Saghafian, Soroush, and Michael H. Veatch. "A cµ Rule for Two-Tiered Parallel Servers." IEEE Transactions on Automatic Control 61.4 (April 2016): 1046-1050.
The cµ rule is known to be optimal in many queueing systems with memoryless service and inter-arrival times. We establish a cµ rule for a parallel flexible server system with two tiers. Multiple job classes arrive and wait in separate queues. The first tier contains classes that can only be served by one server each, and the second tier contains a class that can be served by all servers. The cµ preferences give priority to the first tier. Sequencing decisions are made to minimize linear holding costs.