# Optimal Scheduling and Exact Response Time Analysis for Multistage Jobs

arXiv: https://arxiv.org/abs/1805.06865 · HTML: https://mlsanity.com/paper/1805.06865/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2018.

## Built on by (most cited first, 1 of 1)

- [The Gittins Index: A Design Principle for Decision-Making Under Uncertainty](https://mlsanity.com/paper/2506.10872/) (2025)

## Abstract (arXiv)

Scheduling to minimize mean response time in an M/G/1 queue is a classic problem. The problem is usually addressed in one of two scenarios. In the perfect-information scenario, the scheduler knows each job's exact size, or service requirement. In the zero-information scenario, the scheduler knows only each job's size distribution. The well-known shortest remaining processing time (SRPT) policy is optimal in the perfect-information scenario, and the more complex Gittins policy is optimal in the zero-information scenario. In real systems the scheduler often has partial but incomplete information about each job's size. We introduce a new job model, that of multistage jobs, to capture this partial-information scenario. A multistage job consists of a sequence of stages, where both the sequence of stages and stage sizes are unknown, but the scheduler always knows which stage of a job is in progress. We give an optimal algorithm for scheduling multistage jobs in an M/G/1 queue and an exact response time analysis of our algorithm.