Bounds on the Tail Distributions of Markov-modulated Stochastic Max-plus Systems

نویسنده

  • Zhen LIU
چکیده

In this paper we consider a particular class of linear systems under the max-plus algebra and derive exponential upper bounds for the tail distribution of each component of the state vector in the case of Markov modulated input sequences. Our results are then applied to tandem queues with innnite buuers, Markov modulated arrivals and deterministic service times.

برای دانلود 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

Stochastic bounds for a single server queue with general retrial times

We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indice bounds‎. ‎The main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (FCFS) orbit and general retrial times using the stochastic ordering techniques‎.

متن کامل

On the Exponentiality of Stochastic Linear Systems under the Max-Plus Algebra

In this paper, we consider stochastic linear systems under the max-plus algebra. For such a system, the states are governed by the recursive equation X n = A n X n 1 U n with the initial condition X 0 = x 0 . By transforming the linear system under the max-plus algebra into a sublinear system under the usual algebra, we establish various exponential upper bounds for the tail distributions of th...

متن کامل

A stochastic version analysis of an M/G/1 retrial queue with Bernoulli‎ ‎schedule‎

‎In this work‎, ‎we derive insensitive bounds for various performance measures of a single-server‎ ‎retrial queue with generally distributed inter-retrial times and Bernoulli schedule‎, ‎under the special‎ ‎assumption that only the customer at the head of the orbit queue (i.e.‎, ‎a‎ ‎FCFS discipline governing the flow from the orbit to the server) is allowed‎ ‎to occupy the server‎. ‎The method...

متن کامل

Stochastic Stability in Max-Product and Max-Plus Systems with Markovian Jumps

We study Max-Product and Max-Plus Systems with Markovian Jumps and focus on stochastic stability problems. At first, a Lyapunov function is derived for the asymptotically stable deterministic Max-Product Systems. This Lyapunov function is then adjusted to derive sufficient conditions for the stochastic stability of Max-Product systems with Markovian Jumps. Many step Lyapunov functions are then ...

متن کامل

Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications

In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and s...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1995