Browsing by Subject "Markov processes"

Now showing 1 - 20 of 59

Open Access
Analysis of concurrency control protocols for real-time database systems
(Elsevier, 1998) Ulusoy, Özgür
This paper provides an approximate analytic solution method for evaluating the performance of concurrency control protocols developed for real-time database systems (RTDBSs). Transactions processed in a RTDBS are associated with timing constraints typically in the form of deadlines. The primary consideration in developing a RTDBS concurrency control protocol is the fact that satisfaction of the timing constraints of transactions is as important as maintaining the consistency of the underlying database. The proposed solution method provides the evaluation of the performance of concurrency control protocols in terms of the satisfaction rate of timing constraints. As a case study, a RTDBS concurrency control protocol, called High Priority, is analyzed using the proposed method. The accuracy of the performance results obtained is ascertained via simulation. The solution method is also used to investigate the real-time performance benefits of the High Priority over the ordinary Two-Phase Locking.
Open Access
Analysis of design parameters in safety-critical computers
(IEEE Computer Society, 2018) Ahangari, H.; Atik, F.; Ozkok, Y. I.; Yildirim, A.; Ata, S. O.; Ozturk, O.
Nowadays, safety-critical computers are extensively used in many civil domains like transportation including railways, avionics, and automotive. In evaluating these safety critical systems, previous studies considered different metrics, but some of safety design parameters like failure diagnostic coverage (C) or common cause failure (CCF) ratio have not been seriously taken into account. Moreover, in some cases safety has not been compared with standard safety integrity levels (IEC-61508: SIL1-SIL4) or even have not met them. Most often, it is not very clear that which part of the system is the Achilles heel and how design can be improved to reach standard safety levels. Motivated by such design ambiguities, we aim to study the effect of various design parameters on safety in some prevalent safety configurations, namely, 1oo2 and 2oo3, where 1oo1 is also used as a reference. By employing Markov modeling, we analyzed the sensitivity of safety to important parameters including: failure rate of processor, failure diagnostic coverage, CCF ratio, test and repair rates. This study aims to provide a deeper understanding on the influence of variation in design parameters over safety. Consequently, to meet appropriate safety integrity level, instead of improving some parts of a system blindly, it will be possible to make an informed decision on more relevant parameters. IEEE
Open Access
Analyzing large sparse Markov chains of Kronecker products
(IEEE, 2009) Dayar, Tuğrul
Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. In the Kronecker based approach, the generator matrix underlying the MC is represented using Kronecker products [6] of smaller matrices and is never explicitly generated. The implementation of transient and steady-state solvers rests on this compact Kronecker representation, thanks to the existence of an efficient vector-Kronecker product multiplication algorithm known as the shuffle algorithm [6]. The transient distribution can be computed through uniformization using vector-Kronecker product multiplications. The steady-state distribution also needs to be computed using vector-Kronecker product multiplications, since direct methods based on complete factorizations, such as Gaussian elimination, normally introduce new nonzeros which cannot be accommodated. The two papers [2], [10] provide good overviews of iterative solution techniques for the analysis of MCs based on Kronecker products. Issues related to reachability analysis, vector-Kronecker product multiplication, hierarchical state space generation in Kronecker based matrix representations for large Markov models are surveyed in [5]. Throughout our discussion, we make the assumption that the MC at hand does not have unreachable states, meaning it is irreducible. And we take an algebraic view [7] to discuss recent results related to the analysis of MCs based on Kronecker products independently from modeling formalisms. We provide background material on the Kronecker representation of the generator matrix underlying a CTMC, show that it has a rich structure which is nested and recursive, and introduce a small CTMC whose generator matrix is expressed as a sum of Kronecker products; this CTMC is used as a running example throughout the discussion. We also consider preprocessing of the Kronecker representation so as to expedite numerical analysis. We discuss permuting the nonzero structure of the underlying CTMC symmetrically by reordering, changing the orders of the nested blocks by grouping, and reducing the size of the state space by lumping. The steady-state analysis of CTMCs based on Kronecker products is discussed for block iterative methods, multilevel methods, and preconditioned projection methods, respectively. The results can be extended to DTMCs based on Kronecker products with minor modifications. Areas that need further research are mentioned as they are discussed. Our contribution to this area over the years corresponds to work along iterative methods based on splittings and their block versions [11], associated preconditioners to be used with projection methods [4], near complete decomposability [8], a method based on iterative disaggregation for a class of lumpable MCs [9], a class of multilevel methods [3], and a recent method based on decomposition for weakly interacting subsystems [1]. © 2009 IEEE.
Open Access
An approximate analytical method of analysis of a threshold maintenance policy for a multiphase multicomponent model
(Springer, 2003) Anisimov, V. V.; Gürler, Ü.
