AbstractThis paper studies a cyclic queueing problem arising in civil engineering earthmoving projects. There aremexcavators andntrucks which queue to be loaded by the excavators. The problem is therefore equivalent to a machine interference problem withmoperators andnmachines. The size of the haul fleet must be optimized, so as to minimize the cost per unit volume of earth moved. Graphs which show regions of optimalnin the parameter space are presented for the steady-stateD/D/1,M/D/1 andEk/M/1 models. The effect of operating theM/M/msystem in short work shifts, so that the initial conditions and transient behaviour are important, is then analysed and quantified as a correction to the optimal number of trucks in the haul fleet from the steady-state solution.