Steady-state analysis of M/M/c/c-type retrial queueing systems with constant retrial rate

The paper deals with a research of bivariate Markov process \(\{X(t), t\ge 0\}\) whose state space is a lattice semistrip \(S(X)=\{0,1,{\ldots },c\} \times Z_{+}\). The process \(\{X(t), t\ge 0\}\) describes the service policy of a multi-server retrial queue in which the rate of repeated flow does not depend on the number of sources of retrial calls. In this class of queues, a vector–matrix representation of steady-state distribution was obtained. This representation allows to write down the stationary probabilities through the model parameters in closed form and to propose the closed formulas of its main performance measures. The investigative techniques use an approximation of the initial model by means of the truncated one and the direct passage to the limit.     

Polysilazane-induced aggregation of hydrophobic silver colloids

Adsorbing polymers such as polysilazanes induce irreversible coagulation of hydrophobic silver colloids in nonpolar solvents. This is accompanied by broadening of the surface plasmon resonance (SPR) peak. A method to analyze the coagulation kinetics based on von Smoluchowski's theory utilizing the SPR change is described. The approach allows evaluating extinction spectra of aggregates of small sizes. A model for polymer adsorption kinetics in combination with a modified bridging efficiency model explains the observed coagulation inhibition over time in terms of macromolecules adsorption, spreading, and mutual repulsion.