An application of queuing theory to modelling of melange yarns. Part II: A method of estimating the fibre migration probabilities and a yarn structure simulation algorithm.

A queuing model of staple yarn structure was presented in Part I of this work, where the migration behaviours of fibres were simulated by the movement of customers in a Markovian network of queuing systems. Part II of the series proposes (i) a multi-dimensional minimization method for estimating the migration probabilities of fibres based on the analysis of the distribution of number of fibres in yarn cross-sections; (ii) a yarn structure simulation algorithm which uses the migration probabilities of fibres, yarn technical specifications (e.g. linear density and twist) and colour composition to produce a realistic three-dimensional image of a melange yarn. The result is a high quality three-dimensional image of a melange yarn showing its fibrous structure as well as the formation of hairiness. Due to the generic nature of the model and the simulation algorithm, this approach can be applied to a wide range of yarns including ring-spun or open-end spun yarns of solid shade or produced from melange blends. Further improvements to the proposed model are discussed including the application of inhomogeneous Poisson process and the analysis of energy relationships which govern the migration behaviour of fibres