Reduce the Queue Waiting Time on (i < j) Pre-Emptive Priority Queueing Model

The aim of this paper, propose a mathematical modelling on two stage pre-emptive priority queuing system and minimizing the waiting time. Initially, system can be split into two units such as: ordinary unit and priority unit. Here each unit servers are not dependent and service time considered as K-phase Erlang distribution. According to this quickly assign the server for emergency customer without affecting the ordinary unit. In this case, derive the ’nth’ customer steady state probability in both units. A numerical example is included.