Fair Efficiency, or Low Average Delay without Starvation

File transfer, web download, and many other applications are primarily interested in minimal delay achievable for their messages. In this paper, we investigate allocating the bottleneck link capacity to transmit messages efficiently but fairly. While SRPT (Shortest Remaining Processing Time) is an optimally efficient algorithm that minimizes average delay of messages, large messages might starve under SRPT in heavy load conditions. PS (Processor Sharing) and ViFi (Virtual Finish Time First) are fair but yield higher average delays than under SRPT. We explore the class of fair algorithms further and prove that no online algorithm in this class is optimally efficient. Then, we derive a fair algorithm SFS (Shortest Fair Sojourn) and report extensive experimental evidence that SFS is consistently more efficient than PS and even ViFi during either temporal overload or steady-state operation, with largest benefits achieved when average load is around the bottleneck link capacity. Furthermore, average delay under the fair SFS remains close to the minimum attained under the unfair SRPT.