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


A Mageed, I. (2024). Information Data Length Theory for the Transient M/M/∞ Queueing System. Journal of Intelligent Communication, 4(1), 63–78.


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.


information data length transient queues M/M/∞ queueing system

Author Biography

Dr. Ismail A Mageed, University of Bradford, United Kingdom.

Dr. Ismail A Mageed obtained his doctorate in Applied Probability at The University of Bradford, United Kingdom. Dr Mageed has been nominated by numerous high-profile academic institutions to the world prestigious ABEL PRIZE(NOBLE PRIZE OF MATHEMATICS) FOR THE ACADEMIC YEAR 2025, based on his great services to humanity through revolutionary mathematical applications to advance several scientific disciplines, including Engineering, Computer Science and much more. His current research interests include the unification of queueing theory with information theory and information geometry. His leading research on the relativisation of queuing theory and discovering the geodesic  equation of motion for transient queues was greatly received by the world research community, based on spotlighting novel avenues for a UNIFIED THEOREM ON EVERYTHING. Mageed’s research on finding the analytic solutions of the longstanding simulative approach of The Pointwise Stationary Fluid Flow Approximation theory (PSFFA) was an exceptional discovery to advance PSFFA theory. Dr Mageed has published numerous papers in many highly reputable journals and IEEE conferences. He is also a reviewer  and a member of the editorial board to many international prominent journals. Mageed’s research has been internationally recognized as being revolutionary by providing several breakthroughs and solving many longstanding open problems. He is currently an active member at the NetPen Research Group, which is the strongest research group in queueing networks in the world. Dr Mageed has published a chapter in a book of the best eight queueing theorists in the world, entitled:

Queueing Theory 2: Advanced Trends

By the world-renowned Publishing Company, ISTE WILLEY, which was translated into French by the same Publishing Company. He has also published another chapter in a high-profile book, entitled:

Fractal Analysis - Applications and Updates

By the world leading open access publishing house, IntechOpen. He is currently coaching numerous volunteering  several research teams worldwide to deliver more insights on employing research to serve humanity. He is also a fellow of the Royal Statistical Society (RSS),the OR Society of the United Kingdom, a member of INTISCC (Austria), IEANG (world council of engineering) and a life member of the Islamic Society of Statistical Sciences. 


  • Introducing a revolutionary breakthrough  by unifying information data length and transient queuing systems theories  by revealing 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.
  • An exposition of a significant real-life application of queueing system was addressed, namely the computation of the common average time for unsaturated site visitor flows beneath double-parking situations.
  • The practical implication for the field includes the provision of some challenging open problems, which would open a plethora of several gates to the establishment of contemporary information data length theory of transient queueing systems combined with concluding remarks and future research pathways.


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