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This study of text discusses the analysis of the CDFs of service time in the stable M/G/1 queueing system with 'longrange interactions' of order q (where 0.5 < q < 1). This letter makes a significant contribution since it uses a novel methodology to show how the order q and the Lagrangian multiplier τs affect the increasability and decreasability themes of T-R CDFs. Additionally, the numerical data sets to show the validity of our analytical proofs are introduced. Some Tsallisian and Rényian Entropic applications to SIs are provided. Closing remarks entailed with the next phase of research are given. [ABSTRACT FROM AUTHOR]

A theoretical approach for creating power law behaviour in broadband communication networks with GeoM or SGeoM specifications utilizing the Rényian maximum entropy functional formalism is undertaken. When specifying the SGeoM, the special case of M/M/1 queue's equilibrium distribution emerges. The suggested method simplifies closed-form equations for a queueing distribution, and the service time density and cumulative distribution functions reduce to the appropriate Rényian, Tsallisian, and Shannonian situations. The concept works well in power law activated - communication networks. Some influential applications of GeoM to WSNs are provided. [ABSTRACT FROM AUTHOR]

An exposition is undertaken for the threshold of both Rényian and Tsallisian steady-state probabilities of the stable queueing system with 'long-range interactions' (LRIs). The current work is pivotal for developing revolutionary queueing theory and providing ground-breaking queueingtheoretic unifications with other scientific disciplines. The significance of the novel results of the current letter is based on the novelty of employing a mathematical approach to reveal the impact of the queueing parameters on the decidability procedure on the regions of increasability (decreasability). The numerical data sets to show the validity of our analytical proofs are introduced. Some influential applications of the probability density function (PDF) are presented. Finally, conclusions combined with some challenging open problems combined with the next phase of research are provided. [ABSTRACT FROM AUTHOR]

An exposition is undertaken to solve the open problem of finding the exact analytic closed form solution for GI/M/1 PSFFA model of the D/M/1 queueing system. This paper reveals the general revolutionary analytic solution to this open problem. Moreover, the closed form representation of the root parameter, σ(t), 1 > σ(t) > 0 is devised. Another contribution of this paper is determining the thresholds of the root parameter with respect to both time and the timedependent mean arrival rate, λ(t) are determined. Moreover, the thresholds of the derived analytic solution with respect to time-dependent mean arrival rate, λ(t) is devised. Typical numerical experiments to evidence the significant impact of time, time dependent mean arrival rate of the underlying time varying GI/M/1 queueing system as well as the time dependent root parameter, σ(t), 1 > σ(t) > 0, of the geometric distribution of the new arrival of the GI/M/1 model is given. Some potential applications of PSFFA theory to computer science, engineering and technology works are given. Closing remarks with proposed next research phases are provided. [ABSTRACT FROM AUTHOR]

An exposition is undertaken for the linearity of both stable M/G/1 queue's non-extensive (Rényian)and (Tsallisian) solutions. This current letter provides the mathematical validity for the experimental setup of the information theoretic unification with queueing theory manifested by the Rényian, and Tsallisian linearity profile attained, which is a consequence of the progressive increase of the Shannonian squared coefficient of variation, through the provision of the mathematical proof. Potential applications of Queueing Theory (QT) to Cloud Computing (CC) and Internet of Things(IoT) are given. Closing remarks combined with open problems and future next phase research are provided. [ABSTRACT FROM AUTHOR]

An explanation is made for the stable M/G/1 queueing system's threshold of Rényian and Tsallisian squared coefficient of variation (SCV) with "long-range interactions" of order, q (0.5