Characterizing output processes of Em/Ek/1 queues

Our goal is to study the output process of a queue of which conditions the interdeparture time will preserve the IFR property. We found the interdeparture time doesn’t 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 it by numerical examples that the interdeparture time of Em/Ek/1 retains the IFR property if m ≥ k.