1. A method of resource arbitration for multiple pipelines with a shared resource of a Symmetric Multi-Processor (SMP) computer system comprising the steps of: arbitrating for priority with cross-interrogation arbiter logic within a pipeline of the multiple pipelines to reject a current cache line pipeline operation and to allow for the retry of the rejected current cache line pipeline operation without any destructive effects, while other operations in the pipeline continue without disruption; and determining, while arbitrating for priority, if a shared common resource of the Symmetric Multi-Processor (SMP) computer system is needed by a pipeline operation using information from said current cache line pipeline operation and a remote cache line pipeline to determine if there is a resource conflict with the shared common resource; and rejecting the said current cache line pipeline operation if there is a conflict within the current cache line pipeline with the said shared common resource of the Symmetric Multi-Processor (SMP) computer system.