Ismail’s Ratio Conquers New Horizons: The Non-Stationary Queue’s State Variable Closed Form Expression with Queueing Applications to Traffic Management Optimization
Journal Title: Journal of Operational and Strategic Analytics - Year 2024, Vol 2, Issue 3
Abstract
This paper investigates the search for an exact analytic solution to a temporal first-order differential equation that represents the number of customers in a non-stationary or time-varying M/D/1 queueing system. Currently, the only known solution to this problem is through simulation. However, a study proposes a constant ratio, β (Ismail's ratio), that relates the timedependent mean arrival and mean service rates, offering an exact analytical solution. The stability dynamics of the time-varying M/D/1 queueing system are then examined numerically in relation to time, β, and the queueing parameters. On another note, many potential queueing-theoretic applications to traffic management optimization are provided. The paper concludes with a summary, combined with open problems and future research pathways.
Authors and Affiliations
Ismail A Mageed
Keywords
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- EP ID EP752326
- DOI https://doi.org/10.56578/josa020302
- Views 45
- Downloads 0
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