An M/M/1 Queuing System with Three Types Input Sources
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Keywords:
Queuing Theory, Markovian Process, Laplace Transform, Exponential Distribution, Poisson distribution, Probability Generating FunctionAbstract
This paper considers an M/M/1 queuing system with three types input sources, where the rate of arrival and service capacity follow Poisson distribution. The arrival process consists of three stages said to be active state, sick state and passive state. The system remains in three state for a random time which is exponentially distributed. The queue discipline is first-come-first-serve (FCFS). Laplace transforms of the various probability generating functions are obtained and the steady state results are derived. The probability that the arrival process (input) will be in active state, sick state and passive state, is also analyzed.
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