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Due to the popularity of high-speed networks and advances in packaging and interface technologies, there has been significant efforts for providing high performance applications as network services that can be accessed remotely across the network, thus promoting sharing of both software and hardware. For high-demand network services, in particular, it will often be the case that the network services are installed at multiple sites so that each participating site can handle parts of client requests. We label such services as grid-enabled network services. In this paper, we present two adaptive site selection heuristics that do not depend on accurate predictions of completion times of service requests: weight queue length based heuristic and multi-level queue based selection.