## Abstract

We present an overview of scalable load balancing algorithms which provide favorable delay performance in large-scale systems, and yet only require minimal implementation overhead. Aimed at a broad audience, the paper starts with an introduction to the basic load balancing scenario, consisting of a single dispatcher where tasks arrive that must immediately be forwarded to one of N single-server queues.

A popular class of load balancing algorithms are so-called power-of-d or JSQ(d) policies, where an incoming task is assigned to a server with the shortest queue among d servers selected uniformly at random. This class includes the Join-the-Shortest-Queue (JSQ) policy as a special case (d=N), which has strong stochastic optimality properties and yields a mean waiting time that vanishes as N grows large for any fixed subcritical load. However, a nominal implementation of the JSQ policy involves a prohibitive communication burden in large-scale deployments. In contrast, a random assignment policy (d=1) does not entail any communication overhead, but the mean waiting time remains constant as N grows large for any fixed positive load. In order to examine the fundamental trade-off between performance and implementation overhead, we consider an asymptotic regime where d(N) depends on N. We investigate what growth rate of d(N) is required to match the performance of the JSQ policy on fluid and diffusion scale. The results demonstrate that the asymptotics for the JSQ(d(N)) policy are insensitive to the exact growth rate of d(N), as long as the latter is sufficiently fast, implying that the optimality of the JSQ policy can asymptotically be preserved while dramatically reducing the communication overhead. We additionally show how the communication overhead can be reduced yet further by the so-called Join-the-Idle-Queue scheme, leveraging memory at the dispatcher.

A popular class of load balancing algorithms are so-called power-of-d or JSQ(d) policies, where an incoming task is assigned to a server with the shortest queue among d servers selected uniformly at random. This class includes the Join-the-Shortest-Queue (JSQ) policy as a special case (d=N), which has strong stochastic optimality properties and yields a mean waiting time that vanishes as N grows large for any fixed subcritical load. However, a nominal implementation of the JSQ policy involves a prohibitive communication burden in large-scale deployments. In contrast, a random assignment policy (d=1) does not entail any communication overhead, but the mean waiting time remains constant as N grows large for any fixed positive load. In order to examine the fundamental trade-off between performance and implementation overhead, we consider an asymptotic regime where d(N) depends on N. We investigate what growth rate of d(N) is required to match the performance of the JSQ policy on fluid and diffusion scale. The results demonstrate that the asymptotics for the JSQ(d(N)) policy are insensitive to the exact growth rate of d(N), as long as the latter is sufficiently fast, implying that the optimality of the JSQ policy can asymptotically be preserved while dramatically reducing the communication overhead. We additionally show how the communication overhead can be reduced yet further by the so-called Join-the-Idle-Queue scheme, leveraging memory at the dispatcher.

Original language | English |
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Pages | 3911-3942 |

Number of pages | 32 |

Publication status | Published - Jan 2018 |

Event | International congress of mathematicians (ICM 2018) - Rio de Janeiro, Brazil Duration: 1 Aug 2018 → 9 Aug 2018 |

### Conference

Conference | International congress of mathematicians (ICM 2018) |
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Country/Territory | Brazil |

City | Rio de Janeiro |

Period | 1/08/18 → 9/08/18 |