The Limit Distribution of Queue Length of GI/G/1 Queuing Systems

This paper investigates the queue length of GI/G/1 queueing systems, and obtains its limit distribution based on Markov skeleton processes, in particular, backward equations and limit distribution. The method of Markov skeleton processes is applied because this paper proves that the queue length of GI/G/1 queueing systems is a positive recurrent Doob skeleton process, which is a special case of Markov skeleton processes.