Planning for time-varying volunteer firefighter systems under probabilistic service disruptions

•A multi-period modeling approach for volunteer resources allocation optimizing is proposed to enhance the service reliability.•The geographical heterogeneity of units is captured by modeling hypercube equilibriums with co-existing career and reliable volunteer units.•The hypercube queuing equilibrium under various disruption scenarios is validated through simulations.•The applicability of the proposed model is tested over a case study of a real-world fire service system in China.•Various managerial insights that hold the promise to help develop policies and strategies in practice are revealed.