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In the last years, a progressive migration from single processor chips to multi-core computing devices has taken place in the general-purpose and embedded system market. The development of multi-processor systems is already a core activity for the most important hardware companies. A lot of different solutions have been proposed to overcome the physical limits of single core devices and to address the increasing computational demand of modern multimedia applications. The real-time community followed this trend with an increasing number of results adapting the classical scheduling analysis to parallel computing systems. This paper will contribute to refine the schedulability analysis for symmetric multi-processor (SMP) real-time systems composed by a set of periodic and sporadic tasks. We will focus on both fixed and dynamic priority global scheduling algorithms, where tasks can migrate from one processor to another during execution. By increasing the complexity of the analysis, we will show that an improvement is possible over existing schedulability tests, significantly increasing the number of schedulable task sets detected. The added computational effort is comparable to the cost of techniques widely used in the uniprocessor case. We believe this is a reasonable cost to pay, given the intrinsically higher complexity of multi-processor devices.