Throughput and delay optimality of power-of-d choices in inhomogeneous load balancing systems

It is well-known that the power-of-d choices routing algorithm maximizes throughput and is heavy-traffic optimal in load balancing systems with homogeneous servers. However, if the servers are heterogeneous, throughput optimality does not hold in general. We find necessary and sufficient conditions for throughput optimality of power-of-d choices when the servers are heterogeneous, and we prove that almost the same conditions are sufficient to show heavy-traffic optimality. Additionally, we generalize the sufficient condition for throughput optimality to a larger class of routing policies.