Optimal Routing Under Demand Surges: The Value of Future Arrival Rates

Motivated by the growing availability of advanced demand forecast tools, we study how to use future demand information in designing routing strategies in queueing systems under demand surges. We consider a parallel server system operating in a nonstationary environment with general time-varying arrival rates. Servers are cross-trained to help nonprimary customer classes during demand surges. However, such flexibility comes with various operational costs, such as a loss of efficiency and inconvenience in coordination. We characterize how to incorporate the future arrival information into the routing policy to balance the tradeoff between various costs and quantify the benefit of doing so. Based on transient fluid control analysis, we develop a two-stage index-based look-ahead policy that explicitly takes the overflow costs and future arrival rates into account. The policy has an interpretable structure, is easy to implement and is adaptive when the future arrival information is inaccurate. In the special case of the N-model, we prove that this policy is asymptotically optimal even in the presence of certain prediction errors in the demand forecast. We substantiate our theoretical analysis with extensive numerical experiments, showing that our policy achieves superior performance compared with other benchmark policies (i) in complicated parallel server systems and (ii) when the demand forecast is imperfect with various forms of prediction errors.