The sizes of Internet objects are known to be highly varying. We evaluate an M/G/1 queue under foreground background N (FBN ) scheduling policy for job size distributions with varying coefficient of variability (CoV) to analyze the impact of variability of job sizes to the performance of the policy. We find that FBN is very efficient in reducing the response time and minimizing the number of jobs that are penalized (i.e., have a higher response time under FBN than under processor sharing (PS)) when job sizes have a high CoV. We also propose and analyze variants of FBN called fixed priority FBN (FP \Gamma FBN ) and differential FBN (DF \Gamma FBN ), which introduce service differentiation by classifying jobs into high priority and low priority and then servicing the high priority before low priority jobs in an FBN related order. The numerical analysis conducted for highly varying job sizes reveals that FP \Gamma FBN achieves a perfect service differentiation at the expense of a high penalty for the low priority small jobs. While DF \Gamma FBN offers acceptable service differentiation, it does not penalize small jobs with low priority at all. Moreover, FP \Gamma FBN and DF \Gamma FBN can guarantee the service of high priority jobs even under overload.