Cooperative Intelligent Transport Systems (C-ITS)make road traffic safer and more efficient, but require the mobilenetworks to handle time-critical applications. While some applicationsmay need new dedicated communications technologiessuch as IEEE 802.11p or 5G, other applications can use currentcellular networks. This study evaluates the performance that connectedvehicles can expect from existing networks, and estimatesthe potential gain of multi-access by simultaneously transmittingover several operators. We upload time-critical warning messagesfrom buses in Sweden, and characterise transaction times andnetwork availability. We conduct the experiments with differentprotocols: UDP, TCP, and HTTPS. Our results show that whenusing UDP, the median transaction time for sending a typicalwarning message is 135 ms. We also show that multi-access canbring this value down to 73 ms. For time-critical applicationsrequiring transaction times under 200 ms, multi-access canincrease availability of the network from to 57.4% to 92.0%.