Semi-Markovian Discrete-Time Telegraph Process with Generalized Sibuya Waiting Times

Generalized Semi-Markovian Process Algebra

We present GSMPA, a stochastically timed process algebra that enhances the expressiveness of the stochastically timed process algebra EMPA by allowing arbitrarily distributed durations to be directly modeled through the adoption of the mechanism of action identification as well as the adoption of the preselection policy for alternative actions. GSMPA is introduced together with the definition o...

Parametric estimation for the standard and geometric telegraph process observed at discrete times

The telegraph process X(t), t > 0, (Goldstein, 1951) and the geometric telegraph process S(t) = s0 exp{(μ− 12σ)t+σX(t)} with μ a known constant and σ > 0 a parameter are supposed to be observed at n+1 equidistant time points ti = i∆n, i = 0, 1, . . . , n. For both models λ, the underlying rate of the Poisson process, is a parameter to be estimated. In the geometric case, also σ > 0 has to be es...

Change point estimation for the telegraph process observed at discrete times

The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity +v or −v. The changes of direction are governed by an homogeneous Poisson process with rate λ > 0. In this paper, we consider a change point estimation pr...

Waiting times and Generalized Fibonacci Sequences

Discrete-time single-server finite-buffer queues under discrete Markovian arrival process with vacations

This paper treats a discrete-time single-server finite-buffer exhaustive (singleand multiple-) vacation queueing system with discrete-time Markovian arrival process (D-MAP). The service and vacation times are generally distributed random variables and their durations are integral multiples of a slot duration. We obtain the queue-length distributions at departure, service completion, vacation te...