On two node tandem queueing model with time dependent service rates

摘要

Queueing is a phenomenon associated with congestion. For controlling congestion and to utilize the resources optimally the queueing models are developed. In queueing models, it is customary to consider that the arrival and service processes are stable and follows a Poisson process. But in many systems the service process is time dependent and it can be well characterized by non-homogeneous Poisson process. This paper introduces a tandem queueing model with non-homogeneous Poisson service process. The system performance is analysed by deriving the system performance measure such as, average content of the queues, average waiting time of a customer in the queue and in the system, the throughput of transmitters, and the variance of the number of customers in the system. The effect of various changes in parameter on the system performance measures is carried through sensitivity analysis. It is observed that the time dependent service rate has significant influence on the system performance measures. This model can accurately predict the performance measures, when the service rates are time dependent. Several of the earlier models become particular cases of this model.