We study the steady state properties of a phenomenological two-state predator model in presence of correlated Gaussian white noise. Based on the corresponding Fokker-Planck equation for probability distribution function the steady state solution of the probability distribution function and its extrema have been investigated. We show for a typical value of noise correlation there is a giant loss...

Recently, several gateway-based congestion control mechanisms have been proposed to support the endto-end congestion control mechanism of TCP (Transmission Control Protocol). In this paper, we focus on RED (Random Early Detection), which is a promising gateway-based congestion control mechanism. RED randomly drops an arriving packet with a probability proportional to its average queue length (i...

Consider a two-server, ordered entry, queuing system with heterogeneous servers and finite waiting rooms in front of the servers. Service times are negative exponentially distributed. The arrival process is deterministic. A matrix solution for the steady state probabilities of the number of customers in the system is derived. The overflow probability will be used to formulate the stability cond...

In finite-size population models, one can derive Fokker-Planck equations to describe the fluctuations of the species numbers about the deterministic behaviour. In the steady state of populations comprising two or more species, it is permissible for a probability current to flow. In such a case, the system does not relax to equilibrium but instead reaches a non-equilibrium steady state. In a two...

Whereas product forms such as Jackson’s theorem operate over queueing networks, RCAT operates over the stochastic process algebra components defined in PEPA [3]. In the same way that Jackson’s theorem relates the global steadystate probability to the steady-state distributions of the constituent queueing nodes, so RCAT relates the steady state distribution of the global state space of the PEPA ...