Waste Material Management with a Coxian Arrival and First Exceptional Service Queueing Model

Abstract This paper studies a variant of the C 2 /G/1 queue, where the service time distribution for a customer depends on whether the server is busy or idle when the customer arrives. This class of models is relevant in scenarios where the server may require varying amounts of time when it resumes service after being idle. Customer arrives in the system according to 2‐stage Coxian distribution. By using supplementary variable techniques and recursive method that utilizes generating function, we derived steady‐state probabilities to analyze the distribution of queue length and sojourn time. Queueing models of this type have wide application in streamline operations like waste material management, and ensure effectiveness.