

Principle Seminar of the Department of Probability Theory, Moscow State University
October 5, 2016 17:15–17:45, Moscow, MSU, auditorium 1224






Limit Theorems for infinite server queuing systems with heavytailed distributions of service times
E. Chernsvakaya^{} ^{} Lomonosov Moscow State University

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Abstract:
We study queuing systems with an infinite number of servers. It is assumed that a distribution of service times is
heavytailed. Moreover, we suggest that a distribution of service times have not mathematical expectation. Our aim is
to carry out an asymptotic analysis of the process $q(t)$ determining the number of occupied servers in the system as
time $t$ goes to infinity.We have obtained analogs of the law of large numbers and the central limit theorem for $q(t)$ in the case of doubly stochastic Poisson and regenerative input flows. It is also proved functional convergence of the standardized process $q(t)$ in the case of the Poisson input flow with constant intensity.

