Deterministic optimal routing for two heterogeneous parallel servers

The paper describes the characteristics of an optimal routing that assigns each arriving packet to one of two heterogeneous parallel servers. The characteristics are derived from numerical solutions to a routing problem, which finds an optimal routing that minimizes the average packet delay under the condition that the input traffic is completely deterministic. Four characteristics are presented: (1) under light or moderate traffic, the average packet delay of the optimal routing is almost the same as that of the join the shortest delay (JSD) policy; (2) as traffic becomes heavier, the optimal routing more often uses the fix queue based on size (FS) policy; (3) under heavy traffic, the optimal routing assigns small packets to a slower server; (4) as the ratio of the two servers´ service rates C₁/C₂ (C ₁⩽C₂) decreases, under lighter traffic the optimal routing uses the FS policy. A new adaptive routing policy based on these four characteristics outperforms the JSD policy