%0 Journal Article
%T On time to buffer saturation in a GI/M/1/N-type queue
%A Wojciech Michal Kempa
%J International Journal of Advances in Telecommunications, Electrotechnics, Signals and Systems
%D 2012
%I International Science and Engineering Society, o.s.
%R 10.11601/ijates.v1i2-3.15
%X A GI/M/1/N-type queueing system with independent and generally distributed interarrival times and exponential service times is investigated. A system of equations for conditional distributions of the time to the first buffer saturation is built. The solution is written using a special-type sequence defined by ``input'' distributions of the system. The formula of total probability is used to derive a representation for the distribution of the time to the $k$th buffer saturation for k>=2. Moreover, special cases of the Poisson arrival process and the system with one-place buffer are discussed. Sample numerical results for the 3-Erlang and deterministic distributions of interarrival times are attached as well.
%U http://www.ijates.org/index.php/ijates/article/view/15