Description:
<jats:p>Cohen (1969) has studied the transient and stationary queue length distributions for the <jats:italic>M</jats:italic>/<jats:italic>G</jats:italic>/1, <jats:italic>K</jats:italic> queue, with a fixed maximum number of customers, <jats:italic>K</jats:italic>, in the system at any time. The present note applies Cohen's method to generalize his results to the <jats:italic>M<jats:sup>X</jats:sup>/G<jats:sup>Y</jats:sup>/</jats:italic>1, <jats:italic>K</jats:italic> queue.</jats:p>