Decentralized Vehicle Routing in a Stochastic and Dynamic Environment with Customer Impatience

Consider the following scenario: a spatio-temporal stochastic process generates service requests, localized at points in a bounded region on the plane; these service requests are fulfilled when one of a team of mobile agents visits the location of the request. For example, a service request may represent the detection of an event in a sensor network application, which needs to be investigated on site. Once a service request has been generated, it remains active for an amount of time which is itself a random variable, and then expires. The problem we investigate is the following: what is the minimum number of mobile agents needed to ensure that each service request is fulfilled before expiring, with probability at least 1 − ε? What strategy should they use to ensure this objective is attained? Formulating the probability of successfully servicing requests before expiration as a performance metric, we derive bounds on the minimum number of agents required to ensure a given performance level, and present decentralized motion coordination algorithms that approximate the optimal strategy.