A new emerging class of problems related to the online configuration and optimization of computer systems and networks requires the solution in a very short amount of time of a large number of analytical performance models, often based on queueing networks. In this paper we propose the Geometric Bounds (GB), a new family of fast noniterative bounds on performance metrics of closed productform queueing networks. In spite of their simplicity, the proposed bounds are more accurate than the popular Balanced Job Bounds (BJB), even in the difficult case of networks with multiple bottlenecks or large delays.