Adding servers to reinforce facilities in a spatially distributed queueing system

Abstract

We study the problem of adding servers to reinforce functioning facilities modeled as spatially distributed $M/M/c$ type queuing systems. We consider two modes, stationary and interactive. The stationary mode is for a situation in which adding new servers to functioning facilities does not change the demand distribution (e.g., hospital care or vehicle inspection). The interactive mode is for a situation in which adding servers will likely change the demand distribution (e.g., gas stations, electric vehicle charging stations). Here we use the gravity rule to model demand adjustment. A case study is presented based on allocation of gas servers to existing gas stations in an hurricane evacuation event. Managerial insights are provided based on sensitivity analysis.