Which system is used to verify the operational state of a customer's modem?

The Dynamic Host Configuration Protocol (DHCP) is a network management protocol used to automatically assign IP addresses and other network configuration parameters to devices on a network. In the context of verifying the operational state of a customer's modem, DHCP plays a critical role. When a modem connects to a network, it typically requests an IP address from the DHCP server. The server's response indicates whether the modem is functioning properly and connected to the network, allowing it to communicate with the internet.

This capability of DHCP to provide real-time status about devices' connectivity makes it integral in confirming that modems are operational. If there are issues with the modem—like it being offline or unable to communicate with the DHCP server—it would suggest that the device is not functioning correctly or is not properly configured.

The other systems mentioned have different functions. The Balance Control System is more about managing network load, Automatic Configuration Protocol specifically assists devices in configuring their settings but is not primarily used for verifying operational states, and the Static Host Renewal System is less common and generally pertains to static IP assignments rather than verifying modem status. Therefore, DHCP is the most relevant choice for confirming a modem's operational state effectively.