Computing moments of first passage times to a subset of states in Markov chains 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.
Keywords for this software
References in zbMATH (referenced in 7 articles , 1 standard article )
Showing results 1 to 7 of 7.
- Dayar, Tuǧrul; Orhan, M. Can: Cartesian product partitioning of multi-dimensional reachable state spaces (2016)
- Hunter, Jeffrey J.: Accurate calculations of stationary distributions and mean first passage times in Markov renewal processes and Markov chains (2016)
- Dayar, Tuǧrul; Orhan, M. Can: On vector-Kronecker product multiplication with rectangular factors (2015)
- Rabia, Sherif I.: An improved truncation technique to analyze a $Geo/PH/1$ retrial queue with impatient customers (2014)
- Nemirovsky, Danil: Tensor approach to mixed high-order moments of absorbing Markov chains (2013)
- Dayar, Tuǧrul: Analyzing Markov chains using Kronecker products. Theory and applications (2012)
- Dayar, Tugrul; Akar, Nail: Computing moments of first passage times to a subset of states in Markov chains (2005)