Test-case prioritization is a typical scenario of regression testing, which plays an important role in software maintenance. With the popularity of Web Services, integrating Web Services to build service-centric systems (SCSs) has attracted attention of many researchers and practitioners. During regression testing, as SCSs may use up constituent Web Services' request quotas (e.g., the upper limit of the number of requests that a user can send to a Web Service during a certain time range), the quota constraint may delay fault exposure and the subsequent debugging. In this paper, we investigate quota-constrained test-case prioritization for SCSs, and propose quota-constrained strategies to maximize testing requirement coverage. We divide the testing time into time slots, and iteratively select and prioritize test cases for each time slot using Integer Linear Programming (ILP). We performed an experimental study on our strategies together with three other strategies, and the results show that with the constraint of request quotas, our strategies can schedule test cases for execution in an order with higher effectiveness in exposing faults and achieving total and additional branch coverage.