This paper analyses a multi-stage cyclic queueing system in which there are alternate service and transit Btagea. The service times are negative exponentially distributed, but it is shown that the transit time distributions may be any of a whole range of types, from constant to negative exponential. It is also shown that the production rate of the system does not depend on the individual mean transit times, hut only on the sum of these mean transit times. An explicit expression for the average production rate is derived and used in two examples, (i) a two-stage earthmoving project, and (ii) a four-stage asphalt paving project, to obtain regions of optimal haul fleet size, in the parameter space, so as to minimize the cost of the system.