The asymptotic behavior of queueing systems: Large deviations theory and dominant pole approximation

This paper presents the exact asymptotics of the steady state behavior of a broad class of single-node queueing systems. First we show that the asymptotic probability functions derived using large deviations theory are consistent (in a certain sense) with the result using dominant pole approximations. Then we present an exact asymptotic formula for the cumulative probability function of the queue occupancy and relate it to the cell loss ratio, an important performance measure for service systems such as ATM networks. The analysis relies on a new generalization of the Taylor coefficients of a complex function which we call characteristic coefficients. Finally we apply our framework to obtain new results for the M/D/1 system and for a more intricate multiclass M/D/n system.     

Some aspects of the interactions of orthopositronium with perfect and defect surfaces of insulating materials

ETLA (Elastic Thermalisation Lifetime Analysis) is a new model function for the fitting of lifetime spectra of slowly thermalising orthopositronium in the free space between the grains of insulating oxide powders. From this model one can obtain three fundamental parameters; the mass of the cluster of atoms which scatters the o-Ps, the probability that the o-Ps is forced into two-quantum decay at each collision and the emission energyE(0) of the o-Ps from the powder surface. As a consequence of full thermalisation of the Ps it is shown that the o-Ps quenching constant _q () follows atT ^1/2 dependency for MgO, Al₂O₃ and SiO₂ and for temperatures between 77 and 500 K. In MgO powder at low temperatures the irradiation by the positrons induces surface paramagnetic defects which are identified as Mg⁺ sites. These surface defects do not affect the thermalisation, but they induce paramagnetic o-p conversion i.e., an increase in , and they are also responsible for an increase in the emission energyE(0) of the o-Ps.     

Mortality of iterated Gallai graphs

For a finite or infinite graphG, theGallai graph (G) ofG is defined as the graph whose vertex set is the edge setE(G) ofG; two distinct edges ofG are adjacent in (G) if they are incident but do not span a triangle inG. For any positive integert, thetth iterated Gallai graph ^t (G) ofG is defined by ( ^t–1(G)), where ⁰(G):=G. A graph is said to beGallai-mortal if some of its iterated Gallai graphs finally equals the empty graph. In this paper we characterize Gallai-mortal graphs in several ways.     

Modular curves and Poncelet polygons

Parts of the results and the essential techniques of this note are taken from the Erlangen thesis (1991) of the second author. They were circulated as Nr. 122 of Schriftenreihe Komplexe Mannigfaltigkeiten. Our research was supported by DFG grant Ba 423/3-3 and the European Science Project Geometry of Algebraic Varieties SCI-0398-C(A)