Browsing by Subject "Markov processes."
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Item Open Access Analysis of Erlang transfer lines(Bilkent University, 1997) Dönmez, NebahatTransfer lines are widely used in the modeling and analysis of complex production systems. The literature is mostly devoted to the analysis of transfer lines with exponential processing times. However, most of the time a part is |)rocessed through stages(phases) of exponential processing times. It is possil)le to model such systems by means of processing times that are A,·—Erlang distributed. In the modeling and solution of these systems, significant difficulties arise due to the nature of the problem. In this thesis, we propose a -Markov model for transfer lines consisting of n reliable machines with A—Erlang processing times and finite buffers. The arrivals to the system is Poisson distributed. A program coded in C which is capable of solving the Markov model of a three machine transfer line is also developed. Besides the commonly used performance measures, such as utilization of the machines, mean throughput, mean WIP level, we calculate the variance of VVIP so that it is possible to construct confidence intervals.Item Open Access Asymptotic analysis of highly reliable retrial queueing systems(Bilkent University, 2000) Kurtuluş, MüminThe thesis is concerned with the asymptotic analysis of the time of first loss of a customer and the flow of lost customers in some types of Markov retrial queueing systems with flnite buffer. A retrial queueing system is characterized by the following feature: an arriving customer finding all of the servers busy must leave the service area and join a special buffer. After this it may re-apply for service after some random time. If the buffer is full the customer is lost. The analysis of the time of first loss of a customer is based on the method of so-called S — sets and the results about the asymptotic behavior of the first exit time from the fixed subset of states of semi-Markov process of a special structure (so-called monotone structure). Single server retrial queueing systems [M IM IlIm with retrials) as well as multiple server retrial queueing systems {M IM fsfm with retrials) are analyzed in cases of fast service and both fast service and fast retrials. Exponential approximation for the time of first loss and Poisson approximation for the flow of lost customers are proved for all of the considered cases.Item Open Access Extension operators for spaces of infinitely differentiable functions(Bilkent University, 2005) Altun, MuhammedWe start with a review of known linear continuous extension operators for the spaces of Whitney functions. The most general approach belongs to PawÃlucki and Ple´sniak. Their operator is continuous provided that the compact set, where the functions are defined, has Markov property. In this work, we examine some model compact sets having no Markov property, but where a linear continuous extension operator exists for the space of Whitney functions given on these sets. Using local interpolation of Whitney functions we can generalize the PawÃlucki-Ple´sniak extension operator. We also give an upper bound for the Green function of domains complementary to generalized Cantor-type sets, where the Green function does not have the H¨older continuity property. And, for spaces of Whitney functions given on multidimensional Cantor-type sets, we give the conditions for the existence and non-existence of a linear continuous extension operator.Item Open Access Generation and parameter estimation of Markov random field textures and a parallel network for texture generation(Bilkent University, 1990) Gürelli, Mehmet İzzetIn this thesis, a special class of Markov random fields (MRF), which is defined on two dimensional pixel arrays and represented by a few numbers called the MRF parameters, is studied as a texture model. Specifically, the generation of sample MRF textures and estimation of MRF texture parameters are considered. For the generation of sample MRF textures, an algorithm that can be implemented in a parallel manner is developed together with a parallel network which implements the algorithm. A mathematical description of the algorithm, based on finite state Markov chains is given and the structure of the network is explained. For the estimation of MRF texture parameters, a method based on histogramming of a sample MRF texture is studied cind a mathematical justification of the. method is given. Generation and parameter estimation methods studied in this thesis are tested by some computer programs and the results are observed to be satisfactory for many purposes.Item Open Access Kronecker-based infinite level-dependent QBDS : matrix analytic solution versus simulation(Bilkent University, 2011) Orhan, Muhsin CanMarkovian systems with multiple interacting subsystems under the influence of a control unit are considered. The state spaces of the subsystems are countably in- finite, whereas that of the control unit is finite. A recent infinite level-dependent quasi-birth-and-death (LDQBD) model for such systems is extended by facilitating the automatic representation and generation of the nonzero blocks in its underlying infinitesimal generator matrix with sums of Kronecker products. Experiments are performed on systems of stochastic chemical kinetics having two or more countably infinite state space subsystems. Results indicate that, albeit more memory consuming, there are many cases where a matrix analytic solution coupled with Lyapunov theory yields a faster and more accurate steady-state measure compared to that obtained with simulation.Item Open Access M/M/1 polling models with two finite queues(Bilkent University, 1995) Daşçı, AbdullahPolling models are special kinds of queueing models where multiple-customer type single-stage