A queued task/queued resource state forecaster employs a binomial distribution fitter to fit a composite binomial distribution to operational data of a work management system, such as a call center. The fitter obtains arrival statistics for calls and agents in the call center, determines moments for the net calls in-queue from the obtained arrival statistics, determines parameters of binomial distributions that corresponds to the moments, and fits the determined moments to a linear combination of offset binomial distributions to obtain a composite binomial distribution. The composite binomial distribution is then evaluated by a scheduler which adjusts the operation of the call center accordingly. For example, a task scheduler evaluates the distribution to obtain a probability of an additional call being enqueued by the future point in time in order to determine whether an outbound call should be launched. Or, a resource scheduler evaluates the distribution to obtain an expected number of enqueued calls at some future point in time in order to determine whether another agent should be dispatched.