Method for managing connections on a connection-oriented network such as an ATM network, for use with devices communicating according to a connectionless communication protocol such as IP over Ethernet. Roughly described, a bridging network element (BNE) resides at the ATM point-of-presence through which a data network accesses the ATM network. When the BNE receives an internet ARP (IARP) request from the data network for forwarding onto the ATM network, it forwards it instead to an IARP server. In addition to responding to the IARP request, the IARP server also regards the IARP request as a trigger, and in response thereto, causes the ATM network to establish a connection between the BNE point-of-presence and another point-of-presence on the ATM network through which the target address can be reached. Connection time-out periods are chosen to exceed or to be very likely to exceed the address resolution cache age-out periods on the client devices, thereby ensuring that after a connection timeout, the client device will or will be very likely to transmit another IARP request before it begins streaming transmission of more data packets onto the ATM network.