Regenerative simulation of time-sharing queueing system in random environment

Time-sharing queueing systems in random environments allow only a limited-depth analytical study. In particular, the coinciding necessary and sufficient conditions for the stationary probability distribution existence and an optimization problem for mean total sojourn cost per working tact can be solved only under much stricter assumptions about the time structure of input flows. In this talk a regenerative method is discussed in its application to Monte-Carlo simulation of the class of queueing system

Computer analysis of a cyclic service algorithm with varying durations

For a loss queueing systems of servicing con°ict °ows within a class of cyclic algorithms with variable durations a mathematical model has been constructed in form of a Markov chain with incomes. A numerical search for an optimal control has been carried out

Computer analysis of a cyclic service algorithm with varying durations

For a loss queueing systems of servicing con°ict °ows within a class of cyclic algorithms with variable durations a mathematical model has been constructed in form of a Markov chain with incomes. A numerical search for an optimal control has been carried out

Template-aluminosilicate structures at the early stages of zeolite ZSM-5 formation. A combined preparative, solid-state NMR and computational study

Species at three stages in the self-assembly of zeolite ZSM-5 have been studied with one- and two-dimensional magic-angle-spinning 13C, 27Al, 29Si, and 1H NMR spectroscopy and compared with the earlier proposed structures: (1) precursor species containing 33-36 T sites around a tetrapropylammonium (TPA) cation, (2) nanoslabs consisting of a flat 4 × 3 array of such precursors, and (3) the final TPA-ZSM-5 zeolite. Synthesis was carried out in D2O to suppress the water and silanol protons. Under such conditions, the effective Si-H and Al-H distances measured with 29Si-{1H} and 27Al-{1H} rotational echo double resonance (REDOR) reflect the interactions between TPA cations and the surrounding aluminosilica. The 29Si-{1H} REDOR curves for Q4-type silicon atoms at the three mentioned stages are closely similar, as well as the observed 27Al-1H REDOR curve for the precursor species compared to that for the TPA-ZSM-5. This indicates that in addition to externally attached TPA, there is also internal TPA already incorporated at an early stage into the aluminosilicate in a similar way as in the final zeolite, in accordance with the earlier proposed MFI self-assembly pathway (Kirschhock et al. Angew. Chem. Int. Ed. 2001, 40, 2637). However, the effective distances extracted from the initial REDOR curvatures are significantly (10-15%) larger than those computed for the model. Since there is no temperature effect, we tentatively assign this difference to a reduction of the 29Si-1H and 27Al-1H interactions by multispin decoherence effects or self-decoupling caused by proton spin diffusion. By assuming the computed model distances and fitting Anderson-Weiss curves to the observed REDOR data, we obtain similar decoherence times in the order of 0.1 ms. The observed 29Si-{1H} REDOR dephasing for the Q3 sites in the precursors is significantly faster than that for the Q4 sites. This is tentatively ascribed to a partial deuteron-proton back exchange at the silanol positions