In this paper we prove that the limiting distribution of the general bulk queue exists and is independent of the initial conditions if and only if the traffic intensity is less than one. We further generalize the following heavy traffic results of the GI/G/1 model to the general bulk queue model. When ρ > 1 or ρ = 1 the waiting time is distributed approximately as a Gaussian variable and the absolute value of a Gaussian variable, respectively. The exponential approximation is derived from the Wiener–Hopf matrix equations established in a previous paper while the unstable case ρ ≧ 1 is treated by means of functional central limit theorems for mixing processes.
