Performance analysis of a fluid queue with random service rate in discrete time

We consider a fluid queue in discrete time with random service rate. Such a queue has been used in several recent studies on wireless networks where the packets can be arbitrarily fragmented. We provide conditions on finiteness of moments of stationary delay, its Laplace-Stieltjes transform and various approximations under heavy traffic. Results are extended to the case where the wireless link can transmit in only a few slots during a frame.

A Fast Linear Separability Test by Projection of Positive Points on Subspaces

A geometric and non parametric procedure for testing if two finite set of points are linearly separable is proposed. The Linear Separability Test is equivalent to a test that determines if a strictly positive point h > 0 exists in the range of a matrix A (related to the points in the two finite sets). The algorithm proposed in the paper iteratively checks if a strictly positive point exists in a subspace by projecting a strictly positive vector with equal co-ordinates (p), on the subspace. At the end of each iteration, the subspace is reduced to a lower dimensional subspace. The test is completed within r ≤ min(n, d + 1) steps, for both linearly separable and non separable problems (r is the rank of A, n is the number of points and d is the dimension of the space containing the points). The worst case time complexity of the algorithm is O(nr3) and space complexity of the algorithm is O(nd). A small review of some of the prominent algorithms and their time complexities is included. The worst case computational complexity of our algorithm is lower than the worst case computational complexity of Simplex, Perceptron, Support Vector Machine and Convex Hull Algorithms, if d

Stochastic Algorithms for Discrete Parameter Simulation Optimization

We present two efficient discrete parameter simulation optimization (DPSO) algorithms for the long-run average cost objective. One of these algorithms uses the smoothed functional approximation (SFA) procedure, while the other is based on simultaneous perturbation stochastic approximation (SPSA). The use of SFA for DPSO had not been proposed previously in the literature. Further, both algorithms adopt an interesting technique of random projections that we present here for the first time. We give a proof of convergence of our algorithms. Next, we present detailed numerical experiments on a problem of admission control with dependent service times. We consider two different settings involving parameter sets that have moderate and large sizes, respectively. On the first setting, we also show performance comparisons with the well-studied optimal computing budget allocation (OCBA) algorithm and also the equal allocation algorithm. Note to Practitioners-Even though SPSA and SFA have been devised in the literature for continuous optimization problems, our results indicate that they can be powerful techniques even when they are adapted to discrete optimization settings. OCBA is widely recognized as one of the most powerful methods for discrete optimization when the parameter sets are of small or moderate size. On a setting involving a parameter set of size 100, we observe that when the computing budget is small, both SPSA and OCBA show similar performance and are better in comparison to SFA, however, as the computing budget is increased, SPSA and SFA show better performance than OCBA. Both our algorithms also show good performance when the parameter set has a size of 10(8). SFA is seen to show the best overall performance. Unlike most other DPSO algorithms in the literature, an advantage with our algorithms is that they are easily implementable regardless of the size of the parameter sets and show good performance in both scenarios.

Discrete control algorithms for a tubular ammonia reactor

The specific objective of this paper is to develop direct digital control strategies for an ammonia reactor using quadratic regulator theory and compare the performance of the resultant control system with that under conventional PID regulators. The controller design studies are based on a ninth order state-space model obtained from the exact nonlinear distributed model using linearization and lumping approximations. The evaluation of these controllers with reference to their disturbance rejection capabilities and transient response characteristics, is carried out using hybrid computer simulation.

Power and Discrete Rate Adaptation for Energy Harvesting Wireless Nodes

Energy Harvesting (EH) nodes, which harvest energy from the environment in order to communicate over a wireless link, promise perpetual operation of a wireless network with battery-powered nodes. In this paper, we address the throughput optimization problem for a rate-adaptive EH node that chooses its rate from a set of discrete rates and adjusts its power depending on its channel gain and battery state. First, we show that the optimal throughput of an EH node is upper bounded by the throughput achievable by a node that is subject only to an average power constraint. We then propose a simple transmission scheme for an EH node that achieves an average throughput close to the upper bound. The scheme's parameters can be made to account for energy overheads such as battery non-idealities and the energy required for sensing and processing. The effect of these overheads on the average throughput is also analytically characterized.

Class of linear time-varying discrete systems

A class of linear time-varying discrete systems is considered, and closed-form solutions are obtained in different cases. Some comments on stability are also included.

Discrete Wiener¿Lee transforms

The use of Wiener–Lee transforms to construct one of the frequency characteristics, magnitude or phase of a network function, when the other characteristic is given graphically, is indicated. This application is useful in finding a realisable network function whose magnitude or phase curve is given. A discrete version of the transform is presented, so that a digital computer can be employed for the computation.

New Insights into Optimal Discrete Rate Adaptation for Average Power Constrained Single and Multi-Node Systems

The throughput-optimal discrete-rate adaptation policy, when nodes are subject to constraints on the average power and bit error rate, is governed by a power control parameter, for which a closed-form characterization has remained an open problem. The parameter is essential in determining the rate adaptation thresholds and the transmit rate and power at any time, and ensuring adherence to the power constraint. We derive novel insightful bounds and approximations that characterize the power control parameter and the throughput in closed-form. The results are comprehensive as they apply to the general class of Nakagami-m (m >= 1) fading channels, which includes Rayleigh fading, uncoded and coded modulation, and single and multi-node systems with selection. The results are appealing as they are provably tight in the asymptotic large average power regime, and are designed and verified to be accurate even for smaller average powers.

