Performance analysis of the random early detection algorithm

In this article we consider a finite queue with its arrivals controlled by the random early detection algorithm. This is one of the most prominent congestion avoidance schemes in the Internet routers. The aggregate arrival stream from the population of transmission control protocol sources is locally considered stationary renewal or Markov modulated Poisson process with general packet length distribution. We study the exact dynamics of this queue and provide the stability and the rates of convergence to the stationary distribution and obtain the packet loss probability and the waiting time distribution. Then we extend these results to a two traffic class case with each arrival stream renewal. However, computing the performance indices for this system becomes computationally prohibitive. Thus, in the latter half of the article, we approximate the dynamics of the average queue length process asymptotically via an ordinary differential equation. We estimate the error term via a diffusion approximation. We use these results to obtain approximate transient and stationary performance of the system. Finally, we provide some computational examples to show the accuracy of these approximations.

On the utility of an instrumented impact set-up to characterise the response of discontinuous buffer strips in carbon–epoxy systems in dry and wet conditions

The use of an instrumented impact test set-up to evaluate the influence of water ingress on the impact response of a carbon–epoxy (C–E) laminated composite system containing discontinuous buffer strips (BS) has been examined. The data on the BS-free C–E sample in dry conditions are used as reference to compare with the data derived from those immersed in water. The work demonstrated the utility of an instrumented impact test set-up in characterising the response, first owing to the architectural difference due to introduction of buffer strips and then due to the presence of an additional phase in the form of water ingressed into the sample. The presence of water was found to enhance the energy absorption characteristics of the C–E system with BS insertions. It was also noticed that with an increasing number of BS layer insertions, the load–time plots displayed characteristic changes. The ductility indices (DI) were found to display a lower value for the water immersed samples compared to the dry ones.

The utility of Bacillus subtilis as a bioflocculant for fine coal

The application of Bacillus subtilis as a flocculant for fine coal has been reported here. Zeta-potential measurements showed that both the coal and bacteria had similar surface charge as a function of pH. Surface free energy calculations showed that the coal was hydrophobic while the bacterium was hydrophilic. The adhesion of the bacteria to coal and subsequent settling was studied in detail. Adhesion of bacteria to coal surface and subsequent settling of coal was found to be quick. Both adhesion and settling were found to be independent of pH, which makes the process very attractive for field applications. The presence of an electrolyte along with the bacterium was found to not only enhance adhesion of bacteria, but also produce a clear supernatant. Further, the settled fraction was more compact than with bacteria alone. Interaction energy calculations using the extended DLVO theory showed that the electrical forces along with the acid-base interaction energy play a dominant role in the lower pH range. Above pH 7, the acid-base interaction energy is the predominant attractive force and is sufficient enough to overcome the repulsive forces due to electrical charges to brine about adhesion and thus settling of fine coal. With increase in electrolyte concentration, the change in total interaction energy with pH is minimal which probably leads to better adhesion and hence settling. (C) 2003 Elsevier Science B.V. All rights reserved.

Percolation and Connectivity in AB Random Geometric Graphs

Given two independent Poisson point processes ©(1);©(2) in Rd, the AB Poisson Boolean model is the graph with points of ©(1) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centred at these points contains at least one point of ©(2). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d ¸ 2 and derive bounds for a critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and cn in the unit cube. The AB random geometric graph is de¯ned as above but with balls of radius r. We derive a weak law result for the largest nearest neighbour distance and almost sure asymptotic bounds for the connectivity threshold.

Doubly spectral stochastic finite element method (DSSFEM) for random field problems

Uncertainties in complex dynamic systems play an important role in the prediction of a dynamic response in the mid- and high-frequency ranges. For distributed parameter systems, parametric uncertainties can be represented by random fields leading to stochastic partial differential equations. Over the past two decades, the spectral stochastic finite-element method has been developed to discretize the random fields and solve such problems. On the other hand, for deterministic distributed parameter linear dynamic systems, the spectral finite-element method has been developed to efficiently solve the problem in the frequency domain. In spite of the fact that both approaches use spectral decomposition (one for the random fields and the other for the dynamic displacement fields), very little overlap between them has been reported in literature. In this paper, these two spectral techniques are unified with the aim that the unified approach would outperform any of the spectral methods considered on their own. An exponential autocorrelation function for the random fields, a frequency-dependent stochastic element stiffness, and mass matrices are derived for the axial and bending vibration of rods. Closed-form exact expressions are derived by using the Karhunen-Loève expansion. Numerical examples are given to illustrate the unified spectral approach.

