A method for mapping ready agents to incoming transactions has steps for (a) placing incoming transactions in a first queue managed by software executing from a machine-readable medium on a computerized appliance; (b) issuing a determined number of invitations in a period of time to agents known to be available to consider an invitation to interact with an incoming transaction; (c) placing identification of ready agents, who have accepted an invitation to interact, in a second queue managed by the software; (d) mapping transactions from the first queue to agents from the second queue; (e) monitoring changes in state of both the first and the second queues in the time period; and (f) adjusting determined number of invitations in step (b) in a manner to drive a chosen system performance metric toward a desired target value.