Brownian models of open processing networks: canonical representation of workload

Workload Interpretation for Brownian Models of Stochastic Processing Networks

Brownian networks are a class of stochastic system models that can arise as heavy traffic approximations for stochastic processing networks. In earlier work we developed the “equivalent workload formulation” of a generalized Brownian network: denoting by Z t the state vector of the generalized Brownian network at time t, one has a lower dimensional state descriptor W t =MZ t in the equivalent w...

Two Workload Properties for Brownian Networks

As one approach to dynamic scheduling problems for open stochastic processing networks, J. M. Harrison has proposed the use of formal heavy traffic approximations known as Brownian networks. A key step in this approach is a reduction in dimension of a Brownian network, due to Harrison and Van Mieghem [19], in which the “queue length” process is replaced by a “workload” process. In this paper, w...

Canonical representation for approximating solution of fuzzy polynomial equations

In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters Value, Ambiguity and Fuzziness. 

Brownian Approximations of Multiclass Open-Queueing Networks

Canonical active Brownian motion.

Active Brownian motion is the complex motion of active Brownian particles. They are "active" in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian motion so far imposed couplings between the internal energy and the kinetic energy of the system. We investigate how this idea can be naturally taken furt...