is considered. In this thesis, first an overview and a classification of polling models will be given. Then two-costomer one server M /M /l polling models will be analyzed and the performance of models will be developed for exhaustive, gated, and G-limited service policies. We give analytical methods for a special type of polling model where we solve the system to get mean queue lengths and thruput rates by three methods. The first one is based on solving the steady state distribution of the Markov Process. The second is a decompositon aiming to decrease the size of the problem. The third one is an approximation method that uses the earlier results and it is very accurate. The thesis will be concluded with possible future extensions.Item Open Access Maximizing profit per unit time in cointegration based pairs trading(Bilkent University, 2014) Tutal, DuyguItem Open Access Non-stationary Markov chains(Bilkent University, 1996) Mallak, SaedIn thi.s work, we studierl the Ergodicilv of Non-Stationary .Markov chains. We gave several e.xainples with different cases. We proved that given a sec[uence of Markov chains such that the limit of this sec|uence is an Ergodic Markov chain, then the limit of the combination of the elements of this sequence is again Ergodic (under some condition if the state space is infinite). We also proved that the limit of the combination of an arbitrary sequence of Markov chains on a finite state space is Weak Ergodic if it satisfies some condition. Under the same condition, the limit of the combination of a doubly stochastic sequence of Markov chains is Ergodic.Item Open Access Oscillation properties of stopped random walks on infinite tress(Bilkent University, 2014) Öner, AbdullahWe investigate a random walk on a branching tree with vertices labeled 1; 2; : : : ; r which terminates if two consecutive vertices of a walk are labeled with close numbers. It is proved that expected absorption times and absorption probabilities have surprising oscillating dependencies on starting states.Item Open Access Poisson disorder problem with control on costly observations(Bilkent University, 2012) Kadiyala, BharadwajA Poisson process Xt changes its rate at an unknown and unobservable time θ from λ0 to λ1. Detecting the change time as quickly as possible in an optimal way is described in literature as the Poisson disorder problem. We provide a more realistic generalization of the disorder problem for Poisson process by introducing fixed and continuous costs for being able to observe the arrival process. As a result, in addition to finding the optimal alarm time, we also characterize an optimal way of observing the arrival process. We illustrate the structure of the solution spaces with the help of some numerical examples.Item Open Access Pricing and optimal exercise of perpetual American options with linear programming(Bilkent University, 2010) Bozkaya, Efe BurakAn American option is the right but not the obligation to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option with methods from the linear programming literature. Under the assumption that the underlying’s price follows a discrete time and discrete state Markov process, we formulate the problem with an infinite dimensional linear program using the excessive and majorant properties of the value function. This formulation allows us to solve complementary slackness conditions efficiently, revealing an optimal stopping strategy which highlights the set of stock-prices for which the option should be exercised. Under two different stock-price movement scenarios (simple and geometric random walks), we show that the optimal strategy is to exercise the option when the stock-price hits a special critical value. The analysis also reveals that such a critical value exists only for some special cases under the geometric random walk, dependent on a combination of state-transition probabilities and the economic discount factor. We further demonstrate that the method is useful for determining the optimal stopping time for combinations of plain vanilla options, by solving the same problem for spread and strangle positions under simple random walks.Item Open Access Pricing perpetual American-type strangle option for merton's jump diffusion process(Bilkent University, 2014) Onat, AyşegülA stock price Xt evolves according to jump diffusion process with certain parameters. An asset manager who holds a strangle option on that stock, wants to maximize his/her expected payoff over the infinite time horizon. We derive an optimal exercise rule for asset manager when the underlying stock is dividend paying and non-dividend paying. We conclude that optimal stopping strategy changes according to stock’s dividend rate. We also illustrate the solution on numerical examples.Item Open Access Resampling-based Markovian modeling for automated cancer diagnosis(Bilkent University, 2011) Özdemir, ErdemCorrect diagnosis and grading of cancer is very crucial for planning an effective treatment. However, cancer diagnosis on biopsy images involves visual interpretation of a pathologist, which is highly subjective. This subjectivity may, however, lead to selecting suboptimal treatment plans. In order to circumvent this problem, it has been proposed to use automatic diagnosis and grading systems that help decrease the subjectivity levels by providing quantitative measures. However, one major challenge for designing these systems is the existence of high variance observed in the biopsy images due to the nature of biopsies. Thus, for successful classifications of unseen images, these systems should be trained with a large number of labeled images. However, most of the training sets in this domain have limited size of labeled data since it is quite difficult to collect and label histopathological images. In this thesis, we successfully