The current paper provides a cutting-edge information data length-theoretic approach to the transient M/M/∞ queueing system. This is the first investigation that unifies information data length and queueing theories. Notably, an exposition of a significant real-life application of the M/M/∞ queueing system was addressed, namely the computation of the common average time for unsaturated site visitor flows beneath double-parking situations. This adds another dimension of the significance of the current work. On another note, the significant impact of both time and the number of states for the transient M/M/∞ queue on both the upper and lower bounds of the obtained information data length is observed and noted, which is a completely unprecedented innovative research methodology. The undertaken analytical technique in this paper is based on calculating the information data length for the M/M/∞ transient queue rather than going into higher complexities to go through a non-standard integral to be accomplished. It was a necessity to find both the upper and lower bounds of such a desired-to-be-calculated integration. The data collection process to carry out the numerical validation of the key analytic findings was conducted by choosing values for the parameters of the M/M/∞ transient queue to reveal both obtained upper and lower bounds numerically. The paper concludes with some challenging open problems, combined with concluding remarks and future research pathways.