The Grid is a promising technology for providing access to distributed high-end computational capabilities. Thus, com- putational tasks can be performed spontaneously by other resources in the Grid that are not under the user’s control. How- ever, one of the key problems in the Grid is deciding which jobs are to be allocated to which resources at what time. In this context, the use of market mechanisms for scheduling and allocating Grid resources is a promising approach toward solv- ing these problems. This paper proposes an auction mechanism for allocating and scheduling computer resources such as processors or storage space which have multiple quality attributes. The mechanism is evaluated according to ...