222 citations · 340 across the 26 of their papers we have counts for
23 papers · 1 filter
A Subgeometric Convergence Formula for Total-variation Error of the Level-increment Truncation Approximation of M/G/1-type Markov Chains
Katsuhisa Ouchi, Hiroyuki Masuyama
This paper considers the level-increment (LI) truncation approximation of M/G/1-type Markov chains. The LI truncation approximation is usually used to implement Ramaswami's recursi…
A geometric convergence formula for the level-increment-truncation approximation of M/G/1-type Markov chains
Katsuhisa Ouchi, Hiroyuki Masuyama
This paper considers an approximation usually used when implementing Ramaswami's recursion for the stationary distribution of the M/G/1-type Markov chain. The approximation is call…
Level-wise Subgeometric Convergence of the Level-increment Truncation Approximation of M/G/1-type Markov Chains
Katsuhisa Ouchi, Hiroyuki Masuyama
This paper considers the level-increment (LI) truncation approximation of M/G/1-type Markov chains. The LI truncation approximation is useful for implementing the M/G/1 paradigm, w…
Specific bounds for a probabilistically interpretable solution of the Poisson equation for general state-space Markov chains with queueing applications
Hiroyuki Masuyama
This paper considers the Poisson equation for general state-space Markov chains in continuous time. The main purpose of this paper is to present specific bounds for the solutions o…
A discrete-time single-server Poisson queueing game: Equilibria simulated by an agent-based model
Yutaka Sakuma, Hiroyuki Masuyama, Emiko Fukuda
This paper considers a discrete-time single-server queue with a single acceptance period for a Poissonian population of homogeneous customers. Customers are served on a first-come…
A new matrix-infinite-product-form solution for upper block-Hessenberg Markov chains and its quasi-algorithmic constructibility
Hiroyuki Masuyama
This paper presents a new matrix-infinite-product-form (MIP-form) solution for the stationary distribution in upper block-Hessenberg Markov chains (UBH-MCs). The existing MIP-form…
A sequential update algorithm for computing the stationary distribution vector in upper block-Hessenberg Markov chains
Hiroyuki Masuyama
This paper proposes a new algorithm for computing the stationary distribution vector in continuous-time upper block-Hessenberg Markov chains. To this end, we consider the last-bloc…
A subgeometric convergence formula for finite-level M/G/1-type Markov chains: via a block-decomposition-friendly solution for the Poisson equation of deviation matrix
Hiroyuki Masuyama, Yosuke Katsumata, Tatsuaki Kimura
This paper studies the subgeometric convergence of the stationary distribution in taking the infinite-level limit of a finite-level M/G/1-type Markov chain, that is, in letting the…
Simple perfect samplers using monotone birth-and-death processes
Hiroyuki Masuyama
This paper proposes simple perfect samplers using monotone birth-and-death processes (BD-processes), which draw samples from an arbitrary finite discrete target distribution. We fi…
The stability condition of BMAP/M/ queues
Moeko Yajima, Tuan Phung-Duc, Hiroyuki Masuyama
This paper considers a BMAP/M/ queue with a batch Markovian arrival process (BMAP) and an exponential service time distribution. We first prove that the BMAP/M/ que…
Simple error bounds for the QBD approximation of a special class of two dimensional reflecting random walks
Hiroyuki Masuyama, Yutaka Sakuma, Masahiro Kobayashi
This paper considers the QBD approximation of a special class of two-dimensional reflecting random walks (2D-RRWs). A typical example of the 2D-RRWs is a two-node Jackson network w…
Limit formulas for the normalized fundamental matrix of the northwest-corner truncation of Markov chains: Matrix-infinite-product-form solutions of block-Hessenberg Markov chains
Hiroyuki Masuyama
This paper considers the normalized fundamental matrix for the northwest-corner (NW-corner) truncation of ergodic continuous-time Markov chains, technically, of their infinitesimal…
Error bounds for last-column-block-augmented truncations of block-structured Markov chains
Hiroyuki Masuyama
This paper discusses the error estimation of the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of block-structured Markov chain…
Continuous-time block-monotone Markov chains and their block-augmented truncations
Hiroyuki Masuyama
This paper considers continuous-time block-monotone Markov chains (BMMCs) and their block-augmented truncations. We first introduce the block monotonicity and block-wise dominance…
Error bounds for augmented truncations of discrete-time block-monotone Markov chains under subgeometric drift conditions
Hiroyuki Masuyama
This paper studies the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of discrete-time block-monotone Markov chains under subgeo…
Analysis and Computation of the Joint Queue Length Distribution in a FIFO Single-Server Queue with Multiple Batch Markovian Arrival Streams
Hiroyuki Masuyama, Tetsuya Takine
This paper considers a work-conserving FIFO single-server queue with multiple batch Markovian arrival streams governed by a continuous-time finite-state Markov chain. A particular…
Subexponential Asymptotics of the Stationary Distributions of GI/G/1-Type Markov Chains
Tatsuaki Kimura, Hiroyuki Masuyama, Yutaka Takahashi
This paper considers the subexponential asymptotics of the stationary distributions of GI/G/1-type Markov chains in two cases: (i) the phase transition matrix in non-boundary level…
Error Bounds for Augmented Truncations of Discrete-Time Block-Monotone Markov Chains under Geometric Drift Conditions
Hiroyuki Masuyama
This paper studies the augmented truncation of discrete-time block-monotone Markov chains under geometric drift conditions. We first present a bound for the total variation distanc…
Heavy-traffic asymptotic formulas for the multiclass M/G/1 queue
Hiroshi Miyawaki, Hiroyuki Masuyama, Yutaka Takahashi
This paper studies the heavy-traffic asymptotics for the multiclass FIFO M/G/1 queue. We first derive the probability generating function of the joint queue length distributi…
Subexponential tail equivalence of the queue length distributions of BMAP/GI/1 queues with and without retrials
Hiroyuki Masuyama
The main contribution of this paper is to prove the subexponential tail equivalence of the stationary queue length distributions in the BMAP/GI/1 queues with and without retrials.…
A sufficient condition for the subexponential asymptotics of GI/G/1-type Markov chains with queueing applications
Hiroyuki Masuyama
The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/GI/1-type Markov chain withou…
Tail asymptotics for cumulative processes sampled at heavy-tailed random times with applications to queueing models in Markovian environments
Hiroyuki Masuyama
This paper considers the tail asymptotics for a cumulative process sampled at a heavy-tailed random time . The main contribution of this paper is to establis…
Light-tailed asymptotics of stationary tail probability vectors of Markov chains of M/G/1 type
Tatsuaki Kimura, Kentaro Daikoku, Hiroyuki Masuyama +1
This paper studies the light-tailed asymptotics of the stationary tail probability vectors of a Markov chain of M/G/1 type. Almost all related studies have focused on the typical c…