How does an IGMPv2 router recognize group membership on a local segment?

An IGMPv2 router recognizes group membership on a local segment primarily by maintaining a timer that tracks each group's membership and deletes memberships that timeout. This process is fundamental to managing multicast group membership efficiently.

In IGMPv2, hosts on a local network send Membership Reports to indicate their interest in receiving multicast traffic for specific groups. The router listens for these reports. If the router does not receive a Membership Report for a group within a specified time period (defined by the membership timeout), it assumes that no hosts want to receive the multicast traffic for that group anymore and removes that entry from its membership list. This timer mechanism helps ensure that group membership is current and reflects the active interest of hosts on the local segment.

When considering the other options, sending Query messages does play a role in prompting hosts to report their membership but is not the primary method for recognizing group membership changes. Maintaining fixed membership regardless of traffic does not accurately reflect the dynamic nature of IGMP, as it would not account for hosts joining or leaving groups. Finally, relying solely on Leave messages would neglect the necessary communication of hosts joining the group, which could lead to incomplete or outdated membership information.