We present a process-algebraic framework for performance evaluation of discrete-time discrete-event systems. The modeling of the system builds on a process algebra with conditionallydistributed discrete-time delays and generally-distributed stochastic delays. In the general case, the performance analysis is done with the toolset of the modeling language χ by means of discrete-event simulation. ...

The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). In this work, an explicit finite-difference scheme for TFDE is presented. Discrete models of a non-Markovian random walk are generate for simulating random variables whose spatial probability density evolves...

In this paper, we study the stochastic optimal tracking problems with preview for a class of linear discrete-time Markovian jump systems. The systems are described by the discrete-time switching systems with Markovian mode transitions. The necessary and sufficient conditions for the solvability of the optimal tracking problems are given by coupled Riccati difference equations with terminal cond...

We investigate the behavior of stochastic bistable and excitable dynamics based on a discrete state modeling. In addition to the well known Markovian two state model for bistable dynamics we introduce a non Markovian three state model for excitable systems. Its relative simplicity compared to stochastic models of excitable dynamics with continuous phase space allows to obtain analytical results...

This paper investigates geometric stability and L p-stability of discrete-time Markov chains associated with closed and open queueing networks with Markovian routing. By geometric stability (resp. L p-stability) we mean that the chain is re-generative in the Harris-recurrent sense and that the times between the successive regeneration points have a bounded moment generating function (resp. a bo...

We present a novel stochastic Petri net formalism where both discrete and continuous phase-type firing delays can appear simultaneously in the same model. By capturing non-Markovian behavior in discrete or continuous time, as appropriate, the formalism affords higher modeling fidelity. Alone, discrete or continuous phase-type Petri nets have simple underlying Markov chains, but mixing the two c...

In this paper a two-state Markovian maintenance process where the true state is unknown will be considered. The operating cost per period is a continuous random variable which depends on the state of the process. If investigation cost is incurred at the beginning of any period, the system wit I be returned to the "in-control" state instantaneously. This problem is solved using the average crite...