Reservoir performance under uncertainty in hydrologic impacts of climate change

Relatively few studies have addressed water management and adaptation measures in the face of changing water balances due to climate change. The current work studies climate change impact on a multipurpose reservoir performance and derives adaptive policies for possible futurescenarios. The method developed in this work is illustrated with a case study of Hirakud reservoir on the Mahanadi river in Orissa, India,which is a multipurpose reservoir serving flood control, irrigation and power generation. Climate change effects on annual hydropower generation and four performance indices (reliability with respect to three reservoir functions, viz. hydropower, irrigation and flood control, resiliency, vulnerability and deficit ratio with respect to hydropower) are studied. Outputs from three general circulation models (GCMs) for three scenarios each are downscaled to monsoon streamflow in the Mahanadi river for two future time slices, 2045-65 and 2075-95. Increased irrigation demands, rule curves dictated by increased need for flood storage and downscaled projections of streamflow from the ensemble of GCMs and scenarios are used for projecting future hydrologic scenarios. It is seen that hydropower generation and reliability with respect to hydropower and irrigation are likely to show a decrease in future in most scenarios, whereas the deficit ratio and vulnerability are likely to increase as a result of climate change if the standard operating policy (SOP) using current rule curves for flood protection is employed. An optimal monthly operating policy is then derived using stochastic dynamic programming (SDP) as an adaptive policy for mitigating impacts of climate change on reservoir operation. The objective of this policy is to maximize reliabilities with respect to multiple reservoir functions of hydropower, irrigation and flood control. In variations to this adaptive policy, increasingly more weightage is given to the purpose of maximizing reliability with respect to hydropower for two extreme scenarios. It is seen that by marginally sacrificing reliability with respect to irrigation and flood control, hydropower reliability and generation can be increased for future scenarios. This suggests that reservoir rules for flood control may have to be revised in basins where climate change projects an increasing probability of droughts. However, it is also seen that power generation is unable to be restored to current levels, due in part to the large projected increases in irrigation demand. This suggests that future water balance deficits may limit the success of adaptive policy options. (C) 2010 Elsevier Ltd. All rights reserved.

Stochastic simulations of the origins and implications of long-tailed distributions in gene expression

Gene expression noise results in protein number distributions ranging from long-tailed to Gaussian. We show how long-tailed distributions arise from a stochastic model of the constituent chemical reactions and suggest that, in conjunction with cooperative switches, they lead to more sensitive selection of a subpopulation of cells with high protein number than is possible with Gaussian distributions. Single-cell-tracking experiments are presented to validate some of the assumptions of the stochastic simulations. We also examine the effect of DNA looping on the shape of protein distributions. We further show that when switches are incorporated in the regulation of a gene via a feedback loop, the distributions can become bimodal. This might explain the bimodal distribution of certain morphogens during early embryogenesis.

Solution of MDPS using simulation-based value iteration

This article proposes a three-timescale simulation based algorithm for solution of infinite horizon Markov Decision Processes (MDPs). We assume a finite state space and discounted cost criterion and adopt the value iteration approach. An approximation of the Dynamic Programming operator T is applied to the value function iterates. This 'approximate' operator is implemented using three timescales, the slowest of which updates the value function iterates. On the middle timescale we perform a gradient search over the feasible action set of each state using Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimates, thus finding the minimizing action in T. On the fastest timescale, the 'critic' estimates, over which the gradient search is performed, are obtained. A sketch of convergence explaining the dynamics of the algorithm using associated ODEs is also presented. Numerical experiments on rate based flow control on a bottleneck node using a continuous-time queueing model are performed using the proposed algorithm. The results obtained are verified against classical value iteration where the feasible set is suitably discretized. Over such a discretized setting, a variant of the algorithm of [12] is compared and the proposed algorithm is found to converge faster.

Optimal threshold policies for admission control in communication networks via discrete parameter stochastic approximation

The problem of admission control of packets in communication networks is studied in the continuous time queueing framework under different classes of service and delayed information feedback. We develop and use a variant of a simulation based two timescale simultaneous perturbation stochastic approximation (SPSA) algorithm for finding an optimal feedback policy within the class of threshold type policies. Even though SPSA has originally been designed for continuous parameter optimization, its variant for the discrete parameter case is seen to work well. We give a proof of the hypothesis needed to show convergence of the algorithm on our setting along with a sketch of the convergence analysis. Extensive numerical experiments with the algorithm are illustrated for different parameter specifications. In particular, we study the effect of feedback delays on the system performance.

Hybrid moving block bootstrap for stochastic simulation of multi-site multi-season streamflows

The Hybrid approach introduced by the authors for at-site modeling of annual and periodic streamflows in earlier works is extended to simulate multi-site multi-season streamflows. It bears significance in integrated river basin planning studies. This hybrid model involves: (i) partial pre-whitening of standardized multi-season streamflows at each site using a parsimonious linear periodic model; (ii) contemporaneous resampling of the resulting residuals with an appropriate block size, using moving block bootstrap (non-parametric, NP) technique; and (iii) post-blackening the bootstrapped innovation series at each site, by adding the corresponding parametric model component for the site, to obtain generated streamflows at each of the sites. It gains significantly by effectively utilizing the merits of both parametric and NP models. It is able to reproduce various statistics, including the dependence relationships at both spatial and temporal levels without using any normalizing transformations and/or adjustment procedures. The potential of the hybrid model in reproducing a wide variety of statistics including the run characteristics, is demonstrated through an application for multi-site streamflow generation in the Upper Cauvery river basin, Southern India. (C) 2004 Elsevier B.V. All rights reserved.

