# Efficient Online Strategies for Renting Servers in the Cloud

## Abstract

When scheduling jobs for systems in the cloud, we often deal with jobs that arrive and depart in an online manner. Each job should be assigned to a server upon arrival. Jobs are annotated with sizes which define the amount of resources that they need. Servers have uniform capacity and, at all times, the total size of jobs assigned to a server should not exceed this capacity. This setting is closely related to the classic bin packing problem. The difference is that, in bin packing, the objective is to minimize the total number of used servers. In the cloud systems, however, the cost for each server is proportional to the length of the time interval it is rented for, and the goal is to minimize the cost involved in renting all used servers. Recently, certain bin packing strategies were considered for renting servers in the cloud [Li et al. SPAA’14]. There, it is proved that all Any-Fit strategies have a competitive ratio of at least *μ*, where *μ* is the max/min interval length ratio of jobs. It is also proved that First Fit has a competitive ratio of 2*μ* + 13, while Best Fit is not competitive at all. We observe that the lower bound of *μ* extends to all online algorithms. We also prove that, surprisingly, Next Fit algorithm has a competitive ratio of at most 2 *μ* + 1. We also show that a variant of Next Fit achieves a competitive ratio of *K* × max {1,*μ*/(*K* − 1)} + 1, where *K* is a parameter of the algorithm. In particular, if the value of *μ* is known, the algorithm has a competitive ratio of *μ* + 2; this improves upon the existing upper bound of *μ* + 8. Finally, we introduce a simple algorithm called Move To Front (Mtf) which has a competitive ratio of at most 6*μ* + 8. We experimentally study the average-case performance of different algorithms and observe that the typical behaviour of Mtf is better than other algorithms.

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