Large Deviations in Some Queueing Systems

Logarithmic asymptotics of probabilities of large delays are derived for the “last come—first served” system and system with priorities. Trajectories that determine the mean dynamics of arrival flow under the condition of large delay are described

Large deviations provide good approximation to queueing system with dynamic routing

We consider a system with two infinite-buffer FCFS servers (of speed one). The arrivals processes are three independent Poisson flows Ξ_i , of rates λ_i, i = 0, 1, 2, each with IID task service times. The tasks from Ξ_i are directed to server i, i = 1, 2 (dedicated traffic). The tasks from Ξ_0 are directed to the server that has the shorter workload in the buffer at the time of arrival (opportunistic traffic). We compare the analytical data for the large deviation (LD) probabilities for the virtual waiting time in flow Ξ_0 and empercial delay freqencies from simulations

Percolation properties of non-ideal gas

We estimate locations of the regions of the percolation and of the non-percolation in the plane $(\lambda,\beta)$: the Poisson rate -- the inverse temperature, for interacted particle systems in finite dimension Euclidean spaces. Our results about the percolation and about the non-percolation are obtained under different assumptions. The intersection of two groups of the assumptions reduces the results to two dimension Euclidean space, $\R^2$, and to a potential function of the interactions having a hard core. The technics for the percolation proof is based on a contour method which is applied to a discretization of the Euclidean space. The technics for the non-percolation proof is based on the coupling of the Gibbs field with a branching process.Comment: 28 pages, 3 figure

Thermomagnetic analysis of native iron from the upper sedimentary horizons of Lake Baikal, section GC-99 (Posolskaya Bank)

© 2017 We present results of a thermomagnetic analysis of Late Pleistocene-Holocene bottom sediments from the gravity core GC-99 of the borehole BDP-99 drilled at Posolskaya Bank of Lake Baikal in the framework of the Baikal Drilling Project. The results are compared with the earlier analytical data on the samples from the lower (Miocene) section of the BDP-98 drilled on the Akademichesky Ridge. Native-iron particles were found in only 14 of 61 samples. Their content varies from ~ 10 -5 to 10 -4 %, and their distribution is near-bimodal, with a distinct “zero” mode. The results of the thermomagnetic analysis are confirmed by a probe microanalysis: Only occasional native-iron particles were found. Nickel was detected in only one sample. The samples have a large number of magnetite and titanomagnetite grains. It is shown that the distribution of native-iron particles in the Baikal sediments depends on the rate of sedimentation: The rate increase is accompanied by the increase in the number of the “zero” group samples (free of iron particles). The conclusion is drawn that the native-iron particles in the studied sediments are predominantly of cosmic origin

Thermomagnetic analysis of native iron from the upper sedimentary horizons of Lake Baikal, section GC-99 (Posolskaya Bank)

© 2017 We present results of a thermomagnetic analysis of Late Pleistocene-Holocene bottom sediments from the gravity core GC-99 of the borehole BDP-99 drilled at Posolskaya Bank of Lake Baikal in the framework of the Baikal Drilling Project. The results are compared with the earlier analytical data on the samples from the lower (Miocene) section of the BDP-98 drilled on the Akademichesky Ridge. Native-iron particles were found in only 14 of 61 samples. Their content varies from ~ 10 -5 to 10 -4 %, and their distribution is near-bimodal, with a distinct “zero” mode. The results of the thermomagnetic analysis are confirmed by a probe microanalysis: Only occasional native-iron particles were found. Nickel was detected in only one sample. The samples have a large number of magnetite and titanomagnetite grains. It is shown that the distribution of native-iron particles in the Baikal sediments depends on the rate of sedimentation: The rate increase is accompanied by the increase in the number of the “zero” group samples (free of iron particles). The conclusion is drawn that the native-iron particles in the studied sediments are predominantly of cosmic origin