DOI
10.34229/KCA2522-9664.25.1.12
UDC 519.21
1 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
 i.m.k@ukr.net
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ASYMPTOTIC BEHAVIOR OF THE EXTREME VALUES OF THE QUEUE LENGTHS
AND WAITING TIME IN M |G |1 AND GI |M |1 SYSTEMS
Abstract. The asymptotic behavior of the almost surely extreme values of the queue length and queueing time for queueing systems is analyzed.
First, one general limit theorem on the asymptotics of extreme values of regenerative processes is considered.
Further, applying this theorem to queueing
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.
Keywords: queuing systems M |G |1 and GI |M |1,
extreme values, asymptotic behaviour almost surely
.
full text
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