Jinwoo Shin

Distributed Random Access Algorithm: Scheduling and Congestion Control

This paper provides proofs of the rate stability, Harris recurrence, and ε-optimality of carrier sense multiple access (CSMA) algorithms where the random access (or backoff) parameter of each node is adjusted dynamically. These algorithms require only local information and they 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, in terms of the rates, of the packet flows at 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 ε-optimality in terms of the utilities of the allocated rates. Both algorithms are iterative and we study two versions of each of them. In the first version, both operate with strictly local information but have relatively weaker performance guarantees; under the second version, both provide stronger performance guarantees by utilizing the additional information of the number of nodes in the network.

Randomized scheduling algorithm for queueing networks

There has recently been considerable interest in design of low-complexity, myopic, distributed and stable scheduling policies for constrained queueing network models that arise in the context of emerging communication networks. Here, we consider two representative models. One, a model for the collection of wireless nodes communicating through a shared medium, that represents randomly varying number of packets in the queues at the nodes of networks. Two, a buffered circuit switched network model for an optical core of future Internet, to capture the randomness in calls or flows present in the network. The maximum weight scheduling policy proposed by Tassiulas and Ephremide in 1992 leads to a myopic and stable policy for the packet-level wireless network model. But computationally it is very expensive (NP-hard) and centralized. It is not applicable to the buffered circuit switched network due to the requirement of non-premption of the calls in the service. As the main contribution of this paper, we present a stable scheduling algorithm for both of these models. The algorithm is myopic, distributed and performs few logical operations at each node per unit time.

Delay optimal queue-based CSMA

In the past year or so, an exciting progress has led to throughput optimal design of CSMA-based algorithms for wireless networks. However, such an algorithm suffers from very poor delay performance. A recent work suggests that it is impossible to design a CSMA-like simple algorithm that is throughput optimal and induces low delay for any wireless network. However, wireless networks arising in practice are formed by nodes placed, possibly arbitrarily, in some geographic area. In this paper, we propose a CSMA algorithm with per-node average-delay bounded by a constant, independent of the network size, when the network has geometry (precisely, polynomial growth structure) that is present in any practical wireless network. Two novel features of our algorithm, crucial for its performance, are (a) choice of access probabilities as an appropriate function of queue-sizes, and (b) use of local network topological structures. Essentially, our algorithm is a queue-based CSMA with a minor difference that at each time instance a very small fraction of frozen nodes do not execute CSMA. Somewhat surprisingly, appropriate selection of such frozen nodes, in a distributed manner, lead to the delay optimal performance.

Dynamics in congestion games

Game theoretic modeling and equilibrium analysis of congestion games have provided insights in the performance of Internet congestion control, road transportation networks, etc. Despite the long history, very little is known about their transient (non equilibrium) performance. In this paper, we are motivated to seek answers to questions such as how long does it take to reach equilibrium, when the system does operate near equilibrium in the presence of dynamics, e.g. nodes join or leave. , or the tradeoff between performance and the rate of dynamics. In this pursuit, we provide three contributions in this paper. First, a novel probabilistic model to capture realistic behaviors of agents allowing for the possibility of arbitrariness in conjunction with rationality. Second, evaluation of (a) time to converge to equilibrium under this behavior model and (b) distance to Nash equilibrium. Finally, determination of tradeoff between the rate of dynamics and quality of performance (distance to equilibrium) which leads to an interesting uncertainty principle. The novel technical ingredients involve analysis of logarithmic Sobolov constant of Markov process with time varying state space and methodically this should be of broader interest in the context of dynamical systems.

DRAM Scheduling Policy for GPGPU Architectures Based on a Potential Function

GPGPU architectures (applications) have several different characteristics compared to traditional CPU architectures (applications): highly multithreaded architectures and SIMD-execution behavior are the two important characteristics of GPGPU computing. In this paper, we propose a potential function that models the DRAM behavior in GPGPU architectures and a DRAM scheduling policy α-SJF policy to minimize the potential function. The scheduling policy essentially chooses between SJF and FR-FCFS at run-time based on the number of requests from each thread and whether the thread has a row buffer hit.

Optimal CSMA: A survey

Carrier Sense Multiple Access (CSMA) has been widely used as a medium access control (MAC) scheme in wireless networks mainly due to its simple and totally distributed operations. Recently, it has been reported in the community that even such simple CSMA-type algorithms can achieve optimality in terms of throughput and utility, by smartly controlling its operational parameters such as backoff and holding times. In this survey paper, we summarize the recent research efforts in this area with main focus on the key intuitions and rationales, and conclude by presenting some open problems.

Provable Per-Link Delay-Optimal CSMA for General Wireless Network Topology

In the past few years, an exciting progress has been made on CSMA (Carrier Sense Multiple Access) algorithms that achieve throughput and utility optimality for wireless networks. However, most of these algorithms are known to exhibit poor delay performance making them impractical for implementation. Recently, several papers have addressed the delay issue of CSMA and yet, most of them are limited, in the sense that they focus merely on specific network scenarios with certain conditions rather than general network topology, achieve low delay at the cost of throughput reduction, or lack rigorous provable guarantees. In this paper, we focus on the recent idea of exploiting multiple channels (actually or virtually) for delay reduction in CSMA, and prove that it is per-link delay orderoptimal, i.e., O(1)-asymptotic-delay per link, if the number of virtual channels is logarithmic with respect to mixing time of the underlying CSMA Markov chain. The logarithmic number is typically small, i.e., at most linear with respect to the network size. In other words, our contribution provides not only a provable framework for the multiple-channel based CSMA, but also the required explicit number of virtual-multi-channels, which is of great importance for actual implementation. The key step of our analytic framework lies in using quadratic Lyapunov functions in conjunction with (recursively applying) Lindley equation and Azumas inequality for obtaining an exponential decaying property in certain queueing dynamics. We believe that our technique is of broad interest in analyzing the delay performances of other general queueing systems.

CSMA using the Bethe approximation for utility maximization

CSMA (Carrier Sense Multiple Access), which resolves contentions over wireless networks in a fully distributed fashion, has recently gained a lot of attentions since it has been proved that appropriate control of CSMA parameters guarantees optimality in terms of system-wide utility. Most algorithms rely on the popular MCMC (Markov Chain Monte Carlo) technique, which enables one to find optimal CSMA parameters through iterative loops of simulation-and-update. However, such a simulation-based approach often becomes a major cause of exponentially slow convergence, being poorly adaptive to flow/topology changes. In this paper, we develop a distributed iterative algorithm which produces approximate solutions with convergence in polynomial time. Our approach is motivated by a scheme in statistical physics, referred to as the Bethe approximation, allowing us to express approximate solutions via a certain non-linear system with polynomial size. We provide numerical results to show that the algorithm produces highly accurate solutions and converges much faster than prior ones.

Improved Mixing Condition on the Grid for Counting and Sampling Independent Sets

The hard-core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics, a multicast model of calls in communication networks, and as a weighted independent set problem in combinatorics, probability and theoretical computer science. In this model, each independent set

The Complexity of Approximating a Bethe Equilibrium

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