Information Data Length Theory for the Transient M/M/∞ Queueing System

The current paper provides a cutting-edge information data length-theoretic approach to the transient 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 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 queue on both the upper and lower bounds of the obtained information data length is observed and noted. The undertaken analytical technique in this paper is based on calculating the information data length for the 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 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.