Distributional Properties of Fluid Queues Busy Period and First Passage Times

Batch queues, reversibility and first-passage percolation

We consider a model of queues in discrete time, with batch services and arrivals. The case where arrival and service batches both have Bernoulli distributions corresponds to a discrete-time M/M/1 queue, and the case where both have geometric distributions has also been previously studied. We describe a common extension to a more general class where the batches are the product of a Bernoulli and...

The Busy Period in the Fluid

Consider a uid queue fed by N on/oo sources. It is assumed that the silence periods of the sources are exponentially distributed, whereas the activity periods are generally distributed. The innow rate of each source, when active, is at least as large as the outtow rate of the buuer. We make two contributions to the performance analysis of this model. Firstly, we determine the Laplace-Stieltjes ...

First Passage Times, Lifetimes, and Relaxation Times of Unfolded Proteins.

The dynamics of proteins in the unfolded state can be quantified in computer simulations by calculating a spectrum of relaxation times which describes the time scales over which the population fluctuations decay to equilibrium. If the unfolded state space is discretized, we can evaluate the relaxation time of each state. We derive a simple relation that shows the mean first passage time to any ...

First-passage times of regime switching models

The probability of a stochastic process to first breach an upper and/or a lower level is an important quantity for optimal control and risk management. We present those probabilities for regime switching Brownian motion. In the 2and 3-state model, the Laplace transform of the (single and double barrier) first-passage times is – up to the roots of a polynomial of degree 4 (respectively 6) – deri...

First Passage times in Biology: Approximations