Queuing System with Poisson Arrival Distribution and Mixture Service Time Distribution: An M/Mix/1 Model
DOI:
https://doi.org/10.55544/sjmars.5.2.5Keywords:
Queueing Theory, Markovian Queues, Random Memory Queues, Stochastic Processes, Transition Probabilities, Queue CharacteristicsAbstract
Queueing models play an important role in analyzing congestion phenomena in service systems such as telecommunication networks, computer systems, banks, hospitals, and transportation systems. Traditional queueing models often assume exponential service time distributions; however, real-life service processes frequently exhibit heterogeneous behavior that cannot be adequately captured by a single distribution. In this paper, we propose a single-server queueing model with a Poisson arrival process and a mixture service time distribution, referred to as the M/Mix/1 model. The mixture distribution allows the service mechanism to represent multiple service phases or heterogeneous service requirements. Key characteristics of the mixture distribution including its probability density function, cumulative distribution function, moment generating function, and variance are discussed. The proposed framework demonstrates how mixture distributions can enhance the flexibility of queueing models for realistic service systems.
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