Fundamental Matrix of Transient QBD Generator With Finite States and Level Dependent Transitions

Shin, Yang Woo

doi:10.1142/s0217595909002407

Cited by 18 publications

(22 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…−1 by Shin [58]'s algorithm (see Remark 2.6). In addition, since [n] Q is block-tridiagonal in its unique communicating class F n , we can compute its stationary distribution vector [n] π in an efficient way, which is described as follows.…”

Section: 59) and (265)) Since Q F N Is Block-tridiagonal We Can Ementioning

confidence: 99%

Error Bounds for Last-Column-Block-Augmented Truncations of Block-Structured Markov Chains

Masuyama

2017

JORSJ

View full text Add to dashboard Cite

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 chains (BSMCs) in continuous time. We first derive upper bounds for the absolute difference between the time-averaged functionals of a BSMC and its LC-block-augmented truncation, under the assumption that the BSMC satisfies the general f -modulated drift condition. We then establish computable bounds for a special case where the BSMC is exponentially ergodic. To derive such computable bounds for the general case, we propose a method that reduces BSMCs to be exponentially ergodic. We also apply the obtained bounds to level-dependent quasi-birth-and-death processes (LD-QBDs), and discuss the properties of the bounds through the numerical results on an M/M/s retrial queue, which is a representative example of LD-QBDs. Finally, we present computable perturbation bounds for the stationary distribution vectors of BSMCs.

show abstract

Section: 59) and (265)) Since Q F N Is Block-tridiagonal We Can Ementioning

confidence: 99%

Error Bounds for Last-Column-Block-Augmented Truncations of Block-Structured Markov Chains

Masuyama

2017

JORSJ

View full text Add to dashboard Cite

show abstract

“…Once a(j, k k k) are determined, the stationary distribution π π π of Q P H can be computed by the well known algorithm (e.g. see [45])…”

Section: Algorithm Phmentioning

confidence: 99%

Dimension Reduction for Approximation of Advanced Retrial Queues : Tutorial and Review

Shin¹

2017

Journal of applied mathematics & informatics

Self Cite

View full text Add to dashboard Cite

Retrial queues have been widely used to model the many practical situations arising from telephone systems, telecommunication networks and call centers. An approximation method for a simple Markovian retrial queue by reducing the two dimensional problem to one dimensional problem was presented by Fredericks and Reisner in 1979. The method seems to be a promising approach to approximate the retrial queues with complex structure, but the method has not been attracted a lot of attention for about thirty years. In this paper, we exposit the method in detail and show the usefulness of the method by presenting the recent results for approximating the retrial queues with complex structure such as multiserver retrial queues with phase type distribution of retrial time, impatient customers with general persistent function and/or multiclass customers, etc.

show abstract

“…Using the algorithm in [20], one can calculate the inversion (ηI − Q) −1 by computing inversions of the matrices of size w + 1.…”

Section: Thus R(k J) Is the Linear Combination Of H(n η)mentioning

confidence: 99%

APPROXIMATE ANALYSIS OF M/M/c RETRIAL QUEUE WITH SERVER VACATIONS

Shin¹,

Moon²

2015

Journal of the Korea Society for Industrial and Applied Mathema

Self Cite

View full text Add to dashboard Cite

ABSTRACT. We consider the M/M/c/c queues in which the customers blocked to enter the service facility retry after a random amount of time and some of idle servers can leave the vacation. The vacation time and retrial time are assumed to be of phase type distribution. Approximation formulae for the distribution of the number of customers in service facility and the mean number of customers in orbit are presented. We provide an approximation for M/M/c/c queue with general retrial time and general vacation time by approximating the general distribution with phase type distribution. Some numerical results are presented.

show abstract

Fundamental Matrix of Transient QBD Generator With Finite States and Level Dependent Transitions

Cited by 18 publications

References 9 publications

Error Bounds for Last-Column-Block-Augmented Truncations of Block-Structured Markov Chains

Error Bounds for Last-Column-Block-Augmented Truncations of Block-Structured Markov Chains

Dimension Reduction for Approximation of Advanced Retrial Queues : Tutorial and Review

APPROXIMATE ANALYSIS OF M/M/c RETRIAL QUEUE WITH SERVER VACATIONS

Contact Info

Product

Resources

About