A Generalized M/M/1 Queue with Mixture Service Times: Modeling and Analysis
DOI:
https://doi.org/10.55544/sjmars.5.2.4Keywords:
M/M/1 Queue, , Mixture Service Time Distribution, Queueing Theory, Stochastic Processes, Markov ChainsAbstract
Queuing theory plays an important role in modeling congestion phenomena in service systems such as telecommunications, transportation, healthcare, and computer networks. Classical queuing models often assume exponential service time distributions; however, in many real-world situations service times may follow more complex distributions. In this study, a single-server queuing model with Poisson arrival process and a mixture service time distribution is considered. The proposed model, denoted as M/Mix/1, extends the classical M/M/1 framework by allowing the service time to follow a mixture distribution. The theoretical structure of the model is described, and key distributional properties such as mean, variance, moment generating function, cumulative distribution function, and Laplace transform are discussed. The results demonstrate that mixture distributions provide a flexible approach for modeling heterogeneous service mechanisms in queuing systems.
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