In this paper, we integrate a grid system and a wireless network to present a convenient computational service system, called the Semi-Preemptive Computational Service system (SePCS for short), which provides users with a wireless access environment and through which a user can share his/her resources with others. In the SePCS, each node is dynamically given a score based on its CPU level, available memory size, current length of waiting queue, CPU utilization and bandwidth. With the scores, resource nodes are classified into three levels. User requests based on their time constraints are also classified into three types. Resources of higher levels are allocated to more tightly constrained requests so as to increase the total performance of the system. To achieve this, a resource broker with the Semi-Preemptive Algorithm (SPA) is also proposed. When the resource broker cannot find suitable resources for the requests of higher type, it preempts the resource that is now executing a lower type request so that the request of higher type can be executed immediately. The SePCS can be applied to a Vehicular Ad Hoc Network (VANET), users of which can then exploit the convenient mobile network services and the wireless distributed computing. As
a result, the performance of the system is higher than that of the tested schemes.