When testing large-scale systems with hundreds of test cases in continuous integration, it is crucial to minimize the round-trip time, that is, the time from when a source code change is committed until the test results are reported back to the developer. To this end, scheduling as many test case executions as possible in the minimum amount of time is essential to increasing the effectiveness of continuous integration. This paper introduces TSNIC, a time-aware method for test execution scheduling on multiple machines with constraints on accessible resources, such as measurement devices or network equipment. The method uses as input a test suite, a set of machines, and a set of shared resources and produces an execution schedule. The schedule guarantees that each test will be executed once and minimizes the round-trip time. TSNIC has undergone extensive experimental evaluation using generated test suites derived from existing industrial test suites augmented with randomly-selected values. Our results provide evidence that TSNIC conducts effective test execution scheduling and is suitable for deployment in continuous integration. In particular, we show that automatic optimal scheduling of 500 test cases over 100 machines is reacheable in less than 4 minutes for 96.6% of the instances.