Fluid Models of Parallel Service Systems under FCFS

We study deterministic fluid approximations of parallel service systems operating under first come first served policy (FCFS). The condition for complete resource pooling is identified in terms of the system structure and the customer service times. The static planning linear programming approach (Harrison and Lopez \cite{harrison-lopez:99}) is used to obtain a maximum throughput compatibility tree and to show that FCFS using this compatibility tree is throughput optimal. We investigate matching rates and show by Hotelling's $T^2$-test and simulation that they are dependent on the service time distribution.