The limit of load balancing due to decreasingly available bandwidth is studied. In the computer simulation, the bandwidth of the communication link is translated into 1.) the transfer delay associated with relocating a job and 2.) the uncertainty of the remote queuing status, due to the combined effects of the system dynamics and the non-zero time required in probing the status of the remote stations. The computer simulation is based on a sender-initiated load balancing scheme and is tested for a number of decision thresholds. Among these, an adaptive threshold that is a function of the traffic pattern and the system capability, "balances" the load best; it may not always minimize the average delay, but it always keeps the service stations (or nodes, or processors) similarly loaded. Results are obtained for both stationary and bursty traffics, and for both fixed-length and exponential-length jobs. For all the loading ratios tested, the balancing scheme is capable of improving the system performance over that of the no-balancing cases, when the transfer delay is less than 10 ms. For greater transfer delays, the improvement may drop to negative values.