Wireless distributed computing has several unique problems compared with currently well investigated wireless sensor networks. These problems include the impact of channel variation on power allocation, different traffic pattern with higher utilization, and more restricted delay constraints. This paper investigates the impact of communication channel condition on the average execution time of the computing task within wireless distributed computing networks (WDCN). It has been found that the delay performance of wireless distributed computing is influenced by both the average channel condition and the variation of channels. In addition, the impact of channel heterogeneity is also investigated to show the possibility of the optimal workload distribution for energy saving and robustness. Finally, a workload distribution approach combined with a power allocation scheme exploiting the spatial heterogeneity of the channel condition is proposed to balance energy efficiency and robustness.