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Two of the most popular approximations for the distribution of the steady-state waiting time, W_∞, of the M/G/1 queue are the so-called heavy-traffic approximation and heavy-tailed asymptotic, respectively. If the traffic intensity, ρ, is close to 1 and the processing times have finite variance, the heavy-traffic approximation states that the distribution of W_∞ is roughly exponential at scale O((1-ρ)^-1), while the heavy tailed asymptotic describes power law decay in the tail of thedoi:10.1214/10-aap707 fatcat:qziwliqzo5gffijt2rjjnx36gu