A multicomponent system is investigated that consists of n identical unreliable components whose nonfailure operating time consists of a number of sequential phases with exponential times. A maintenance policy is studied that proposes the instant replacement of all the components as soon as the number of components that are in some doubtful state (before a failure) amounts to a predefined threshold value. A cost function averaged over a large period is studied. For a fixed n, an analytical approach is considered. If n increases, a new approximate analytical approach is proposed, which is based on results of the type of the averaging principle for recurrent semi-Markovian processes. The conditions of existence and properties of the optimal strategy are studied. An example is considered and possibilities of generalizations are discussed.
Open Access
Automatic detection of compound structures by joint selection of region groups from a hierarchical segmentation
(Institute of Electrical and Electronics Engineers, 2016) Akçay, H. G.; Aksoy, S.
A challenging problem in remote sensing image analysis is the detection of heterogeneous compound structures such as different types of residential, industrial, and agricultural areas that are composed of spatial arrangements of simple primitive objects such as buildings and trees. We describe a generic method for the modeling and detection of compound structures that involve arrangements of an unknown number of primitives in large scenes. The modeling process starts with a single example structure, considers the primitive objects as random variables, builds a contextual model of their arrangements using a Markov random field, and learns the parameters of this model via sampling from the corresponding maximum entropy distribution. The detection task is formulated as the selection of multiple subsets of candidate regions from a hierarchical segmentation where each set of selected regions constitutes an instance of the example compound structure. The combinatorial selection problem is solved by the joint sampling of groups of regions by maximizing the likelihood of their individual appearances and relative spatial arrangements. Experiments using very high spatial resolution images show that the proposed method can effectively localize an unknown number of instances of different compound structures that cannot be detected by using spectral and shape features alone.
Open Access
Averaging methods for transient regimes in overloading retrial queueing systems
(Elsevier, 1999) Anisimov, V. V.
A new approach is suggested to study transient and stable regimes in overloading retrial queueing systems. This approach is based on limit theorems of averaging principle and diffusion approximation types for so-called switching processes. Two models of retrial queueing systems of the types M̄/Ḡ/1̄/w.r (multidimensional Poisson input flow, one server with general service times, retrial system) and M/M/m/w.r (m servers with exponential service) are considered in the case when the intensity of calls that reapply for the service tends to zero. For the number of re-applying calls, functional limit theorems of averaging principle and diffusion approximation types are proved.
Open Access
Bant genişliği kısıtı altında videonun en iyi iletimi
(IEEE, 2006-04) Gürses, E.; Akar, G. B.; Akar, Nail
In this paper, we propose an optimal video streaming framework using retransmissions based on the theory of Markov Decision Processes (MDP). Using MDPs, we calculate average reward optimal policies so as to maximize the on time delivery probability of video frames in the transmission window while conforming to network-imposed available bandwidth constraints. The effectiveness of the proposed approach is validated by comparing the results with theoretically obtained rate-distortion curves corresponding to the optimal policies by using the distortion model in [2] © 2006 IEEE.
Open Access
Block SOR for Kronecker structured representations
(Elsevier, 2004) Buchholz, P.; Dayar, Tuğrul
The Kronecker structure of a hierarchical Markovian model (HMM) induces nested block partitionings in the transition matrix of its underlying Markov chain. This paper shows how sparse real Schur factors of certain diagonal blocks of a given partitioning induced by the Kronecker structure can be constructed from smaller component matrices and their real Schur factors. Furthermore, it shows how the column approximate minimum degree (COLAMD) ordering algorithm can be used to reduce fill-in of the remaining diagonal blocks that are sparse LU factorized. Combining these ideas, the paper proposes three-level block successive over-relaxation (BSOR) as a competitive steady state solver for HMMs. Finally, on a set of numerical experiments it demonstrates how these ideas reduce storage required by the factors of the diagonal blocks and improve solution time compared to an all LU factorization implementation of the BSOR solver. © 2004 Elsevier Inc. All rights reserved.
Open Access
Block SOR preconditioned projection methods for Kronecker structured Markovian representations
(SIAM, 2005) Buchholz, Peter; Dayar, Tuğrul
Kronecker structured representations are used to cope with the state space explosion problem in Markovian modeling and analysis. Currently, an open research problem is that of devising strong preconditioners to be used with projection methods for the computation of the stationary vector of Markov chains (MCs) underlying such representations. This paper proposes a block successive overrelaxation (BSOR) preconditioner for hierarchical Markovian models (HMMs1) that are composed of multiple low-level models and a high-level model that defines the interaction among low-level models. The Kronecker structure of an HMM yields nested block partitionings in its underlying continuous-time MC which may be used in the BSOR preconditioner. The computation of the BSOR preconditioned residual in each iteration of a preconditioned projection method becomes the problem of solving multiple nonsingular linear systems whose coefficient matrices are the diagonal blocks of the chosen partitioning. The proposed BSOR preconditioner solves these systems using sparse LU or real Schur factors of diagonal blocks. The fill-in of sparse LU factorized diagonal blocks is reduced using the column approximate minimum degree (COLAMD) ordering. A set of numerical experiments is presented to show the merits of the proposed BSOR preconditioner.
