

“…The complete proof can be found in [12]. The proof is based on a Markov Chain Monte Carlo (MCMC) approach [18,25,40] from statistical physics.…”

“…LEMMA 2. With fixed η, the network Markov chain, resulted from overall interactions among the nodes according to the transition rates (18), has the steady state distribution…”

Modelling complex stochastic systems: approaches to management and stability

“…with (κ 1 ∨ κ 2 ) + κ 3 + κ 6 = 1, and 0 < α < (κ 3 ∧ κ 6 ). Then the main result of Ghaderi et al in [90] implies that there exists a constant * (κ, α) < 1, such that for all ∈ ( * (κ, α), 1] the Markov process is transient under the given parameter conditions.…”

“…So far we have presented classical examples that facilitated the assessment of the algorithm's performance. In our final example we address a contemporary area of research initiated by [90], exploring the stability properties of a wireless network with a queue-based random-access algorithm. We focus on a network consisting of nodes {1, 2, .…”