AbstractThe queue network studied consists ofninfinite queues in parallel served by independent servers and by other servers all linked to form a hierarchical structure. The total service a unit receives depends partially on other units in service. We call this type of servicing partially shared servicing. All interarrival times as well as service times are assumed exponentially distributed. The characteristic of interest is the traffic intensity of the infinite queues. Some simple formulae are obtained. An application to modelling a disc I/O system is described. The model turns out to be useful and accurate with wide applicability.