Open Access
Çok kollu haydutlar ile dinamik ambulans konumlandırma
(IEEE, 2019-04) Şahin, Ümitcan; Yücesoy, V.
Bir ülkenin acil yardım sistemlerinin iyileştirilmesi, daha çok acil vakaya zamanında müdahale edilmesi ve daha çok hayatın kurtarılmasını sağlar. 112 Acil Yardım sisteminin bir parçası olan ambulans konumlandırma problemi, ambulansların vakalara mümkün olan en kısa sürede ulaşmasını sağlayacak şekilde konumlandırılmasını sağlayan birçok yöntemden oluşur. Bu çalışmada ambulanslar, literatürdeki yöntemlerin aksine, bir çok kollu haydut (ÇKH) algoritması kullanılarak konumlandırılmaktadır. OpenStreetMap (OSM) harita uygulaması kullanılarak oluşturulmuş iki yönlü kenarlardan ve toplam 2400 düğümden oluşan bir Ankara şehri haritası üzerinde konumlandırma işlemi yapılmaktadır. Düğümler üzerindeki vaka dağılımları ve aralarındaki seyahat süreleri ÇKH algoritması tarafından bilinmemektedir ve zamanla öğrenilmektedir. Bu öğrenim keşif ve istifade arasındaki ödünleşim sistemi ile sağlanmaktadır. Algoritma karşılaştırmaları için literatürde sıkça kullanılan ve dinamik bir konumlandırma yöntemi olan DMEXCLP modeli kullanılmıştır. Simülasyonlarda algoritma karşılaştırmaları için iki ölçüt değerlendirilmiştir: 1) vakalara ortalama müdahale süresi ve 2) 15 dakika altında varılan vaka yüzdesi. Sonuç olarak aynı şartlar altında önerilen ÇKH algoritmasının DMEXCLP modeline göre bu iki ölçüt açısından daha iyi performans verdiği gösterilmiştir.
Open Access
Compact representation of solution vectors in Kronecker-based Markovian analysis
(Springer, 2016-08) Buchholz, P.; Dayar, Tuğrul; Kriege, J.; Orhan, M. Can
It is well known that the infinitesimal generator underlying a multi-dimensional Markov chain with a relatively large reachable state space can be represented compactly on a computer in the form of a block matrix in which each nonzero block is expressed as a sum of Kronecker products of smaller matrices. Nevertheless, solution vectors used in the analysis of such Kronecker-based Markovian representations still require memory proportional to the size of the reachable state space, and this becomes a bigger problem as the number of dimensions increases. The current paper shows that it is possible to use the hierarchical Tucker decomposition (HTD) to store the solution vectors during Kroneckerbased Markovian analysis relatively compactly and still carry out the basic operation of vector-matrix multiplication in Kronecker form relatively efficiently. Numerical experiments on two different problems of varying sizes indicate that larger memory savings are obtained with the HTD approach as the number of dimensions increases. © Springer International Publishing Switzerland 2016.
Open Access
Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering
(Elsevier, 2005) Pekergin, N.; Dayar T.; Alparslan, D. N.
This paper presents an improved version of a componentwise bounding algorithm for the state probability vector of nearly completely decomposable Markov chains, and on an application it provides the first numerical results with the type of algorithm discussed. The given two-level algorithm uses aggregation and stochastic comparison with the strong stochastic (st) order. In order to improve accuracy, it employs reordering of states and a better componentwise probability bounding algorithm given st upper- and lower-bounding probability vectors. Results in sparse storage show that there are cases in which the given algorithm proves to be useful. © 2004 Elsevier B.V. All rights reserved.
Open Access
Computational methods for risk-averse undiscounted transient markov models
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2014) Çavuş, O.; Ruszczyński, A.
The total cost problem for discrete-time controlled transient Markov models is considered. The objective functional is a Markov dynamic risk measure of the total cost. Two solution methods, value and policy iteration, are proposed, and their convergence is analyzed. In the policy iteration method, we propose two algorithms for policy evaluation: the nonsmooth Newton method and convex programming, and we prove their convergence. The results are illustrated on a credit limit control problem.
