A stochastic analysis of resource sharing with logarithmic weights

The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to $\log(1+x)$, the logarithm of its current load. A detailed fluid scaling analysis of such a network with two nodes is presented. It is shown that the interaction of several time scales plays an important role in the evolution of such a system, in particular its coordinates may live on very different time and space scales. As a consequence, the associated stochastic processes turn out to have unusual scaling behaviors. A heavy traffic limit theorem for the invariant distribution is also proved. Finally, we present a generalization to the resource sharing algorithm for which the $\log$ function is replaced by an increasing function. Possible generalizations of these results with $J>2$ nodes or with the function $\log$ replaced by another slowly increasing function are discussed.Comment: Published at http://dx.doi.org/10.1214/14-AAP1057 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Delay QoS Provisioning and Optimal Resource Allocation for Wireless Networks

Recent years have witnessed a significant growth in wireless communication and networking due to the exponential growth in mobile applications and smart devices, fueling unprecedented increase in both mobile data traffic and energy demand. Among such data traffic, real-time data transmissions in wireless systems require certain quality of service (QoS) constraints e.g., in terms of delay, buffer overflow or packet drop/loss probabilities, so that acceptable performance levels can be guaranteed for the end-users, especially in delay sensitive scenarios, such as live video transmission, interactive video (e.g., teleconferencing), and mobile online gaming. With this motivation, statistical queuing constraints are considered in this thesis, imposed as limitations on the decay rate of buffer overflow probabilities. In particular, the throughput and energy efficiency of different types of wireless network models are analyzed under QoS constraints, and optimal resource allocation algorithms are proposed to maximize the throughput or minimize the delay. In the first part of the thesis, the throughput and energy efficiency analysis for hybrid automatic repeat request (HARQ) protocols are conducted under QoS constraints. Approximations are employed for small QoS exponent values in order to obtain closed-form expressions for the throughput and energy efficiency metrics. Also, the impact of random arrivals, deadline constraints, outage probability and QoS constraints are studied. For the same system setting, the throughput of HARQ system is also analyzed using a recurrence approach, which provides more accurate results for any value of the QoS exponent. Similarly, random arrival models and deadline constraints are considered, and these results are further extended to the finite-blocklength coding regime. Next, cooperative relay networks are considered under QoS constraints. Specifically, the throughput performance in the two-hop relay channel, two-way relay channel, and multi-source multi-destination relay networks is analyzed. Finite-blocklength codes are considered for the two-hop relay channel, and optimization over the error probabilities is investigated. For the multi-source multi-destination relay network model, the throughput for both cases of with and without CSI at the transmitter sides is studied. When there is perfect CSI at the transmitter, transmission rates can be varied according to instantaneous channel conditions. When CSI is not available at the transmitter side, transmissions are performed at fixed rates, and decoding failures lead to retransmission requests via an ARQ protocol. Following the analysis of cooperative networks, the performance of both half-duplex and full-duplex operations is studied for the two-way multiple input multiple output (MIMO) system under QoS constraints. In full-duplex mode, the self-interference inflicted on the reception of a user due to simultaneous transmissions from the same user is taken into account. In this setting, the system throughput is formulated by considering the sum of the effective capacities of the users in both half-duplex and full-duplex modes. The low signal to noise ratio (SNR) regime is considered and the optimal transmission/power-allocation strategies are characterized by identifying the optimal input covariance matrices. Next, mode selection and resource allocation for device-to-device (D2D) cellular networks are studied. As the starting point, ransmission mode selection and resource allocation are analyzed for a time-division multiplexed (TDM) cellular network with one cellular user, one base station, and a pair of D2D users under rate and QoS constraints. For a more complicated setting with multiple cellular and D2D users, two joint mode selection and resource allocation algorithms are proposed. In the first algorithm, the channel allocation problem is formulated as a maximum-weight matching problem, which can be solved by employing the Hungarian algorithm. In the second algorithm, the problem is divided into three subproblems, namely user partition, power allocation and channel assignment, and a novel three-step method is proposed by combining the algorithms designed for the three subproblems. In the final part of the thesis, resource allocation algorithms are investigated for content delivery over wireless networks. Three different systems are considered. Initially, a caching algorithm is designed, which minimizes the average delay of a single-cell network. The proposed algorithm is applicable in settings with very general popularity models, with no assumptions on how file popularity varies among different users, and this algorithm is further extended to a more general setting, in which the system parameters and the distributions of channel fading change over time. Next, for D2D cellular networks operating under deadline constraints, a scheduling algorithm is designed, which manages mode selection, channel allocation and power maximization with acceptable complexity. This proposed scheduling algorithm is designed based on the convex delay cost method for a D2D cellular network with deadline constraints in an OFDMA setting. Power optimization algorithms are proposed for all possible modes, based on our utility definition. Finally, a two-step intercell interference (ICI)-aware scheduling algorithm is proposed for cloud radio access networks (C-RANs), which performs user grouping and resource allocation with the goal of minimizing delay violation probability. A novel user grouping algorithm is developed for the user grouping step, which controls the interference among the users in the same group, and the channel assignment problem is formulated as a maximum-weight matching problem in the second step, which can be solved using standard algorithms in graph theory

Complexity, parallel computation and statistical physics

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to simulate it. Depth provides an objective, irreducible measure of history applicable to systems of the kind studied in statistical physics. It is argued that physical complexity cannot occur in the absence of substantial depth and that depth is a useful proxy for physical complexity. The ideas are illustrated for a variety of systems in statistical physics.Comment: 21 pages, 7 figure

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

Queue-Based Random-Access Algorithms: Fluid Limits and Stability Issues

We use fluid limits to explore the (in)stability properties of wireless networks with queue-based random-access algorithms. Queue-based 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. Simulation experiments are conducted to illustrate and validate the analytical results

ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry

This paper presents the current state of the global gyrokinetic code ORB5 as an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177 409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of equations using a PIC scheme and also includes collisions and strong flows. The code assumes multiple gyrokinetic ion species at all wavelengths for the polarization density and drift-kinetic electrons. Variants of the physical model can be selected for electrons such as assuming an adiabatic response or a ``hybrid'' model in which passing electrons are assumed adiabatic and trapped electrons are drift-kinetic. A Fourier filter as well as various control variates and noise reduction techniques enable simulations with good signal-to-noise ratios at a limited numerical cost. They are completed with different momentum and zonal flow-conserving heat sources allowing for temperature-gradient and flux-driven simulations. The code, which runs on both CPUs and GPUs, is well benchmarked against other similar codes and analytical predictions, and shows good scalability up to thousands of nodes