An M/E k /1 queues with emergency non-preemptive priority of a diagnostic resource

Each patient is assigned to a specific scanner in CT department of a large‐size hospital. Emergency patients have non‐preemptive priority access to service. The service time of each CT scanner follows an Erlang distribution by data analysis from this hospital. We develop an M/E k /1 queueing model with emergency non‐preemptive priority. Firstly, the expected waiting time of the jth phase regular patient in the waiting queue is given by Laplace transform. Using this and generating function of the steady‐state of phase distribution, the expected waiting time of an arbitrary regular patient is obtained. A total cost function which includes the penalty cost for unutilized medical resources and waiting cost of regular patients is constructed. The optimal arrival rate of regular patients so as to minimize the total cost is given by Kuhn–Tucker condition. Some numerical examples which are based on real data are given.