Efficiently Approximating Query Optimizer Plan Diagrams

Given a parametrized n-dimensional SQL query template and a choice of query optimizer, a plan diagram is a color-coded pictorial enumeration of the execution plan choices of the optimizer over the query parameter space. These diagrams have proved to be a powerful metaphor for the analysis and redesign of modern optimizers, and are gaining currency in diverse industrial and academic institutions. However, their utility is adversely impacted by the impractically large computational overheads incurred when standard brute-force exhaustive approaches are used for producing fine-grained diagrams on high-dimensional query templates. In this paper, we investigate strategies for efficiently producing close approximations to complex plan diagrams. Our techniques are customized to the features available in the optimizer's API, ranging from the generic optimizers that provide only the optimal plan for a query, to those that also support costing of sub-optimal plans and enumerating rank-ordered lists of plans. The techniques collectively feature both random and grid sampling, as well as inference techniques based on nearest-neighbor classifiers, parametric query optimization and plan cost monotonicity. Extensive experimentation with a representative set of TPC-H and TPC-DS-based query templates on industrial-strength optimizers indicates that our techniques are capable of delivering 90% accurate diagrams while incurring less than 15% of the computational overheads of the exhaustive approach. In fact, for full-featured optimizers, we can guarantee zero error with less than 10% overheads. These approximation techniques have been implemented in the publicly available Picasso optimizer visualization tool.

Search on a Hypercubic Lattice using Quantum Random Walk

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d=2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article [ A. Patel and M. A. Rahaman Phys. Rev. A 82 032330 (2010)] provides an O(√NlnN) algorithm, which is not optimal. The scaling behavior can be improved to O(√NlnN) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78 012310 (2008). We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.

Power control and transmission scheduling for network utility maximization in wireless networks

We consider a joint power control and transmission scheduling problem in wireless networks with average power constraints. While the capacity region of a wireless network is convex, a characterization of this region is a hard problem. We formulate a network utility optimization problem involving time-sharing across different "transmission modes," where each mode corresponds to the set of power levels used in the network. The structure of the optimal solution is a time-sharing across a small set of such modes. We use this structure to develop an efficient heuristic approach to finding a suboptimal solution through column generation iterations. This heuristic approach converges quite fast in simulations, and provides a tool for wireless network planning.

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.

Evolving Random Geometric Graph Models for Mobile Wireless Networks

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.

Quantum Random Walks without Coin Toss

We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of classical randomised algorithms. We use this algorithm to search for a marked vertex on a hypercubic lattice in arbitrary dimensions. Our numerical and analytical results match the scaling behaviour of earlier algorithms that use a coin toss instruction.

Phenylboronic acids in crystal engineering: Utility of the energetically unfavorable syn,syn-conformation in co-crystal design