Open Access
Computing moments of first passage times to a subset of states in Markov chains
(SIAM, 2005) Dayar T.; Akar, N.
This paper presents a relatively efficient and accurate method to compute the moments of first passage times to a subset of states in finite ergodic Markov chains. With the proposed method, the moment computation problem is reduced to the solution of a linear system of equations with the right-hand side governed by a novel recurrence for computing the higher-order moments. We propose using a form of the Grassmann-Taksar-Heyman (GTH) algorithm to solve these linear equations. Due to the form of the linear systems involved, the proposed method does not suffer from the drawbacks associated with GTH in a row-wise sparse implementation. © 2005 Society for Industrial and Applied Mathematics.
Open Access
Conditional steady-state bounds for a subset of states in Markov chains
(ACM, 2006-10) Dayar, Tuğrul; Pekergin, N.; Younès, S.
The problem of computing bounds on the conditional steady-state probability vector of a subset of states in finite, ergodic discrete-time Markov chains (DTMCs) is considered. An improved algorithm utilizing the strong stochastic (st-)order is given. On standard benchmarks from the literature and other examples, it is shown that the proposed algorithm performs better than the existing one in the strong stochastic sense. Furthermore, in certain cases the conditional steady-state probability vector of the subset under consideration can be obtained exactly. Copyright 2006 ACM.
Open Access
Decompositional analysis of Kronecker structured Markov chains
(Kent State University, 2008) Bao, Y.; Bozkur, I. N.; Dayar, T.; Sun, X.; Trivedi, K. S.
This contribution proposes a decompositional iterative method with low memory requirements for the steadystate analysis ofKronecker structured Markov chains. The Markovian system is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions. Even though the interactions among subsystems, which are captured by synchronized transitions, need not be weak, numerical experiments indicate that the solver benefits considerably from weak interactions among subsystems, and is to be recommended specifically in this case. © 2008, Kent State University.
Open Access
Detection of compound structures by region group selection from hierarchical segmentations
(IEEE, 2016-07) Akçay, H. Gökhan; Aksoy, Selim
Detection of compound structures that are comprised of different arrangements of simpler primitive objects has been a challenging problem as commonly used bag-of-words models are limited in capturing spatial information. We have developed a generic method that considers the primitive objects as random variables, builds a contextual model of their arrangements using a Markov random field, and detects new instances of compound structures through automatic selection of subsets of candidate regions from a hierarchical segmentation by maximizing the likelihood of their individual appearances and relative spatial arrangements. In this paper, we extend the model to handle different types of primitive objects that come from multiple hierarchical segmentations. Results are shown for the detection of different types of housing estates in a WorldView-2 image. © 2016 IEEE.
Open Access
Detection of compound structures using multiple hierarchical segmentations
(IEEE, 2014) Akçay, Hüseyin Gökhan; Aksoy, Selim
In this paper, we present a method for automatic compound structure detection in high-resolution images. Given a query compound structure, our aim is to detect coherent regions with similar spatial arrangement and characteristics in multiple hierarchical segmentations. A Markov random field is constructed by representing query regions as variables and connecting the vertices that are spatially close by edges. Then, a maximum entropy distribution is assumed over the query region process and selection of similar region processes among a set of region hierarchies is achieved by maximizing the query model. Experiments using WorldView-2 images show the efficiency of probabilistic modeling of compound structures. © 2014 IEEE.
Open Access
Diferansiyel PIR algılayıcılarla dalgacık tabanlı alev tespiti
(IEEE, 2012-04) Erden, F.; Töreyin, B. U.; Soyer, E. B.; İnaç, İ.; Günay, O.; Köse, K.; Çetin, A. Enis
Bu makalede, diferansiyel kızılberisi algılayıcı (PIR) kullanılarak geliştirilen bir alev tespit sistemi önerilmektedir. Diferansiyel kızılberisi algılayıcılar, yalnızca görüş alanlarındaki ani sıcaklık değişikliklerine duyarlıdır ve zamanla değişen sinyaller üretir. Algılayıcı sinyaline ait dalgacık dönüşümü, öznitelik çıkarmak için kullanılır ve bu öznitelik vektörü hızlı titreşen kontrolsüz bir ateşin alevi ve bir kişinin yürümesi olaylarıyla eğitilmiş Markov modellerine sokulur. En yüksek olasılıkla sonuçlanan modele karar verilir. Karşılaştırmalı sonuçlar, sistemin geniş odalarda ateş tespiti için kullanılabileceğini düşündürmektedir.
Open Access
Discrete-time pricing and optimal exercise of American perpetual warrants in the geometric random walk model
(2013) Vanderbei, R. J.; Pınar, M. Ç.; Bozkaya, E. B.
An American option (or, warrant) 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 (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.