How can packets be optimally routed to minimize delay in heterogeneous parallel servers? This paper presents characteristics of optimal routing for assigning arriving packets to two heterogeneous parallel servers, each with its own queue. It derives these characteristics from numerical solutions to an optimization problem, aiming to minimize average packet delay given complete knowledge of arrival times and packet sizes. The study identifies four key characteristics: Under light or moderate traffic, optimal routing closely resembles the join the shortest delay (JSD) policy. Under heavier traffic, it increasingly favors a fix queue based on size (FS) policy. Under heavy traffic, optimal routing assigns small packets to the slower server. As the service rate ratio between servers decreases, optimal routing uses FS policy more often, even under lighter traffic. These characteristics are validated by the fact that a mimic optimal routing designed based on them achieves almost the same performance as optimal routing, offering insights for practical routing strategies.
Published in the International Journal of Foundations of Computer Science, this paper is relevant to the journal's focus on theoretical foundations and practical applications of computer science. The analysis of optimal routing for parallel servers contributes to the understanding of fundamental concepts in computer science and has practical implications for system design.