A loss system with skill based servers under assign to longest idle server policy

We consider a memoryless loss system with servers S = {1, …, J}, and with customer types C = {1, …, I}. Servers are multi-type: server j works at rate µj, and can serve a subset of customer types C(j). An arriving customer will go to the longest idling server which can serve him, or be lost. We obtain a simple explicit steady-state distribution for this system, and calculate various performance measures of this system in steady state. We provide some illustrative examples. We compare this system with a similar system discussed recently by Adan, Hurkens, and Weiss [1]. We also show that this system is insensitive, the results hold also for general service time distributions.