Characterizing output processes of Em/Ek/1 queues

Our goal is to study which conditions of the output process of a queue preserve the Increasing Failure Rate (IFR) property in the interdeparture time. We found that the interdeparture time does not always preserve the IFR property even if the interarrival time and service time are both Erlang distributions with IFR. We give theoretic analysis and present numerical results of Em/Ek/1 queues. We show, by numerical examples, that the interdeparture time of Em/Ek/1 retains the IFR property if m = k.