Symmetry and Analysis of Fluid Queueing Systems Driven by Non-Truncated Erlangian Service Queues

This paper investigates the behavior of a fluid queue driven by a non-truncated Erlangian service queue, focusing on the symmetrical properties within the system. This study determines the formulations of the steady-state distribution of both the buffer content and stationary state probabilities of a background queueing system. The efficient generating function technique is employed, utilizing a new generalization of the modified Bessel function of the second kind. Performance metrics such as mean buffer content and throughput are calculated, and server utilization is examined. The results contribute to the understanding of fluid queueing systems and offer insights into their performance in various applications, including telecommunications, manufacturing systems, healthcare operations, and ecological models, where symmetry plays a critical role in optimizing performance.