Jointly Optimal Channel and Power Assignment for Dual-Hop Multi-channel Multi-user Relaying

We consider the problem of jointly optimizing channel pairing, channel-user assignment, and power allocation, to maximize the weighted sum-rate, in a single-relay cooperative system with multiple channels and multiple users. Common relaying strategies are considered, and transmission power constraints are imposed on both individual transmitters and the aggregate over all transmitters. The joint optimization problem naturally leads to a mixed-integer program. Despite the general expectation that such problems are intractable, we construct an efficient algorithm to find an optimal solution, which incurs computational complexity that is polynomial in the number of channels and the number of users. We further demonstrate through numerical experiments that the jointly optimal solution can significantly improve system performance over its suboptimal alternatives.Comment: This is the full version of a paper to appear in the IEEE Journal on Selected Areas in Communications, Special Issue on Cooperative Networking - Challenges and Applications (Part II), October 201

Dynamically Spontaneous Symmetry Breaking and Masses of Lightest Nonet Scalar Mesons as Composite Higgs Bosons

Based on the (approximate) chiral symmetry of QCD Lagrangian and the bound state assumption of effective meson fields, a nonlinearly realized effective chiral Lagrangian for meson fields is obtained from integrating out the quark fields by using the new finite regularization method. As the new method preserves the symmetry principles of the original theory and meanwhile keeps the finite quadratic term given by a physically meaningful characteristic energy scale $M_c$, it then leads to a dynamically spontaneous symmetry breaking in the effective chiral field theory. The gap equations are obtained as the conditions of minimal effective potential in the effective theory. The instanton effects are included via the induced interactions discovered by 't Hooft and found to play an important role in obtaining the physical solutions for the gap equations. The lightest nonet scalar mesons($\sigma$, $f_0$, $a_0$ and $\kappa$) appearing as the chiral partners of the nonet pseudoscalar mesons are found to be composite Higgs bosons with masses below the chiral symmetry breaking scale $\Lambda_{\chi} \sim 1.2$ GeV. In particular, the mass of the singlet scalar (or the $\sigma$) is found to be $m_{\sigma} \simeq 677$ MeV.Comment: 15 pages, Revtex, published version, Eur. Phys. J. C (2004) (DOI) 10.1140/epjcd/s2004-01-001-

Dominant Resource Fairness in Cloud Computing Systems with Heterogeneous Servers

We study the multi-resource allocation problem in cloud computing systems where the resource pool is constructed from a large number of heterogeneous servers, representing different points in the configuration space of resources such as processing, memory, and storage. We design a multi-resource allocation mechanism, called DRFH, that generalizes the notion of Dominant Resource Fairness (DRF) from a single server to multiple heterogeneous servers. DRFH provides a number of highly desirable properties. With DRFH, no user prefers the allocation of another user; no one can improve its allocation without decreasing that of the others; and more importantly, no user has an incentive to lie about its resource demand. As a direct application, we design a simple heuristic that implements DRFH in real-world systems. Large-scale simulations driven by Google cluster traces show that DRFH significantly outperforms the traditional slot-based scheduler, leading to much higher resource utilization with substantially shorter job completion times

Dynamic Control of Tunable Sub-optimal Algorithms for Scheduling of Time-varying Wireless Networks

It is well known that for ergodic channel processes the Generalized Max-Weight Matching (GMWM) scheduling policy stabilizes the network for any supportable arrival rate vector within the network capacity region. This policy, however, often requires the solution of an NP-hard optimization problem. This has motivated many researchers to develop sub-optimal algorithms that approximate the GMWM policy in selecting schedule vectors. One implicit assumption commonly shared in this context is that during the algorithm runtime, the channel states remain effectively unchanged. This assumption may not hold as the time needed to select near-optimal schedule vectors usually increases quickly with the network size. In this paper, we incorporate channel variations and the time-efficiency of sub-optimal algorithms into the scheduler design, to dynamically tune the algorithm runtime considering the tradeoff between algorithm efficiency and its robustness to changing channel states. Specifically, we propose a Dynamic Control Policy (DCP) that operates on top of a given sub-optimal algorithm, and dynamically but in a large time-scale adjusts the time given to the algorithm according to queue backlog and channel correlations. This policy does not require knowledge of the structure of the given sub-optimal algorithm, and with low overhead can be implemented in a distributed manner. Using a novel Lyapunov analysis, we characterize the throughput stability region induced by DCP and show that our characterization can be tight. We also show that the throughput stability region of DCP is at least as large as that of any other static policy. Finally, we provide two case studies to gain further intuition into the performance of DCP.Comment: Submitted for journal consideration. A shorter version was presented in IEEE IWQoS 200