Mobile ad hoc computational Grids are characterized by unreliable and dynamic communication environment. The bandwidth at different network portions varies over the time and different nodes often experience different connection quality at the same time due to traffic load and constrained communication environment. Therefore, an effective and robust resource allocation scheme should consider connection quality between nodes in addition to other factors such as transmission power, processing speed and task size. In this paper, two resource allocation schemes are described with their pros and cons. The first resource scheme exploits transmission power control mechanism in order to improve energy efficiency and network capacity whereas the second resource allocation scheme takes into account the connection quality and traffic load in order to reduce data transfer time. The relationship between data transfer time and transmission energy consumption has also been investigated in detail. The schemes are validated in a simulated environment using various workloads and parameters.