Strong tail optimality in the partial-information M/G/1 (nonpreemptive)

Determine whether, in an M/G/1 queue with a light‑tailed job size distribution and only label information available to the scheduler (labels L with sizes S drawn from an arbitrary joint distribution), the quantity C* = liminf_{θ→γ} [(γ−θ)/γ] E[exp(θ T_{Cheat-Boost_θ})] equals the infimum tail constant over all nonpreemptive scheduling policies that observe only labels and arrival times; equivalently, ascertain whether the Boost_γ policy with boost function b_γ(l) = (1/γ) log( E[e^{γS}|L=l] / (E[e^{γS}|L=l]−1) achieves this optimal tail constant, where γ solves γ = λ(E[e^{γS}]−1) and Cheat-Boost_θ is the “cheating” Boost policy allowed to serve any job that will arrive in the current busy period.

Background

The paper proves strong tail optimality of Boost_γ in the full‑information M/G/1 and defines a lower bound C* via a liminf over θ approaching the decay rate γ using a cheating variant of Boost. In the partial‑information setting, labels are observed but exact sizes are unknown.

The authors show that Boost_γ’s tail constant equals C* in partial information but cannot conclude that C* is minimal among all nonpreemptive label‑only policies. They therefore explicitly conjecture that C* characterizes the optimal tail constant in this setting, which would imply Boost_γ’s optimality among such policies.