We consider in this paper a class of vector valued processes that have the form Yn+1 = An(Yn)+ Bn. Bn is assumed to be stationary ergodic and An is assumed to have a divisibility property. This class includes linear stochastic difference equations as well as multi-type branching processes (with a discrete or with a continuous state space). We derive explicit expressions for the probability dist...

Interest rates have traditionally been modeled in the literature as following continuous-time Markov processes, and more specifically diffusions. By contrast, recent term structure models often imply non-Markovian continuous-time dynamics. Can discretely sampled interest rate data help decide which continuous-time models are sensible? First, how reasonable is the Markovian assumption? A test of...

In recent years, formal methods have been used as an important tool for performance evaluation and verification of a wide range of systems. In the view points of engineers and practitioners, however, there are still some major difficulties in using formal methods. In this paper, we introduce a new formal modeling language to fill the gaps between object-oriented programming languages (OOPLs) us...

In recent years, formal methods have been used as an important tool for performance evaluation and verification of a wide range of systems. In the view points of engineers and practitioners, however, there are still some major difficulties in using formal methods. In this paper, we introduce a new formal modeling language to fill the gaps between object-oriented programming languages (OOPLs) us...

In this paper a method is proposed called circulant matching method to approximate the superposition of a number of discrete time batch Markovian arrival sources by a circulant batch Markovian process while matching the stationary cumulative distribution and the autocorrelation sequence of the input rate process Special attention is paid to periodic sources The method is applied to the superpos...

The discrete-time batch Markovian arrival process (D-BMAP) was first defined in [2]. The D-BMAP can represent a variety of arrival processes which include, as special cases, the Bernoulli arrival process, the Markov-modulated Bernoulli process (MMBP), the discrete-time Markovian arrival process (D-MAP), and their superpositions. It is the discrete-time version of the versatile Markovian point p...

We study fluid limits based on ordinary differential equations (ODEs) for Markovian queueing models where nonexponential service times are fit by appropriate Coxian distributions to match their first and second moments. We focus on a heavy-load regime, whereby the fluid limit of the queue-length process of the nonexponential queue estimates a bottleneck situation. Under this condition, we show ...

in this paper, we investigate the delay-dependent robust stability of fuzzy cohen-grossberg neural networks with markovian jumping parameter and mixed time varying delays by delay decomposition method. a new lyapunov-krasovskii functional (lkf) is constructed by nonuniformly dividing discrete delay interval into multiple subinterval, and choosing proper functionals with different weighting matr...

This paper introduces an analytical method for approximating the performability of a firm realtime system modeled by a multi-server queue. The service discipline in the queue is earliestdeadline- first (EDF), which is an optimal scheduling algorithm. Real-time jobs with exponentially distributed relative deadlines arrive according to a Poisson process. All jobs have deadlines until the end of s...

The wound process in patients with diabetes mellitus in addition to VAC-therapy (Vacuum-assisted closure — VAC® therapy) is examined. The model of the biological system describing the wound process is built on three independently functioning subsystems; it is assumed to be ergodic and presented with a symmetric graph. The mathematical model of the wound process dynamics is constructed based on ...