Journal ArticleDOI
An Operational Calculus for Matrix-Exponential Distributions, with Applications to a Brownian q, Q Inventory Model
Soqren Asmussen,David Perry +1 more
TLDR
An operator calculus is developed, where the key step is manipulation of analytic functions f(z) extended to matrix arguments extended to Matrix arguments for matrix-exponential distributions.Abstract:
A 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].read more
Citations
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Journal ArticleDOI
A multi-dimensional martingale for Markov additive processes and its applications
Søren Asmussen,Offer Kella +1 more
TL;DR: In this paper, the authors established new multidimensional martingales for Markov additive processes and certain modifications of such processes (e.g., such processes with reflecting barriers), which generalize corresponding one-dimensional martingale results for Levy processes.
Journal ArticleDOI
Characterization of Matrix-Exponential Distributions
TL;DR: For a rational Laplace-Stieltjes transform that has a pole of maximal real part that is real and negative, this paper gave a geometric description of all admissible numerator polynomials that give rise to matrix-exponential distributions.
Journal ArticleDOI
A generalized impulse control model of cash management
TL;DR: In this article, a general model of cash management, viewed as an impulse control problem for a stochastic money flow process, is presented, and the closed-form results can be used to determine optimal values for the target and trigger values numerically.
BookDOI
Constructive Computation in Stochastic Models with Applications
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT, and the €(D) includes 7% for Germany, the€(A) includes 10% for Austria.
References
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Journal ArticleDOI
Multiple channel queues in heavy traffic. I
Donald L. Iglehart,Ward Whitt +1 more
TL;DR: The queueing systems considered in this paper consist of r independent arrival channels and s independent service channels, where as usual the arrival and service channels are independent.
Journal ArticleDOI
A Deterministic Inventory System with an Inventory-Level-Dependent Demand Rate
Richard Baker,Timothy L. Urban +1 more
TL;DR: In this article, a continuous, deterministic case of an inventory system in which the demand rate of an item is of a polynomial functional form, dependent on the inventory level is analyzed.
Book
Queueing Theory: A Linear Algebraic Approach
TL;DR: This second edition of Queueing Theory has been updated throughout including a new chapter on Semi Markov Processes and new material on matrix representations of distributions and Power-tailed distribution.