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Asymptotic Distributions of Maximum Queue Lengths for M/G/1 and GI/M/i Systems
Park, You-Sung The Korean Statistical Society 1995 Journal of the Korean Statistical Society Vol.24 No.1
In this paper, we investigate the asymptotic distributions of maximum queue length for M/G/1 and GI/M/1 systems which are positive recurrent. It is well knwon that for any positive recurrent queueing systems, the distributions of their maxima linearly normalized do not have non-degenerate limits. We show, however, that by concerning an array of queueing processes limiting behaviors of these maximum queue lengths can be established under certain conditions.
A TRIAL SOLUTION APPROACH TO THE GI=M=1QUEUE WITH N-POLICY AND EXPONENTIALVACATIONSy
채경철,Sang Min Lee,Nam Ki Kim,Jin Dong Kim,이호우 한국통계학회 2004 Journal of the Korean Statistical Society Vol.33 No.3
We present a trial solution approach to GI=M=1 queues with generalized vacations. Specic types of generalized vacations we consider are N-policy and a combination of N-policy and exponential multiple vacations. Discus- sions about how to nd trial solutions are given.
Busy period analysis for the GI/M/1 queue with phase-type vacations
김길환,양원석 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.1
We consider the busy period in the GI/M/1 queue with multiple phase-type vacations. We derive the transform of the joint distribution of the length of a busy period, the number of customers served during the busy period, and the residual interarrival time at the instant the busy period ends.