address this issue by presenting a new resampling framework. This framework relies on increasing the generalization capacity of a classifier by augmenting the size and variation in the training set. To this end, we generate multiple sequences from an image, each of which corresponds to a perturbed sample of the image. Each perturbed sample characterizes different parts of the image, and hence, they are slightly different from each other. The use of these perturbed samples for representing the image increases the size and variability of the training set. These samples are modeled with Markov processes which are used to classify unseen image. Working with histopathological tissue images, our experiments demonstrate that the proposed framework is more effective for both larger and smaller training sets compared against other approaches. Additionally, they show that the use of perturbed samples is effective in a voting scheme which boosts the performance of the classifier.Item Open Access Stochastig modeling with continuous feedback markov fluid queues(Bilkent University, 2014) Yazıcı, Mehmet AkifMarkov fluid queues (MFQ) are systems in which a continuous-time Markov chain determines the net rate into (or out of ) a buffer. We deal with continuous feedback MFQs (CFMFQ) for which the infinitesimal generator of the background process and the drifts in each state are allowed to depend on the buffer level through continuous functions. Explicit solutions of CFMFQs for a few special cases has been reported, but usually numerical methods are preferred. A numerically stable solution method based on ordered Schur decomposition is already known for multi-regime MFQs (MRMFQ). We propose a framework for approximating CFMFQs by MRMFQs via discretizing the buffer space. The parameters of the CFMFQ are approximated by piecewise constant functions. Then, the solution is obtained by block-tridiagonal LU decomposition for the related MRMFQ. Moreover, we describe a numerical method that enables us to solve large scale systems efficiently. We model basically two different stochastic systems with CFMFQs. The first is the workload-bounded MAP/PH/1 queue, to which the arrivals occur according to a workload-dependent MAP (Markovian Arrival Process), and the arriving job size distribution is phase-type. The jobs that would cause the buffer to overflow are rejected partially or completely. Also, the service speed is allowed to depend on the buffer level. As the second application, we model the horizon-based delayed reservation mechanism in Optical Burst Switching networks with or without fiber delay lines. We allow multiple traffic classes and the effect of offset-based and FDL-based differentiation among traffic classes in terms of burst blocking is investigated. Lastly, we propose a distributed algorithm for air-time fairness in multi-rate WLANs that overcomes the performance anomaly in IEEE 802.11 WLANs. We also give a stochastic model of the proposed model, and provide a novel and elaborate proof for its effectiveness. We also present an extensive simulation study.Item Open Access Vision based behavior recognition of laboratory animals for drug analysis and testing(Bilkent University, 2009) Sandıkcı, SelçukIn pharmacological experiments, a popular method to discover the effects of psychotherapeutic drugs is to monitor behaviors of laboratory mice subjected to drugs by vision sensors. Such surveillance operations are currently performed by human observers for practical reasons. Automating behavior analysis of laboratory mice by vision-based methods saves both time and human labor. In this study, we focus on automated action recognition of laboratory mice from short video clips in which only one action is performed. A two-stage hierarchical recognition method is designed to address the problem. In the first stage, still actions such as sleeping are separated from other action classes based on the amount of the motion area. Remaining action classes are discriminated by the second stage for which we propose four alternative methods. In the first method, we project 3D action volume onto 2D images by encoding temporal variations of each pixel using discrete wavelet transform (DWT). Resulting images are modeled and classified by hidden Markov models in maximum likelihood sense. The second method transforms action recognition problem into a sequence matching problem by explicitly describing pose of the subject in each frame. Instead of segmenting the subject from the background, we only take temporally active portions of the subject into consideration in pose description. Histograms of oriented gradients are employed to describe poses in frames. In the third method, actions are represented by a set of histograms of normalized spatio-temporal gradients computed from entire action volume at different temporal resolutions. The last method assumes that actions are collections of known spatio-temporal templates and can be described by histograms of those. To locate and describe such templates in actions, multi-scale 3D Harris corner detector and histogram of oriented gradients and optical flow vectors are employed, respectively. We test the proposed action recognition framework on a publicly available mice action dataset. In addition, we provide comparisons of each method with well-known studies in the literature. We find that the second and the fourth methods outperform both related studies and the other two methods in our framework in overall recognition rates. However, the more successful methods suffer from heavy computational cost. This study shows that representing actions as an ordered sequence of pose descriptors is quite effective in action recognition. In addition, success of the fourth method reveals that sparse spatio-temporal templates characterize the content of actions quite well.