Approaching Throughput-optimality in Distributed CSMA Scheduling Algorithms with Collisions

It was shown recently that CSMA (Carrier Sense Multiple Access)-like distributed algorithms can achieve the maximal throughput in wireless networks (and task processing networks) under certain assumptions. One important, but idealized assumption is that the sensing time is negligible, so that there is no collision. In this paper, we study more practical CSMA-based scheduling algorithms with collisions. First, we provide a Markov chain model and give an explicit throughput formula which takes into account the cost of collisions and overhead. The formula has a simple form since the Markov chain is "almost" time-reversible. Second, we propose transmission-length control algorithms to approach throughput optimality in this case. Sufficient conditions are given to ensure the convergence and stability of the proposed algorithms. Finally, we characterize the relationship between the CSMA parameters (such as the maximum packet lengths) and the achievable capacity region.Comment: To appear in IEEE/ACM Transactions on Networking. This is the longer versio

Distributed Random Access Algorithm: Scheduling and Congesion Control

This paper provides proofs of the rate stability, Harris recurrence, and epsilon-optimality of CSMA algorithms where the backoff parameter of each node is based on its backlog. These algorithms require only local information and are easy to implement. The setup is a network of wireless nodes with a fixed conflict graph that identifies pairs of nodes whose simultaneous transmissions conflict. The paper studies two algorithms. The first algorithm schedules transmissions to keep up with given arrival rates of packets. The second algorithm controls the arrivals in addition to the scheduling and attempts to maximize the sum of the utilities of the flows of packets at the different nodes. For the first algorithm, the paper proves rate stability for strictly feasible arrival rates and also Harris recurrence of the queues. For the second algorithm, the paper proves the epsilon-optimality. Both algorithms operate with strictly local information in the case of decreasing step sizes, and operate with the additional information of the number of nodes in the network in the case of constant step size

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

Privacy-preserving Energy Scheduling for Smart Grid with Renewables

We consider joint demand response and power procurement to optimize the average social welfare of a smart power grid system with renewable sources. The renewable sources such as wind and solar energy are intermittent and fluctuate rapidly. As a consequence, the demand response algorithm needs to be executed in real time to ensure the stability of a smart grid system with renewable sources. We develop a demand response algorithm that converges to the optimal solution with superlinear rates of convergence. In the simulation studies, the proposed algorithm converges roughly thirty time faster than the traditional subgradient algorithm. In addition, it is fully distributed and can be realized either synchronously or in asynchronous manner, which eases practical deployment

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

Time-resolved Measurement of Quadrupole Wakefields in Corrugated Structures

Corrugated structures have recently been widely used for manipulating electron beam longitudinal phase space and for producing THz radiation. Here we report on time-resolved measurements of the quadrupole wakefields in planar corrugated structures. It is shown that while the time- dependent quadrupole wakefield produced by a planar corrugated structure causes significant growth in beam transverse emittance, it can be effectively canceled with a second corrugated structure with orthogonal orientation. The strengths of the time-dependent quadrupole wakefields for various corrugated structure gaps are also measured and found to be in good agreement with theories. Our work should forward the applications of corrugated structures in many accelerator based scientific facilities