An operational calculus for matrixexponential disributions, with applicaions to a Brownian (q,Q) inventory model
(1998) In Mathematics of Operations Research 23(1). p.166176 Abstract
 distribution G on [math not displayed] is called matrixexponential if the density has the form αeTz s where α is a row vector, T a square matrix and s a column vector. Equivalently, the Laplace transform is rational. For such distributions, we develop an operator calculus, where the key step is manipulation of analytic functions f(z) extended to matrix arguments. The technique is illustrated via an inventory model moving according to a reflected Brownian motion with negative drift, such that an order of size Q is placed when the stock process downcrosses some level q. Explicit formulas for the stationary density are found under the assumption that the leadtime Z has a matrixexponential distribution, and involve expressions of the form... (More)
 distribution G on [math not displayed] is called matrixexponential if the density has the form αeTz s where α is a row vector, T a square matrix and s a column vector. Equivalently, the Laplace transform is rational. For such distributions, we develop an operator calculus, where the key step is manipulation of analytic functions f(z) extended to matrix arguments. The technique is illustrated via an inventory model moving according to a reflected Brownian motion with negative drift, such that an order of size Q is placed when the stock process downcrosses some level q. Explicit formulas for the stationary density are found under the assumption that the leadtime Z has a matrixexponential distribution, and involve expressions of the form f(T) where [math not displayed]. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1273198
 author
 Asmussen, Sören ^{LU} and Perry, David
 organization
 publishing date
 1998
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Measurement, Performance, Theory, Verification, (s, S) model, Brownian motion, EOQ model, computer algebra, inventory system, matrixexponential distribution, operator calculus, phasetype distribution, stochastic decomposition, storage model
 in
 Mathematics of Operations Research
 volume
 23
 issue
 1
 pages
 166  176
 publisher
 Informs
 external identifiers

 scopus:0031996381
 ISSN
 0364765X
 language
 English
 LU publication?
 yes
 id
 f44499903da74aa9ae92b7f830684bfb (old id 1273198)
 date added to LUP
 20160404 07:55:23
 date last changed
 20220129 02:49:01
@article{f44499903da74aa9ae92b7f830684bfb, abstract = {{distribution G on [math not displayed] is called matrixexponential if the density has the form αeTz s where α is a row vector, T a square matrix and s a column vector. Equivalently, the Laplace transform is rational. For such distributions, we develop an operator calculus, where the key step is manipulation of analytic functions f(z) extended to matrix arguments. The technique is illustrated via an inventory model moving according to a reflected Brownian motion with negative drift, such that an order of size Q is placed when the stock process downcrosses some level q. Explicit formulas for the stationary density are found under the assumption that the leadtime Z has a matrixexponential distribution, and involve expressions of the form f(T) where [math not displayed].}}, author = {{Asmussen, Sören and Perry, David}}, issn = {{0364765X}}, keywords = {{Measurement; Performance; Theory; Verification; (s; S) model; Brownian motion; EOQ model; computer algebra; inventory system; matrixexponential distribution; operator calculus; phasetype distribution; stochastic decomposition; storage model}}, language = {{eng}}, number = {{1}}, pages = {{166176}}, publisher = {{Informs}}, series = {{Mathematics of Operations Research}}, title = {{An operational calculus for matrixexponential disributions, with applicaions to a Brownian (q,Q) inventory model}}, volume = {{23}}, year = {{1998}}, }