This paper presents characteristics of optimal routing that assigns each arriving packet to one of two heterogeneous parallel servers, each with its own queue. The characteristics are derived from numerical solutions to an optimization problem, which is to find optimal routing that minimizes the average packet delay under the condition that all of the packets' arrival times as well as all of the packets' sizes are completely known in advance. There are four characteristics: (1) Under light or moderate traffic, the average packet delay of optimal routing is almost the same as that of join the shortest delay (JSD) policy. (2) Under heavier traffic, optimal routing comes to more often use fix queue based on size (FS) policy. (3) Under heavy traffic, optimal routing assigns small packets to the slower server. (4) As the ratio of the slower server's service rate to the faster server's service rate decreases, optimal routing comes to more often use FS policy under light or moderated traffic. These characteristics are verified by the fact that a mimic optimal routing designed based on the four characteristics attains almost the same performance as optimal routing.
Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: asymptotic optimality of a threshold policy
