Finite queues in parallel under a generalized channel selection rule

Consider a queueing system of the following type: random arrivals enter the system, where they are assigned to one of r service channels. Each arrival is then serviced and discharged from the system. The classical results for this class of problems are based upon systems where customers join a single queue and then are randomly assigned to an available server from this queue. (See, for instance, Takács (1962).)