Markov Chain Model for Cracking Behavior of Reinforced Concrete Beams

In this paper, nonhomogeneous Markov chains are proposed for modeling the cracking behavior of reinforced concrete beams subjected to monotonically increasing loads. The model facilitates prediction of the maximum crackwidth at a given load given the crackwidth at a lower load level, and thus leads to a better understanding of the cracking phenomenon. To illustrate the methodology developed, the results of three reinforced concrete beams tested in the laboratory are analyzed and presented.

Markov chain modeling of evolution of strains in reinforced concrete flexural beams

From the analysis of experimentally observed variations in surface strains with loading in reinforced concrete beams, it is noted that there is a need to consider the evolution of strains (with loading) as a stochastic process. Use of Markov Chains for modeling stochastic evolution of strains with loading in reinforced concrete flexural beams is studied in this paper. A simple, yet practically useful, bi-level homogeneous Gaussian Markov Chain (BLHGMC) model is proposed for determining the state of strain in reinforced concrete beams. The BLHGMC model will be useful for predicting behavior/response of reinforced concrete beams leading to more rational design.

Methodology for Pavement Design Reliability and Back Analysis Using Markov Chain Monte Carlo Simulation

Given the increasing cost of designing and building new highway pavements, reliability analysis has become vital to ensure that a given pavement performs as expected in the field. Recognizing the importance of failure analysis to safety, reliability, performance, and economy, back analysis has been employed in various engineering applications to evaluate the inherent uncertainties of the design and analysis. The probabilistic back analysis method formulated on Bayes' theorem and solved using the Markov chain Monte Carlo simulation method with a Metropolis-Hastings algorithm has proved to be highly efficient to address this issue. It is also quite flexible and is applicable to any type of prior information. In this paper, this method has been used to back-analyze the parameters that influence the pavement life and to consider the uncertainty of the mechanistic-empirical pavement design model. The load-induced pavement structural responses (e.g., stresses, strains, and deflections) used to predict the pavement life are estimated using the response surface methodology model developed based on the results of linear elastic analysis. The failure criteria adopted for the analysis were based on the factor of safety (FOS), and the study was carried out for different sample sizes and jumping distributions to estimate the most robust posterior statistics. From the posterior statistics of the case considered, it was observed that after approximately 150 million standard axle load repetitions, the mean values of the pavement properties decrease as expected, with a significant decrease in the values of the elastic moduli of the expected layers. An analysis of the posterior statistics indicated that the parameters that contribute significantly to the pavement failure were the moduli of the base and surface layer, which is consistent with the findings from other studies. After the back analysis, the base modulus parameters show a significant decrease of 15.8% and the surface layer modulus a decrease of 3.12% in the mean value. The usefulness of the back analysis methodology is further highlighted by estimating the design parameters for specified values of the factor of safety. The analysis revealed that for the pavement section considered, a reliability of 89% and 94% can be achieved by adopting FOS values of 1.5 and 2, respectively. The methodology proposed can therefore be effectively used to identify the parameters that are critical to pavement failure in the design of pavements for specified levels of reliability. DOI: 10.1061/(ASCE)TE.1943-5436.0000455. (C) 2013 American Society of Civil Engineers.

Markov chain splitting methods in structural reliability integral estimation

Monte Carlo simulation methods involving splitting of Markov chains have been used in evaluation of multi-fold integrals in different application areas. We examine in this paper the performance of these methods in the context of evaluation of reliability integrals from the point of view of characterizing the sampling fluctuations. The methods discussed include the Au-Beck subset simulation, Holmes-Diaconis-Ross method, and generalized splitting algorithm. A few improvisations based on first order reliability method are suggested to select algorithmic parameters of the latter two methods. The bias and sampling variance of the alternative estimators are discussed. Also, an approximation to the sampling distribution of some of these estimators is obtained. Illustrative examples involving component and series system reliability analyses are presented with a view to bring out the relative merits of alternative methods. (C) 2015 Elsevier Ltd. All rights reserved.

Ergodic control of partially observed Markov chains

The ergodic or long-run average cost control problem for a partially observed finite-state Markov chain is studied via the associated fully observed separated control problem for the nonlinear filter. Dynamic programming equations for the latter are derived, leading to existence and characterization of optimal stationary policies.

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.

Performance analysis of UDP with energy efficient link layer on Markov fading channels

In this paper, we analyze the throughput and energy efficiency performance of user datagram protocol (UDP) using linear, binary exponential, and geometric backoff algorithms at the link layer (LL) on point-to-point wireless fading links. Using a first-order Markov chain representation of the packet success/failure process on fading channels, we derive analytical expressions for throughput and energy efficiency of UDP/LL with and without LL backoff. The analytical results are verified through simulations. We also evaluate the mean delay and delay variation of voice packets and energy efficiency performance over a wireless link that uses UDP for transport of voice packets and the proposed backoff algorithms at the LL. We show that the proposed LL backoff algorithms achieve energy efficiency improvement of the order of 2-3 dB compared to LL with no backoff, without compromising much on the throughput and delay performance at the UDP layer. Such energy savings through protocol means will improve the battery life in wireless mobile terminals.

