# Why is the Greedy Algorithm for Online Scheduling on uniform machines NOT competitive?

Consider the Online Scheduling Problem with m machines and different speeds.

Each instance $$\sigma$$ consists of a sequence of jobs with different sizes $$j_i\in\mathbb{R^+}$$. At each step in time any algorithm gets to know the one new job of $$\sigma$$ which needs to be assigned to one machine. The goal is to minimize the makespan (by the end of the online sequence \sigma\$ ).

I want to find an instance such that the Greedy Algorithm, which assigns each new job to the machine which finishes it first, is only $$\Theta(\log m)$$-competitive.

Any ideas? I can’t find any articles regarding my problem.