On-line machine scheduling has been studied extensively, but the fundamental issue of fairness 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 [IBM Journal of Research and Development 27(2) (1983), 133-139]. 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.
Bibliographical noteFunding Information:
*E-mail: firstname.lastname@example.org. ²Supported by NSF Grants CCR-94-10228 and CCR-94-15410. During part of this research this author was visiting IBM Almaden Research Center. E-mail: email@example.com. ³Incumbent of the Morris and Rose Goldman Career Development Chair, Department of Applied Mathematics and Computer Science, Weizmann Institute, Israel. Research supported by an Alon Fellowship and a grant from the Israel Science Foundation administered by the Israeli Academy of Sciences. E-mail: firstname.lastname@example.org. §Work at ICSI supported by a Rothschild postdoctoral fellowship. Work at MIT supported by ARPA/Army Contract DABT63-93-C-0038. Present address: Department of Computer Science, University of Toronto, Toronto, Ontario M5S 1A4. E-mail: email@example.com. ¶Work supported by an NSF postdoctoral fellowship. E-mail: firstname.lastname@example.org. ISupported by an NSF postdoctoral fellowship. Part of this work was done while this author was at IBM Almaden Research Center. E-mail: email@example.com.