A Markov Decision Theoretic Approach to Pilot Allocation and Receive Antenna Selection

This paper considers antenna selection (AS) at a receiver equipped with multiple antenna elements but only a single radio frequency chain for packet reception. As information about the channel state is acquired using training symbols (pilots), the receiver makes its AS decisions based on noisy channel estimates. Additional information that can be exploited for AS includes the time-correlation of the wireless channel and the results of the link-layer error checks upon receiving the data packets. In this scenario, the task of the receiver is to sequentially select (a) the pilot symbol allocation, i.e., how to distribute the available pilot symbols among the antenna elements, for channel estimation on each of the receive antennas; and (b) the antenna to be used for data packet reception. The goal is to maximize the expected throughput, based on the past history of allocation and selection decisions, and the corresponding noisy channel estimates and error check results. Since the channel state is only partially observed through the noisy pilots and the error checks, the joint problem of pilot allocation and AS is modeled as a partially observed Markov decision process (POMDP). The solution to the POMDP yields the policy that maximizes the long-term expected throughput. Using the Finite State Markov Chain (FSMC) model for the wireless channel, the performance of the POMDP solution is compared with that of other existing schemes, and it is illustrated through numerical evaluation that the POMDP solution significantly outperforms them.

LANDSCAPE DYNAMICS MODELING THROUGH INTEGRATED MARKOV, FUZZY-AHP AND CELLULAR AUTOMATA

Multi temporal land use information were derived using two decades remote sensing data and simulated for 2012 and 2020 with Cellular Automata (CA) considering scenarios, change probabilities (through Markov chain) and Multi Criteria Evaluation (MCE). Agents and constraints were considered for modeling the urbanization process. Agents were nornmlized through fiizzyfication and priority weights were assigned through Analytical Hierarchical Process (AHP) pairwise comparison for each factor (in MCE) to derive behavior-oriented rules of transition for each land use class. Simulation shows a good agreement with the classified data. Fuzzy and AHP helped in analyzing the effects of agents of growth clearly and CA-Markov proved as a powerful tool in modelling and helped in capturing and visualizing the spatiotemporal patterns of urbanization. This provided rapid land evaluation framework with the essential insights of the urban trajectory for effective sustainable city planning.

Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

Risk-Sensitive Ergodic Control of Continuous Time Markov Processes With Denumerable State Space

In this article, we study risk-sensitive control problem with controlled continuous time Markov chain state dynamics. Using multiplicative dynamic programming principle along with the atomic structure of the state dynamics, we prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.

Multiaction learning automata possessing ergodicity of the mean

Multiaction learning automata which update their action probabilities on the basis of the responses they get from an environment are considered in this paper. The automata update the probabilities according to whether the environment responds with a reward or a penalty. Learning automata are said to possess ergodicity of the mean if the mean action probability is the state probability (or unconditional probability) of an ergodic Markov chain. In an earlier paper [11] we considered the problem of a two-action learning automaton being ergodic in the mean (EM). The family of such automata was characterized completely by proving the necessary and sufficient conditions for automata to be EM. In this paper, we generalize the results of [11] and obtain necessary and sufficient conditions for the multiaction learning automaton to be EM. These conditions involve two families of probability updating functions. It is shown that for the automaton to be EM the two families must be linearly dependent. The vector defining the linear dependence is the only vector parameter which controls the rate of convergence of the automaton. Further, the technique for reducing the variance of the limiting distribution is discussed. Just as in the two-action case, it is shown that the set of absolutely expedient schemes and the set of schemes which possess ergodicity of the mean are mutually disjoint.

A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems

Motivated by certain situations in manufacturing systems and communication networks, we look into the problem of maximizing the profit in a queueing system with linear reward and cost structure and having a choice of selecting the streams of Poisson arrivals according to an independent Markov chain. We view the system as a MMPP/GI/1 queue and seek to maximize the profits by optimally choosing the stationary probabilities of the modulating Markov chain. We consider two formulations of the optimization problem. The first one (which we call the PUT problem) seeks to maximize the profit per unit time whereas the second one considers the maximization of the profit per accepted customer (the PAC problem). In each of these formulations, we explore three separate problems. In the first one, the constraints come from bounding the utilization of an infinite capacity server; in the second one the constraints arise from bounding the mean queue length of the same queue; and in the third one the finite capacity of the buffer reflect as a set of constraints. In the problems bounding the utilization factor of the queue, the solutions are given by essentially linear programs, while the problems with mean queue length constraints are linear programs if the service is exponentially distributed. The problems modeling the finite capacity queue are non-convex programs for which global maxima can be found. There is a rich relationship between the solutions of the PUT and PAC problems. In particular, the PUT solutions always make the server work at a utilization factor that is no less than that of the PAC solutions.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

On the optimality of exhaustive service policies in multiclass queueing systems with modulated arrivals and switchovers

Consider a single-server multiclass queueing system with K classes where the individual queues are fed by K-correlated interrupted Poisson streams generated in the states of a K-state stationary modulating Markov chain. The service times for all the classes are drawn independently from the same distribution. There is a setup time (and/or a setup cost) incurred whenever the server switches from one queue to another. It is required to minimize the sum of discounted inventory and setup costs over an infinite horizon. We provide sufficient conditions under which exhaustive service policies are optimal. We then present some simulation results for a two-class queueing system to show that exhaustive, threshold policies outperform non-exhaustive policies.