Phenylboronic acids can exist, in principle, in three different conformers (syn,syn; syn,anti and anti,anti) with distinct energy profiles. In their native state, these compounds prefer the energetically favored syn, anti-conformation. In molecular complexes, however, the functionality exhibits conformational diversity. In this paper we report a series of co-crystals, with N-donor compounds, prepared by a design strategy involving the synthons based on the syn, syn-conformation of the boronic acid functionality. For this purpose, we employed compounds with the 1,2-diazo fragment (alprazolam, 1H-tetrazole, acetazolamide and benzotriazole), 1,10-phenanthroline and 2,2'-bipyridine for the co-crystallization experiments. However, our study shows that the mere presence of the 1,2-diazo fragment in the coformer does not guarantee the successful formation of co-crystals with a syn, syn-conformation of the boronic acid. [GRAPHICS] The -B(OH)(2) fragment makes unsymmetrical O-H center dot center dot center dot N heterosynthons with alprazolam (ALP) and 1,10-phenanthroline (PHEN). In the co-crystals of phenylboronic acids with 1H-tetrazole (TETR) and 2,2'-bipyridine (BPY), the symmetrical boronic acid dimer is the major synthon. In the BPY complex, boronic acid forms linear chains and the pyridine compound interacts with the lateral OH of boronic acid dimers that acts as a connector, thus forming a ladder structure. In the TETR complex, each heterocycle interacts with three boronic acids. While two boronic acids interact using the phenolic group, the third molecule generates O-H center dot center dot center dot N hydrogen bonds using the extra OH group, of -B(OH)(2) fragment, left after the dimer formation. Thus, although molecules were selected retrosynthetically with the 1,2-diazo fragment or with nearby hetero-atoms to induce co-crystal formation using the syn,syn-orientation of the -B(OH)(2) functionality, co-crystal formation is in fact selective and is probably driven by energy factors. Acetazolamide (ACET) contains self-complementary functional groups and hence creates stable homosynthons. Phenylboronic acids being weak competitors fail to perturb the homosynthons and hence the components crystallize separately. Therefore, besides the availability of possible hydrogen bond acceptors in the required position and orientation, the ability of the phenyl-boronic acid to perturb the existing interactions is also a prerequisite to form co-crystals. This is illustrated in the table below. In the case of ALP, PHEN and BPY, the native structures are stabilized by weak interactions and may be influenced by the boronic acid fragment. Thus phenylboronic acids can attain co-crystals with those compounds, wherein the cyclic O-H center dot center dot center dot N hydrogen bonds are stronger than the individual homo-interactions. This can lower the lattice energy of the molecular complex as compared with the individual crystals. [GRAPHICS] Phenylboronic acids show some selectivity in the formation of co-crystals with N-heterocycles. The differences in solubility of the components fall short to provide a possible reason for the selective formation of co-crystals only with certain compounds. These compounds, being weak acids, do not follow the Delta pK(a) analysis and hence fail to provide any conclusive observation. Theoretical results show that of the three conformers possible, the syn,anti conformer is the most stable. The relative stabilities of the three conformers syn,anti,syn,syn and anti,anti are 0.0, 2.18 and 3.14 kcal/mol, respectively. The theoretical calculations corroborate the fact that only energetically favorable synthons can induce the formation of heterosynthons, as in ALP and PHEN complexes. From a theoretical and structural analysis it is seen that phenylboronic acids will form interactions with those molecules wherein the heterocyclic and acidic fragments can interrupt the homosynthons. However, the energy profile is shallow and can be perturbed easily by the presence of competing functional groups (such as OH and COOH) in the vicinity. [GRAPHICS] .

Dioxomolybdenum reagents in organic synthesis: utility of redox capability to design reduction and oxidation

The usefulness of dioxomolybdenum reagents in oxo-transfer reactions have been reviewed. The redox ability of dioxomolybdenum reagent has been utilized in designing several synthetic methods, which are useful in organic synthesis. Several reactions such as oxidation of alcohols, sulfides, amines, azides olefins etc are accomplished by using dioxomolybdenum reagents. Similarly, it is also demonstrated that dioxomolybdenum complex is useful in performing reduction of aldehydes, ketones, esters, azides etc. A fine tuning of reaction conditions provides suitable conditions to perform either oxidation or reduction by using catalytic amount of reagents. The oxidation reactions are further simplified by employing the polymer supported molybdenum reagents.

A Refined Methodology for Durability-Based Service Life Estimation of Reinforced Concrete Structural Elements Considering Fuzzy and Random Uncertainties

A reliable method for service life estimation of the structural element is a prerequisite for service life design. A new methodology for durability-based service life estimation of reinforced concrete flexural elements with respect to chloride-induced corrosion of reinforcement is proposed. The methodology takes into consideration the fuzzy and random uncertainties associated with the variables involved in service life estimation by using a hybrid method combining the vertex method of fuzzy set theory with Monte Carlo simulation technique. It is also shown how to determine the bounds for characteristic value of failure probability from the resulting fuzzy set for failure probability with minimal computational effort. Using the methodology, the bounds for the characteristic value of failure probability for a reinforced concrete T-beam bridge girder has been determined. The service life of the structural element is determined by comparing the upper bound of characteristic value of failure probability with the target failure probability. The methodology will be useful for durability-based service life design and also for making decisions regarding in-service inspections.