Job Dispatching Policies for Queueing Systems with Unknown Service Rates

TL;DR

This paper addresses the challenge of dispatching jobs in multi-server queueing systems without known service rates, proposing a bandit-based policy that learns service rates and optimally distributes jobs to minimize delays.

Contribution

It introduces a novel bandit-based exploration policy for dispatching in queueing systems with unknown service rates, including a regret analysis and simulation results.

Findings

The proposed policy effectively learns service rates from noisy observations.

It balances exploration and exploitation to minimize queueing delays.

Simulation results demonstrate improved performance over baseline methods.

Abstract

In multi-server queueing systems where there is no central queue holding all incoming jobs, job dispatching policies are used to assign incoming jobs to the queue at one of the servers. Classic job dispatching policies such as join-the-shortest-queue and shortest expected delay assume that the service rates and queue lengths of the servers are known to the dispatcher. In this work, we tackle the problem of job dispatching without the knowledge of service rates and queue lengths, where the dispatcher can only obtain noisy estimates of the service rates by observing job departures. This problem presents a novel exploration-exploitation trade-off between sending jobs to all the servers to estimate their service rates, and exploiting the currently known fastest servers to minimize the expected queueing delay. We propose a bandit-based exploration policy that learns the service rates from observed job departures. Unlike the standard multi-armed bandit problem where only one out of a finite set of actions is optimal, here the optimal policy requires identifying the optimal fraction of incoming jobs to be sent to each server. We present a regret analysis and simulations to demonstrate the effectiveness of the proposed bandit-based exploration policy.