Browsing by Author "Dayar, Tuğrul"
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Analyzing large sparse Markov chains of Kronecker products
Dayar, Tuğrul (IEEE, 2009)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 ... 
Block SOR for Kronecker structured representations
Buchholz, P.; Dayar, Tuğrul (Elsevier, 2004)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 ... 
Block SOR preconditioned projection methods for Kronecker structured Markovian representations
Buchholz, Peter; Dayar, Tuğrul (SIAM, 2005)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 ... 
Compact representation of solution vectors in Kroneckerbased Markovian analysis
Buchholz, P.; Dayar, Tuğrul; Kriege, J.; Orhan, M. Can (Springer, 201608)It is well known that the infinitesimal generator underlying a multidimensional 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 ... 
Computational methods for CTMCs
Dayar, Tuğrul; Stewart, W. J. (John Wiley & Sons, 2011)This article concerns the computation of stationary and transient distributions of continuous‐time Markov chains (CTMCs). Once the problem has been formulated, it is shown how computational methods for computing stationary ... 
Conditional steadystate bounds for a subset of states in Markov chains
Dayar, Tuğrul; Pekergin, N.; Younès, S. (ACM, 200610)The problem of computing bounds on the conditional steadystate probability vector of a subset of states in finite, ergodic discretetime Markov chains (DTMCs) is considered. An improved algorithm utilizing the strong ... 
Effects of reordering and lumping in the analysis of discretetime sans
Dayar, Tuğrul (Birkhäuser, Basel, 2000)In a recent paper [13],it is shown that discretetime stochastic automata networks (SANs) are lumpable under rather general conditions. Therein, the authors present an efficient iterative aggregationdisaggregation (IAD) ... 
Efficient transient analysis of a class of compositional fluid stochastic petri nets
Buchholz, P.; Dayar, Tuğrul (IEEE, 2018)Fluid Stochastic Petri Nets (FSPNs) which have discrete and continuous places are an established model class to describe and analyze several dependability problems for computer systems, software architectures or critical ... 
A generalization of a TCP model: multiple sourcedestination case with arbitrary LAN as the access network
Gusak, O.; Dayar, Tuğrul (CRC Press, 2000)This paper introduces an analytical model of an access scheme for Wide Area Network resources. The model is based on the TCPmodified Engset model of Heyman, Lakshman, and Neidhardt. The proposed model employs a LAN ... 
On compact vector formats in the solution of the chemical master equation with backward differentiation
Dayar, Tuğrul; Orhan, M. C. (John Wiley and Sons, 2018)A stochastic chemical system with multiple types of molecules interacting through reaction channels can be modeled as a continuoustime Markov chain with a countably infinite multidimensional state space. Starting from an ... 
Preface
Aykanat, Cevdet; Dayar, Tuğrul; Körpeoğlu, İbrahim (Springer, 2004) 
State space orderings for GaussSeidel in Markov chains revisited
Dayar, Tuğrul (SIAM, 1998)States of a Markov chain may be reordered to reduce the magnitude of the subdominant eigenvalue of the GaussSeidel (GS) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the ...