Summary: Fairness in Scheduling
Miklos Ajtai \Lambda James Aspnes y Moni Naor z Yuval Rabani x
Leonard J. Schulman -- Orli Waarts k
July 5, 1998
Online machine scheduling has been studied extensively, but the fundamental issue of fair
ness in scheduling is still mostly open. In this paper we explore the issue in settings where there
are long lived processes which should be repeatedly scheduled for various tasks throughout the
lifetime of a system. For any such instance we develop a notion of desired load of a process,
which is a function of the tasks it participates in. The unfairness of a system is the maximum,
taken over all processes, of the difference between the desired load and the actual load.
An example of such a setting is the carpool problem suggested by Fagin and Williams .
In this problem, a set of n people form a carpool. On each day a subset of the people arrive and
one of them is designated as the driver. A scheduling rule is required so that the driver will be
determined in a `fair' way.
We investigate this problem under various assumptions on the input distribution. We also
show that the carpool problems can capture several other problems of fairness in scheduling.
1.1 Our results
Consider the following edge orientation problem: on a set of n nodes labeled f1; : : : ; ng there is a