This section is devoted to the discussion of two fundamental (partial) differential equations, that arise in the context of Markov diffusion processes. After giving a brief introduction of continuous-time continuous state Markov processes, we introduce the forward and backward equation, and provide a heuristic derivation of these equations for diffusion processes. We also discuss some examples ...

In this paper we study a type of production-inventory system in which the production and demand rates are modulated by a background state process modeled as a finite state Continuous Time Markov Chain (CTMC). When the production rate exceeds the demand rate, the inventory level increases, and when the demand rate exceeds the production rate, it decreases. When the inventory level reaches zero, ...

In this paper, we present an approach to improve the efficiency of stochastic simulation for large and dense networks. We are using stochastic Petri nets as modelling framework. The underlying continuoustime Markov chain (CTMC) is converted to an equivalent discrete-time Markov chain (DTMC), this itself gains no efficiency. We improve the efficiency via discrete-time leaps, even though this res...

In a millimeter wave (mmWave) network, user association– the process of deciding as to which base station (BS) given should associate with– is crucial process, affects throughput and delay performance seen by users in network amount load at each BS. existing research literature, stability region association policy, i.e. , set arrival rates for policy stabilizes has not been analytically charact...

Many problems of practical interest rely on Continuous-time Markov chains (CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible with existing methods. For problems with countably infinite states, where classical methods such as matrix exponentiation are not applicable, the main alternati...

in the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional fredholm integral equations of the second kind‎. ‎the solution of the‎ integral equation is described by the neumann series expansion‎. ‎each term of this expansion can be considered as an expectation which is approximated by a continuous markov chain monte carlo method‎. ‎an algorithm is proposed to sim...

Traditionally, IT security investment decisions are made in isolation. However, as firms that compete for customers in an industry are closely interlinked, a macro perspective is needed in analyzing the IT security spending decisions and this is a key contribution of the paper. We introduce the notions of directand cross-risk elasticity to describe the customer response to adverse IT security e...

There is several challenges in LTE system capacity and performance evaluation. Among other things, traffic modeling and distributions, the quality of services (QoS) requirements of such traffic, the instantaneous propagation conditions, and the number of users in the system can influence the system capacity a great deal. The convergence between the internet traffic and the LTE traffic can compl...

This paper proposes a novel Adaptive Stochastic Radio Access Selection (ASRAS) scheme for mobile users in heterogeneous Cellular-WLAN systems. In this scheme, a mobile user located in dual coverage area randomly selects WLAN with probability of ω when there is a need for downloading a chunk of data. The value of ω is optimised according to the status of both networks in terms of network load an...