The paper examines the influence of heterogeneous behaviour on the output of finite source queues. Specifically general procedures are established for deterministic assumptions which by analogy with the homogeneous case should provide an upper bound on queue output. Consideration of priority treatment of customers arises when customers present themselves for service simultaneously. Different priority and heterogeneity assumptions result in different output and suggest an optimization of queue behaviour. The results are applied to earthmoving-type operations employing loading equipment (as servers) and hauling equipment (as customers'). Such operations are characteristically heterogeneous and also finite source; their treatment to date has been through approximations and the solution of the homogeneous case.