Transient staffing at the beginning of work

Production and service systems often rely on stationary queueing formulas to determine the number of agents that need to be scheduled. However, this results in over-staffing decisions when the system starts empty. To address this issue, we propose a solution called transient staffing, which involves providing appointment times for agents to ensure that the expected queue length remains below a certain threshold. We model the system as a transient Erlang-A queue. To compute the appointment times, we employ a uniformized approximation that discretizes the elapsed time, which can be made as accurate as desired. We prove that the appointment times decrease with the arrival rate and traffic intensity, while increasing with the abandonment rate. Through numerical investigations, we find that adopting a transient staffing strategy leads to substantial cost savings, especially in scenarios where demand is high, customers are patient, traffic intensity is low, and the service level objective is intermediate. Furthermore, we use a fluid approximation to derive closed-form expressions for the agents' appointment times, and prove the impact of the system parameters. We show that this approximation performs well in predicting the first appointment times in contexts with high demand, low traffic intensity, and lax service level objective.