Abstract
Load balancing plays a crucial role in achieving low latency in large distributed systems. Recent load balancing strategies often rely on replication or use placeholders to further improve latency. However assessing the performance and stability of these strategies is challenging and is therefore often simulation based. In this paper we introduce a unified approach to analyze the performance and stability of a broad class of workload dependent load balancing strategies. This class includes many replication policies, such as replicate below threshold, delayed replication and replicate only small jobs, as well as strategies for fork-join systems. We consider systems with general job size distributions where jobs may experience server slowdown. We show that the equilibrium workload distribution of the cavity process satisfies a functional differential equation and conjecture that the cavity process captures the limiting behavior of the system as its size tends to infinity. We study this functional differential equation in more detail for a variety of load balancing policies and propose a numerical method to solve it. The numerical method relies on a fixed point iteration or a simple Euler iteration depending on the type of functional differential equation involved. We further show that additional simplifications can be made if certain distributions are assumed to be phase-type. Various numerical examples are included that validate the numerical method and illustrate its strength and flexibility.
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