Fast Mixing of Parallel Glauber Dynamics and Low-Delay CSMA Scheduling

Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. It has been used to analyze and design distributed CSMA (Carrier Sense Multiple Access) scheduling algorithms for multi-hop wireless networks. In this paper we derive bounds on the mixing time of a generalization of Glauber dynamics where multiple links are allowed to update their states in parallel and the fugacity of each link can be different. The results can be used to prove that the average queue length (and hence, the delay) under the parallel Glauber dynamics based CSMA grows polynomially in the number of links for wireless networks with bounded-degree interference graphs when the arrival rate lies in a fraction of the capacity region. We also show that in specific network topologies, the low-delay capacity region can be further improved.Comment: 12 page

Throughput Analysis of CSMA Wireless Networks with Finite Offered-load

This paper proposes an approximate method, equivalent access intensity (EAI), for the throughput analysis of CSMA wireless networks in which links have finite offered-load and their MAC-layer transmit buffers may be empty from time to time. Different from prior works that mainly considered the saturated network, we take into account in our analysis the impacts of empty transmit buffers on the interactions and dependencies among links in the network that is more common in practice. It is known that the empty transmit buffer incurs extra waiting time for a link to compete for the channel airtime usage, since when it has no packet waiting for transmission, the link will not perform channel competition. The basic idea behind EAI is that this extra waiting time can be mapped to an equivalent "longer" backoff countdown time for the unsaturated link, yielding a lower link access intensity that is defined as the mean packet transmission time divided by the mean backoff countdown time. That is, we can compute the "equivalent access intensity" of an unsaturated link to incorporate the effects of the empty transmit buffer on its behavior of channel competition. Then, prior saturated ideal CSMA network (ICN) model can be adopted for link throughput computation. Specifically, we propose an iterative algorithm, "Compute-and-Compare", to identify which links are unsaturated under current offered-load and protocol settings, compute their "equivalent access intensities" and calculate link throughputs. Simulation shows that our algorithm has high accuracy under various offered-load and protocol settings. We believe the ability to identify unsaturated links and compute links throughputs as established in this paper will serve an important first step toward the design and optimization of general CSMA wireless networks with offered-load control.Comment: 6 pages. arXiv admin note: text overlap with arXiv:1007.5255 by other author

Speeding up Glauber Dynamics for Random Generation of Independent Sets

The maximum independent set (MIS) problem is a well-studied combinatorial optimization problem that naturally arises in many applications, such as wireless communication, information theory and statistical mechanics. MIS problem is NP-hard, thus many results in the literature focus on fast generation of maximal independent sets of high cardinality. One possibility is to combine Gibbs sampling with coupling from the past arguments to detect convergence to the stationary regime. This results in a sampling procedure with time complexity that depends on the mixing time of the Glauber dynamics Markov chain. We propose an adaptive method for random event generation in the Glauber dynamics that considers only the events that are effective in the coupling from the past scheme, accelerating the convergence time of the Gibbs sampling algorithm

Delay Performance and Mixing Times in Random-Access Networks

We explore the achievable delay performance in wireless random-access networks. While relatively simple and inherently distributed in nature, suitably designed queue-based random-access schemes provide the striking capability to match the optimal throughput performance of centralized scheduling mechanisms in a wide range of scenarios. The specific type of activation rules for which throughput optimality has been established, may however yield excessive queues and delays. Motivated by that issue, we examine whether the poor delay performance is inherent to the basic operation of these schemes, or caused by the specific kind of activation rules. We derive delay lower bounds for queue-based activation rules, which offer fundamental insight in the cause of the excessive delays. For fixed activation rates we obtain lower bounds indicating that delays and mixing times can grow dramatically with the load in certain topologies as well

Scheduling strategies to mitigate the impact of bursty traffic in wireless networks

Recent work has shown that certain queue-length based scheduling algorithms, such as max-weight, can lead to poor delays in the presence of bursty traffic. To overcome this phenomenon, we consider the problem of designing scheduling policies that are robust to bursty traffic, while also amenable to practical implementation. Specifically, we discuss two mechanisms, one based on adaptive CSMA, and the second based on maximum-weight scheduling with capped queue lengths. We consider a simple queueing network consisting of two conflicting links. The traffic served by the first link is bursty, and is modeled as being heavy-tailed, while traffic at the second link is modeled using a light-tailed arrival process. In this setting, previous work has shown that even the light-tailed traffic would experience heavy-tailed delays under max-weight scheduling. In contrast, we demonstrate a threshold phenomenon in the relationship between the arrival rates and the queue backlog distributions. In particular, we show that with an adaptive CSMA scheme, when the arrival rate of the light-tailed traffic is less than a threshold value, the light-tailed traffic experiences a light-tailed queue backlog at steady state, whereas for arrival rates above the same threshold, the light-tailed traffic experiences a heavy-tailed queue backlog. We also show that a similar threshold behavior for max-weight scheduling with capped queue lengthsNational Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (Grant CNS-1217048)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

Optimal CSMA-based Wireless Communication with Worst-case Delay and Non-uniform Sizes

Carrier Sense Multiple Access (CSMA) protocols have been shown to reach the full capacity region for data communication in wireless networks, with polynomial complexity. However, current literature achieves the throughput optimality with an exponential delay scaling with the network size, even in a simplified scenario for transmission jobs with uniform sizes. Although CSMA protocols with order-optimal average delay have been proposed for specific topologies, no existing work can provide worst-case delay guarantee for each job in general network settings, not to mention the case when the jobs have non-uniform lengths while the throughput optimality is still targeted. In this paper, we tackle on this issue by proposing a two-timescale CSMA-based data communication protocol with dynamic decisions on rate control, link scheduling, job transmission and dropping in polynomial complexity. Through rigorous analysis, we demonstrate that the proposed protocol can achieve a throughput utility arbitrarily close to its offline optima for jobs with non-uniform sizes and worst-case delay guarantees, with a tradeoff of longer maximum allowable delay