1. A method, in a workload manager, for distributing workload items to a plurality of dispatchers, each dispatcher being associated with a different computing system of a plurality of computing systems, the workload items comprising workload items of a plurality of different workload types, the method performed by the workload manager comprising: obtaining a capacity value for a combination of a given workload type and a given computing system in the plurality of computing systems, the capacity value representing a total capacity of workload items of the given workload type that the given computing system may process in a given time period; obtaining for the combination of the given workload type and the given computing system, a queue length of a given dispatcher associated with the given computing system; calculating, for the combination of the given workload type and the given computing system, a relative share of incoming workloads based on the queue length for the given dispatcher and the capacity value associated with the given workload type and the given computing system; and routing incoming workload items to the given dispatcher based on the calculated relative share for the given dispatcher.