Optimal non-linear reinforcement schemes for stochastic automata

Two optimal non-linear reinforcement schemes—the Reward-Inaction and the Penalty-Inaction—for the two-state automaton functioning in a stationary random environment are considered. Very simple conditions of symmetry of the non-linear function figuring in the reinforcement scheme are shown to be necessary and sufficient for optimality. General expressions for the variance and rate of learning are derived. These schemes are compared with the already existing optimal linear schemes in the light of average variance and average rate of learning.

Performance analysis of a suprathreshold, stochastic resonance based nonlinear detector

In this paper we introduce a nonlinear detector based on the phenomenon of suprathreshold stochastic resonance (SSR). We first present a model (an array of 1-bit quantizers) that demonstrates the SSR phenomenon. We then use this as a pre-processor to the conventional matched filter. We employ the Neyman-Pearson(NP) detection strategy and compare the performances of the matched filter, the SSR-based detector and the optimal detector. Although the proposed detector is non-optimal, for non-Gaussian noises with heavy tails (leptokurtic) it shows better performance than the matched filter. In situations where the noise is known to be leptokurtic without the availability of the exact knowledge of its distribution, the proposed detector turns out to be a better choice than the matched filter.

Dynamic programming based optimum non-uniform samples for speech reconstruction and coding

Non-uniform sampling of a signal is formulated as an optimization problem which minimizes the reconstruction signal error. Dynamic programming (DP) has been used to solve this problem efficiently for a finite duration signal. Further, the optimum samples are quantized to realize a speech coder. The quantizer and the DP based optimum search for non-uniform samples (DP-NUS) can be combined in a closed-loop manner, which provides distinct advantage over the open-loop formulation. The DP-NUS formulation provides a useful control over the trade-off between bitrate and performance (reconstruction error). It is shown that 5-10 dB SNR improvement is possible using DP-NUS compared to extrema sampling approach. In addition, the close-loop DP-NUS gives a 4-5 dB improvement in reconstruction error.

A generalized Linear Programming based approach to optimal divisible load scheduling

In this paper we propose a general Linear Programming (LP) based formulation and solution methodology for obtaining optimal solution to the load distribution problem in divisible load scheduling. We exploit the power of the versatile LP formulation to propose algorithms that yield exact solutions to several very general load distribution problems for which either no solutions or only heuristic solutions were available. We consider both star (single-level tree) networks and linear daisy chain networks, having processors equipped with front-ends, that form the generic models for several important network topologies. We consider arbitrary processing node availability or release times and general models for communication delays and computation time that account for constant overheads such as start up times in communication and computation. The optimality of the LP based algorithms is proved rigorously.

Stochastic models of IEEE 802.11e wireless net works with multimedia applications

We provide a survey of some of our recent results ([9], [13], [4], [6], [7]) on the analytical performance modeling of IEEE 802.11 wireless local area networks (WLANs). We first present extensions of the decoupling approach of Bianchi ([1]) to the saturation analysis of IEEE 802.11e networks with multiple traffic classes. We have found that even when analysing WLANs with unsaturated nodes the following state dependent service model works well: when a certain set of nodes is nonempty, their channel attempt behaviour is obtained from the corresponding fixed point analysis of the saturated system. We will present our experiences in using this approximation to model multimedia traffic over an IEEE 802.11e network using the enhanced DCF channel access (EDCA) mechanism. We have found that we can model TCP controlled file transfers, VoIP packet telephony, and streaming video in the IEEE802.11e setting by this simple approximation.

A suprathreshold stochastic resonance based pre-processor for direction-of-arrival estimation

In this paper we propose a nonlinear preprocessor for enhancing the performance of processors used for direction-of-arrival (DOA) estimation in heavy-tailed non-Gaussian noise. The preprocessor based on the phenomenon of suprathreshold stochastic resonance (SSR), provides SNR gain. The preprocessed data is used for DOA estimation by the MUSIC algorithm. Simulation results are presented to show that the SSR preprocessor provides a significant improvement in the performance of MUSIC in heavy-tailed noise at low SNR.

Second order cone programming approaches for handling missing and uncertain data

We propose a novel second order cone programming formulation for designing robust classifiers which can handle uncertainty in observations. Similar formulations are also derived for designing regression functions which are robust to uncertainties in the regression setting. The proposed formulations are independent of the underlying distribution, requiring only the existence of second order moments. These formulations are then specialized to the case of missing values in observations for both classification and regression problems. Experiments show that the proposed formulations outperform imputation.

Online client-AP association in WLANs

In many IEEE 802.11 WLAN deployments, wireless clients have a choice of access points (AP) to connect to. In current systems, clients associate with the access point with the strongest signal to noise ratio. However, such an association mechanism can lead to unequal load sharing, resulting in diminished system performance. In this paper, we first provide a numerical approach based on stochastic dynamic programming to find the optimal client-AP association algorithm for a small topology consisting of two access points. Using the value iteration algorithm, we determine the optimal association rule for the two-AP topology. Next, utilizing the insights obtained from the optimal association ride for the two-AP case, we propose a near-optimal heuristic that we call RAT. We test the efficacy of RAT by considering more realistic arrival patterns and a larger topology. Our results show that RAT performs very well in these scenarios as well. Moreover, RAT lends itself to a fairly simple implementation.

PROMIDS: A PROtotype multi-rIng data flow system for functional programming languages

This paper presents a detailed description of the hardware design and implementation of PROMIDS: a PROtotype Multi-rIng Data flow System for functional programming languages. The hardware constraints and the design trade-offs are discussed. The design of the functional units is described in detail. Finally, we report our experience with PROMIDS.