Allocation Processes with Variable Channel Queues

A dynamic model is formulated for determining optimum operating policies in a variable channel queuing situation. Such policies are required when workers must be allocated to one of several jobs which have associated with them different waiting costs. In this model, two such jobs are considered: (a) a "queue job" i.e., serving customers in a queue, and (b) performing another task which does not involve waiting customers (called "fixed work"). The criterion of the model is a minimization of the sum of these costs: the cost of customer waiting, the cost of fixed work, and the cost of changing tasks. Decision rules involving the assignment of workers depended upon the number of waiting customers, the anticipated arrival pattern, and the amount of uncompleted fixed work remaining. The model was run using arrival and service data obtained from a medium sized suburban bank together with implicitly derived cost data.