Асимптотична поведінка екстремальних значень довжини черги та часу очікування в 1системах M|G|1 та GI|M|1

Abstract

The asymptotic behavior of the almost certainly extreme values of the queue length and waiting time in the queue for mass service systems was studied. On- first of all, one general limit theorem on the asymptotics of extreme values of regenerative processes is considered. Further, applying this theorem to mass service systems M G| |1 and GI M| |1, the law of the repeated logarithm for lim sup and the law of the triple logarithm for lim inf are formulated, as well as some of their refinements