Recent computing applications such as videoconferencing and grid computing run their tasks on distributed computing resources connected through networks. For such applications, knowledge of the network status such as delay, jitter, and available bandwidth can help them select proper network resources to meet the Quality-of-Service (QoS) requirements. Also, the applications can dynamically change the resource selection if the current selection is found to experience poor performance. For such purposes, Internet Service Providers (ISPs) have started to instrument their networks with Network Measurement Infrastructures (NMIs) that run active measurement tasks periodically and/or on demand. However, one problem that most network engineers have overlooked is the measurement conflict problem, which happens when multiple active measurement tasks inject probing packets into the same network segment at the same time, resulting in misleading reports of network performance due to their combined effects. This paper proposes enhanced Earliest Deadline First (EDF) algorithms that allow "Concurrent Executions" to orchestrate offline/online measurement jobs in a conflict-free manner. The simulation study shows that our measurement scheduling mechanism can improve the schedulable utilization of offline measurement tasks up to 300 percent and the response time of on-demand jobs up to 50 percent. Further, we implement and deploy our scheduling mechanism in a real working NMI for monitoring the Internet2 Abilene network. As a case study, we show the utility of our algorithms in the widely used Network Weather Service (NWS).