Reflected Brownian Motion in an Orthant: Numerical Methods for Steady–State Analysis

نویسندگان

  • J. G. Dai
  • J. M. Harrison
چکیده

Abstract This paper is concerned with a class of multidimensional diffusion processes, variously known as reflected Brownian motions, regulated Brownian motions, or just RBM’s, that arise as approximate models of queueing networks. We develop an algorithm for numerical analysis of a semimartingale RBM with state space S Rd (the non-negative orthant of d-dimensional Euclidean space). This algorithm lies at the heart of the QNET method [13] for approximate two-moment analysis of open queueing networks.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Return Time for a Reflected Fractional Brownian Motion Process on the Positive Orthant

We consider a d-dimensional reflected fractional Brownian motion (RFBM) process on the positive orthant S = R+, with drift r0 ∈ R and Hurst parameterH ∈ ( 1 2 , 1). Under a natural stability condition on the drift vector r0 and reflection directions, we establish a return time result for theRFBMprocessZ; that is, for some δ, κ > 0, supx∈B Ex [τB(δ)] < ∞, where B = {x ∈ S : |x| ≤ κ} and τB(δ) = ...

متن کامل

Validity of Heavy Traffic Steady-State Approximations in Open Queueing Networks

We consider a single class open queueing network, also known as a Generalized Jackson Network (GJN). A classical result in heavy traffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a Reflected Brownian Motion (RBM) in the orthant, as the traffic intensity approaches unity. However, barring simple instances, it is still not known whether th...

متن کامل

Nonexistence of Brownian models for certain multiclass queueing networks

It has been demonstrated that Brownian models are effective for approximate analysis of queueing networks, particularly when no explicit analytical methods are available [3,4,1]. In 1988 Harrison [2] proposed Brownian models as approximations for multiclass open queueing networks. That work was expanded by Harrison and Nguyen in two recent papers [3,4] with the aim of developing a systematic me...

متن کامل

A Geometric Drift Inequality for a Reflected Fractional Brownian Motion Process on the Positive Orthant

We study a d-dimensional reflected fractional Brownian motion (RFBM) process on the positive orthant S = R+, with drift r0 ∈ R and Hurst parameter H ∈ ( 1 2 , 1). Under a natural stability condition on the drift vector r0 and reflection directions, we establish a geometric drift towards a compact set for the 1-skeleton chain Z̆ of the RFBM process Z; that is, there exist β, b ∈ (0,∞) and a compa...

متن کامل

Steady-state Simulation of Reflected Brownian Motion and Related Stochastic Networks

This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson (possibly Markov modulated) input. In this case, we analyze the complexity of our procedure as the dimension of the network increases and show that, under certa...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999