## 105 Citations

NEW FRONTIERS IN APPLIED PROBABILITY

- Mathematics
- 2011

For a random walk with both downward and upward jumps (increments), the joint distribution of the exit time across a given level and the undershoot or overshoot at crossing is determined through its…

Service with a queue and a random capacity cart: random processing batches and E-limited policies

- Mathematics
- 2015

A queueing model with Poisson arrivals, service phases of random length, and vacations, and its applications to the analysis of production systems in which material handling plays an important role is examined.

Exit times for a class of random walks exact distribution results

- MathematicsJournal of Applied Probability
- 2011

For a random walk with both downward and upward jumps (increments), the joint distribution of the exit time across a given level and the undershoot or overshoot at crossing is determined through its…

Absorption Probabilities for Sums of Random Variables Defined on a Finite Markov Chain

- Mathematics
- 1962

This paper is essentially a continuation of the previous one (5) and the notation established therein will be freely repeated. The sequence {ξ r } of random variables is defined on a positively…

Evaluating first passage times in markov chains form the perspective of asymptotic and empirical information

- Computer Science
- 2013

In this study, a transition matrix was estimated by taking into account the closingvalues of Istanbul Stock Exchange (ISE -100) index from 20.01.2009 to 18.

Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs

- MathematicsOper. Res.
- 1969

Almost any pure stationary policy for starting and stopping service in a single-server queue with respect to the state space consisting of queue length and whether or not the service facility is operating is shown to be equivalent to one that depends on two parameters.

Wald's identity and random walk models for neuron firing

- MathematicsAdvances in Applied Probability
- 1976

A class of probability models for the firing of neurons is introduced and treated analytically. The cell membrane potential is assumed to be a one-dimensional random walk on the continuum; the first…

An Operational Calculus for Matrix-Exponential Distributions, with Applications to a Brownian (q, Q) Inventory Model

- MathematicsMath. Oper. Res.
- 1998

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.

A method for studying the integral functionals of stochastic processes with applications: I. Markov chain case

- Mathematics
- 1971

The subject of this paper is the study of the distribution of integrals of the type
where { X ( t ); t ≧ 0} is some appropriately defined continuous-time parameter stochastic process, and f is a…