Elasto-plastic analysis of jointed rocks using discrete continuum and equivalent continuum approaches

Results from elasto-plastic numerical simulations of jointed rocks using both the equivalent continuum and discrete continuum approaches are presented, and are compared with experimental measurements. Initially triaxial compression tests on different types of rocks with wide variation in the uniaxial compressive strength are simulated using both the approaches and the results are compared. The applicability and relative merits and limitations of both the approaches for the simulation of jointed rocks are discussed. It is observed that both the approaches are reasonably good in predicting the real response. However, the equivalent continuum approach has predicted somewhat higher stiffness values at low strains. Considering the modelling effort involved in case of discrete continuum approach, for problems with complex geometry, it is suggested that a proper equivalent continuum model can be used, without compromising much on the accuracy of the results. Then the numerical analysis of a tunnel in Japan is taken up using the continuum approach. The deformations predicted are compared well against the field measurements and the predictions from discontinuum analysis. (C) 2012 Elsevier Ltd. All rights reserved.

Receive Antenna Selection for Time-Varying Channels Using Discrete Prolate Spheroidal Sequences

Receive antenna selection (AS) has been shown to maintain the diversity benefits of multiple antennas while potentially reducing hardware costs. However, the promised diversity gains of receive AS depend on the assumptions of perfect channel knowledge at the receiver and slowly time-varying fading. By explicitly accounting for practical constraints imposed by the next-generation wireless standards such as training, packetization and antenna switching time, we propose a single receive AS method for time-varying fading channels. The method exploits the low training overhead and accuracy possible from the use of discrete prolate spheroidal (DPS) sequences based reduced rank subspace projection techniques. It only requires knowledge of the Doppler bandwidth, and does not require detailed correlation knowledge. Closed-form expressions for the channel prediction and estimation error as well as symbol error probability (SEP) of M-ary phase-shift keying (MPSK) for symbol-by-symbol receive AS are also derived. It is shown that the proposed AS scheme, after accounting for the practical limitations mentioned above, outperforms the ideal conventional single-input single-output (SISO) system with perfect CSI and no AS at the receiver and AS with conventional estimation based on complex exponential basis functions.

Capacity region of K-user discrete memoryless interference channels with a mixed strong-very strong interference

The capacity region of the 3-user Gaussian Interference Channel (GIC) with mixed strong-very strong interference was established in [1]. The mixed strong-very strong interference conditions considered in [1] correspond to the case where, at each receiver, one of the interfering signals is strong and the other is very strong. In this paper, we derive the capacity region of K-user (K ≥ 3) Discrete Memoryless Interference Channels (DMICs) with a mixed strong-very strong interference. This corresponds to the case where, at each receiver one of the interfering signals is strong and the other (K - 2) interfering signals are very strong. This includes, as a special case, the 3-user DMIC with mixed strong-very strong interference. The proof is specialized to the 3-user GIC case and hence an alternative derivation for the capacity region of the 3-user GIC with mixed strong-very strong interference is provided.

A nested linear codes approach to distributed function computation over subspaces

In this paper, we consider a distributed function computation setting, where there are m distributed but correlated sources X1,...,Xm and a receiver interested in computing an s-dimensional subspace generated by [X1,...,Xm]Γ for some (m × s) matrix Γ of rank s. We construct a scheme based on nested linear codes and characterize the achievable rates obtained using the scheme. The proposed nested-linear-code approach performs at least as well as the Slepian-Wolf scheme in terms of sum-rate performance for all subspaces and source distributions. In addition, for a large class of distributions and subspaces, the scheme improves upon the Slepian-Wolf approach. The nested-linear-code scheme may be viewed as uniting under a common framework, both the Korner-Marton approach of using a common linear encoder as well as the Slepian-Wolf approach of employing different encoders at each source. Along the way, we prove an interesting and fundamental structural result on the nature of subspaces of an m-dimensional vector space V with respect to a normalized measure of entropy. Here, each element in V corresponds to a distinct linear combination of a set {Xi}im=1 of m random variables whose joint probability distribution function is given.

Multi-objective optimization of satellite image registration using discrete Pparticle swarm optimisation

A new multi-sensor image registration technique is proposed based on detecting the feature corner points using modified Harris Corner Detector (HDC). These feature points are matched using multi-objective optimization (distance condition and angle criterion) based on Discrete Particle Swarm Optimization (DPSO). This optimization process is more efficient as it considers both the distance and angle criteria to incorporate multi-objective switching in the fitness function. This optimization process helps in picking up three corresponding corner points detected in the sensed and base image and thereby using the affine transformation, the sensed image is aligned with the base image. Further, the results show that the new approach can provide a new dimension in solving multi-sensor image registration problems. From the obtained results, the performance of image registration is evaluated and is concluded that the proposed approach is efficient.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.