Resource Planning Under Hypercube Queuing Equilibrium With Server Disruptions and Cooperative Dispatches

This paper proposes a reliable hypercube queuing problem where servers (e.g., vehicles) can be dispatched either individually or jointly as cooperative units, and these servers are subjected to probabilistic disruptions. The probability of a server disruption depends on the amount of resources (e.g., firefighter staffing number) allocated to this server. If any server in a cooperation unit is disrupted, a less preferred (e.g., based on capabilities and source station) but functioning and available unit will be dispatched instead. This paper derives formulas for steady-state system performance metrics for this new hypercube queuing system. The queuing model is embedded into a mixed-integer non-linear program to optimize the allocation of resources so as to minimize the total costs under server disruptions. An empirical case study is used to compare the system performance measures under a range of implementation scenarios, and sensitivity analyses are conducted to reveal insights.