Accessibility, vulnerability, and resilience in a stochastic model of sustainable ecotourism

We show how the notions of accessibility, vulnerability, and resilience can be used to shed light on the sustainable management of a natural area that is used for ecotourism. To this end, we construct and analyze two queuing-theoretic models that approach the problem of sustainable management in different ways. In the first model, there is a capacity constraint on the number of ecotourists that are permitted to visit the natural area and the optimal rate at which an ecotourist agency manager provides service to the ecotourists is endogenously determined. In the second model, there is no capacity constraint but the manager endogenously ascertains the optimal number of ecotourists who are allowed into the natural area before he provides service to these ecotourists. The sustainability aspect of the management problem is addressed in two ways. First, the conceptualizations of accessibility, vulnerability, and resilience depend on certain long run metrics. Second, the objective functions in the two models that the manager optimizes are formulated using these long run metrics.