Mechanism Design for Queueing with Capacity-Constrained Shifts

We study a single-server queue with fixed-length shifts $T > 1$ where service of unit length jobs is non-pre-emptive; residual time shorter than one job, namely fractional part of $T$, at boundaries is lost. Agents have constant private unit waiting costs. The efficient rule partitions agents into feasible shifts, orders shifts by the sum of members' costs, and orders agents within each shift by their costs. We show, by \citet{Holmstrom} and \citet{Suijs} type arguments, that only Vickrey-Clarke-Groves (VCG) transfers implement efficiency in dominant strategies. We then delineate when efficiency and DSIC implementation can be combined with budget balance (first-best mechanisms). If shifts are of unit-capacity ($1 2$ is non-integral (so each shift can host at least two agents but leaves residual slack), no first-best mechanism exists. The proof uses a the cubical-array lemma of \citet{Walker} adapted to our setting.