We propose a system and method for providing a ``throughput versus delay'' differentiated service for IP packets. We distinguish two types of traffic: type A and type B. It is expected that type A traffic receives less throughput per flow than type B. On the other hand, type A packets experience considerably smaller delay. The method is intended to be implemented in Internet routers. No bandwidth or buffer reservation is assumed in this system. The service remains a Best Effort service, thus supporting flat rates and free access to all applications. This is intended to be fully compatible with the current Internet. Furthermore, no change in the applications or protocols is required. The system we propose is based on a collection of processing procedures to be implemented in IP routers. These procedures are organised in four modules and are designed to achieve the asymmetric performance for the two types of packets. The originality of this work is two fold: we give the definition of the asymmetric performance in a best effort environment and propose the original algorithms and procedures to be implemented in network nodes to achieve the said definition.