In this paper, we assess the impact of heterogeneity for scheduling independent tasks on master-slave platforms. We assume a realistic one-port model where the master can communicate with a single slave at any time-step. We target on-line scheduling problems, and we focus on simpler instances where all tasks have the same size. While such problems can be solved in polynomial time on homogeneous platforms, we show that there does not exist any optimal de-terministic algorithm for heterogeneous platforms. Whether the source of heterogeneity comes from computation speeds, or from communication bandwidths, or from both, we establish lower bounds on the competitive ratio of any determin-istic algorithm. We provide such bounds for the most important objective functions: the minimization of the makespan (or total execution time), the minimization of the maximum response time (difference between completion time and release time), and the minimization of the sum of all response times. Altogether, we obtain nine theorems which nicely assess the impact of heterogeneity on on-line scheduling. These theoretical contributions are complemented on the practical side by the implementation of several heuristics on a small but fully heterogeneous MPI platform. Our (prelim-inary) results show the superiority of those heuristics which fully take into account the relative capacity of the communication links.