This paper introduces and compares different schemes for assignment of replicated services in Jini -- an object-oriented middleware architecture for network-centric computing. Each client in Jini has to be assigned a service selected from the pool of available services, which have joined the Jini federation and registered with the lookup service. Both early and delayed assignments are considered as basic options in our evaluation. The information for the system load can be collected at four different levels of detail in order to be used in the process of assignment decisions. In our analysis, we concentrate on the scenario where the requests for service generated by the clients follow independent user-initiated or machine-initiated transactions. The performance evaluation of the assignment schemes follows the queuing systems methodology. The comparisons are done with regard to the mean residence time of the clients in the system as well as the control overhead imposed by the assignment schemes. A case study of the scheme using the lowest information level proves the effectiveness, applicability and limitations of the delayed assignment in comparison to the early one. These results are a first step towards developing a methodology for building large-scale applications for Jini-based distributed systems.