It is expected that future wireless systems will consist of several distinct radio access technologies (including WCDMA/HSDPA, GSM/EDGE/GPRS, WLAN and others) forming a multi-access system that offers advanced voice and multimedia services. Previous works have shown that the combined capacity region of such systems depend on the service allocation policy that assigns user sessions to the available subsystems. The currently available service allocation policies typically operate off-line implying that the actual service mix is assumed to be known prior to the service allocation taking place. In this paper we consider the on-line problem according to which sessions arrive one after the other and no assumptions on the service mix can be made. We adopt four on-line bin-packing algorithms to the multi-access environment and study their performance by means of simulation in terms of the class-wise blocking probability and throughput. We find that the algorithm termed LessVoice provides the best performance in terms of the blocking probabilities and imposes the least slow down for elastic sessions.