Transform-free analysis of the GI/G/1/K queue through the decomposed Little's formula

In this paper, we consider the steady-state queue length distribution of the GI/G/1/K queue. As a result, we obtain transform-free expressions for the steady-state queue length distributions at an arrival, at a departure and at an arbitrary time, all in product forms. The results are obtained by what we call the decomposed Little’s formula, which applies the Little’s formula W L λ = to the n waiting position in the queue. Utilizing the results, we improve and generalize existing bounds on the difference between the time average and arrival (departure) average mean queue lengths, and propose a twomoment approximation for the queue length. To evaluate the approximation, we focus * Tel: +82-42-869-2915; Fax: +82-42-869-3110. E-mail address: [email protected]