Renting Servers in the Cloud: The Case of Equal Duration Jobs

TL;DR

This paper analyzes online algorithms for assigning equal-duration jobs to cloud servers to minimize rental costs, establishing tight bounds on their competitive ratios and improving understanding of their efficiency.

Contribution

It proves a tight bound of 2 for NextFit's competitive ratio and provides new bounds for FirstFit, advancing theoretical understanding of online server rental algorithms.

Findings

NextFit has a tight competitive ratio bound of 2.

FirstFit's competitive ratio lower bound is 2.519.

For specific job arrival and duration cases, bounds are refined to between 1.89 and 2.

Abstract

Renting servers in the cloud is a generalization of the bin packing problem, motivated by job allocation to servers in cloud computing applications. Jobs arrive in an online manner, and need to be assigned to servers; their duration and size are known at the time of arrival. There is an infinite supply of identical servers, each having one unit of computational capacity per unit of time. A server can be rented at any time and continues to be rented until all jobs assigned to it finish. The cost of an assignment is the sum of durations of rental periods of all servers. The goal is to assign jobs to servers to minimize the overall cost while satisfying server capacity constraints. We focus on analyzing two natural algorithms, NextFit and FirstFit, for the case of jobs of equal duration. It is known that the competitive ratio of NextFit and FirstFit are at most 3 and 4 respectively for this case. We prove a tight bound of 2 on the competitive ratio of NextFit. For FirstFit, we establish a lower bound of 2.519 on the competitive ratio, even when jobs have only two distinct arrival times. For the case when jobs have arrival times 0 and 1 and duration 2, we show a lower bound of 1.89 and an upper bound of 2 on the strict competitive ratio of FirstFit. Finally, using the weight function technique, we obtain stronger results for the case of uniform servers.