“…We believe that the non-stationary load will exhibit sinusoidal mean behaviour, which will describe the cyclic load pattern over a specified time period (for example, day) in accordance with the prior research on non-stationary analysis of communication networks [2][3][4][5][6], namely ๐(๐ก) = ๐ด + ๐ต๐ ๐๐(๐ค๐ก + ๐ท), for more details see [7][8][9].…”
Section: The ๐ฎ๐ฐ/๐ด/ ๐ Queueing Modelsupporting
The current work reveals the fine tuning between stability zones and randomness of GI/M/1 Pointwise Stationary Fluid Flow Approximation (PSFFA) model of the non-stationary D/M/1 queueing system. More specifically, this clearly provides more insights into developing a contemporary PSFFA theory that unifies non-stationary queueing theory with chaos theory and fields in both theoretical physics and chaotic systems. This opens new grounds for stability analysis of non-stationary queueing systems. A notable application of GI/M/1 queueing model to achieve ultra-low latency of autonomous driving service is highlighted. Concluding remarks associated with future avenues of research are given.
“…We believe that the non-stationary load will exhibit sinusoidal mean behaviour, which will describe the cyclic load pattern over a specified time period (for example, day) in accordance with the prior research on non-stationary analysis of communication networks [2][3][4][5][6], namely ๐(๐ก) = ๐ด + ๐ต๐ ๐๐(๐ค๐ก + ๐ท), for more details see [7][8][9].…”
Section: The ๐ฎ๐ฐ/๐ด/ ๐ Queueing Modelsupporting
The current work reveals the fine tuning between stability zones and randomness of GI/M/1 Pointwise Stationary Fluid Flow Approximation (PSFFA) model of the non-stationary D/M/1 queueing system. More specifically, this clearly provides more insights into developing a contemporary PSFFA theory that unifies non-stationary queueing theory with chaos theory and fields in both theoretical physics and chaotic systems. This opens new grounds for stability analysis of non-stationary queueing systems. A notable application of GI/M/1 queueing model to achieve ultra-low latency of autonomous driving service is highlighted. Concluding remarks associated with future avenues of research are given.
“…We believe that the non-stationary load will exhibit sinusoidal mean behaviour, which will describe the cyclic load pattern over a specified time period (for example, day) in accordance with the prior research on non-stationary analysis of communication networks [2][3][4][5][6], namely ๐(๐ก) = ๐ด + ๐ต๐ ๐๐(๐ค๐ก + ๐ท), for more details see [7][8][9].…”
Section: The ๐ฎ๐ฐ/๐ด/ ๐ Queueing Modelsupporting
The current work reveals the fine tuning between stability zones and randomness of GI/M/1 Pointwise Stationary Fluid Flow Approximation (PSFFA) model of the non-stationary D/M/1 queueing system. More specifically, this clearly provides more insights into developing a contemporary PSFFA theory that unifies non-stationary queueing theory with chaos theory and fields in both theoretical physics and chaotic systems. This opens new grounds for stability analysis of non-stationary queueing systems. A notable application of GI/M/1 queueing model to achieve ultra-low latency of autonomous driving service is highlighted. Concluding remarks associated with future avenues of research are given.
“…Both Figures 1 and 2(c.f., [2]) provide two real life applictions of Time Varying queueing systems. In Figure 1, the Mean number of calls per minute at a central office switch -measured in 15 minutes intervals averaged over 10 work days are observed .…”
An exposition is undertaken to reveal the significant impact of the time-dependent root parameter, on the stability of Pointwise Stationary Fluid Flow Approximation (PSFFA) model of the non-stationary queueing system. This opens new grounds to stability analysis of non-stationary queueing systems. Potential PSFFA applications of IoT are highlighted.
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