Author(s): Ch. Ganapathi Swamy, K Srinivasa Rao, S Govinda Rao and Ch. Varahala Swamy

Abstract: A stochastic process associated with queuing system is specified by the knowledge of (i) Arrival\process (ii) queue discipline (iii) Service process. The service process is the most crucial of these three since system operators can manage it. It is typical to assume that the inter-service times are exponential, along with many other presumptions. Erlangian service time is a generalization of it, where it is assumed that there are k phases of service and that they are all uniformly distributed as negative exponentials Distribution. But the service times differ in many real-world scenarios. This model work well when the service times of the customers in the system are homogeneous. But in some situations the service time required by the customers are heterogeneous even though they follow the Additive exponential distribution. The homogeneous nature of the service times can be characterized by a two component mixture of Additive exponential distribution. Hence in this paper, we develop and analyse a single server queuing models with Poisson arrivals having two component mixture of Additive exponential service time distribution. Using the probability generating function the system size distribution is derived. The system behavious analysed by deriving the system characteristics like, average number of customer in the system, the variability of system size, etc. The waiting time distribution of the system is also derived. The sensitivity of the model with respect to the parameter is analyzed. It is observed that the system performance is influenced by the service time distribution parameters. This model includes M/M/1, M/E/1 models as particular cases for specific or timely value of parameters.

Pages: 105-116 | Views: 70 | Downloads: 5

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