An operational calculus for matrix-exponential disributions, with applicaions to a Brownian (q,Q) inventory model
(1998) In Mathematics of Operations Research 23(1). p.166-176- Abstract
- distribution G on [math not displayed] is called matrix-exponential 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 down-crosses some level q. Explicit formulas for the stationary density are found under the assumption that the leadtime Z has a matrix-exponential distribution, and involve expressions of the form... (More)
- distribution G on [math not displayed] is called matrix-exponential 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 down-crosses some level q. Explicit formulas for the stationary density are found under the assumption that the leadtime Z has a matrix-exponential 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:
http://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, matrix-exponential distribution, operator calculus, phase-type distribution, stochastic decomposition, storage model
- in
- Mathematics of Operations Research
- volume
- 23
- issue
- 1
- pages
- 166 - 176
- publisher
- Informs
- ISSN
- 0364-765X
- language
- English
- LU publication?
- yes
- id
- f4449990-3da7-4aa9-ae92-b7f830684bfb (old id 1273198)
- date added to LUP
- 2008-12-09 13:59:28
- date last changed
- 2018-05-29 11:57:05
@article{f4449990-3da7-4aa9-ae92-b7f830684bfb, abstract = {distribution G on [math not displayed] is called matrix-exponential 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 down-crosses some level q. Explicit formulas for the stationary density are found under the assumption that the leadtime Z has a matrix-exponential distribution, and involve expressions of the form f(T) where [math not displayed].}, author = {Asmussen, Sören and Perry, David}, issn = {0364-765X}, keyword = {Measurement,Performance,Theory,Verification,(s,S) model,Brownian motion,EOQ model,computer algebra,inventory system,matrix-exponential distribution,operator calculus,phase-type distribution,stochastic decomposition,storage model}, language = {eng}, number = {1}, pages = {166--176}, publisher = {Informs}, series = {Mathematics of Operations Research}, title = {An operational calculus for matrix-exponential disributions, with applicaions to a Brownian (q,Q) inventory model}, volume = {23}, year = {1998}, }