Project Server is sensitive tool with regard to performance.
When we plan to install and configure Project Server, we need to verify a lot of requirements, and we need to know that the Project Server is meeting those requirements. There are a lot of impacts for users in terms of performance in case we can't meet one or more requirements.
First step: We need to determine the data set size of our environment based-on a table present in the article How datasets affect performance and capacity in Project Server 2013: https://technet.microsoft.com/pt-br/library/fp161198.aspx
Second step: After determine if we have a small, medium, or large environment, we will need to check necessary hardware. To do this, we can use the article Hardware and software requirements for Project Server 2013: https://technet.microsoft.com/pt-br/library/ee683978.aspx. Remember that these are the minimums and may not sufficient for your needs.
Third step: Now we know exactly how many projects, resources, and transactions we will have and we are able to determine recommended hardware and software to reach a satisfactory performance. But, this is not enough. Generally, the company PMO will determine Project Server configuration to meet their project management process, and we need to check another article which explains about Optimization. Optimize performance in Project Server 2013: https://technet.microsoft.com/pt-br/library/fp161228.aspx. Through this article we will learn about limitations: baseline, master projects, security settings, views, custom fields, queue optimization and more.
Fourth step: If we have an environment that is totally problematic in terms of performance, we can use all the above articles and include another one that is responsible for showing us some common bottlenecks, causes, and resolutions. Performance troubleshooting in Project Server 2013: https://technet.microsoft.com/pt-br/library/fp161227.aspx.
For further information about Project Server, use Project Server site in TechNet: https://technet.microsoft.com/pt-br/library/cc303399.aspx