Abstract
Modeling real-life scenarios as differential equation models have displayed numerous advantages as the model is able to infuse more realistic features of the scenario under consideration. Adopting a differential equation flow model to estimate server utilization rate in queuing systems has not attracted much attention due to the challenges to obtain an exact solution to the model. However, this concern is bypassed by adopting approximate methods. Thus, this article adopts a first order differential equation model to calculate the rate at which work arrives and the capacity of workstation. The values were obtained as the independent variable becomes large, which expresses the values of the utilization of resources which is now infused into conventional queuing expressions to obtain the required information about the queuing systems. A new novel and convergent one-step second-derivative method is developed in this article to obtain the required value of the server utilization rate.
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