Abstract: A system and a method for allocating limited resources to agents that reveal their stochastic demands on arrival over a finite horizon in a proportionally fair manner that exhausts available resource budgets are provided. The method includes: receiving, from an entity, a request for a resource for which a predetermined maximum amount of the resource is available for allocation; estimating a number of future requests and amounts of the resource to be requested within a predetermined time interval; adjusting a result of the estimating by calculating a standard deviation of an uncertainty of at least one future request; and determining, based on the estimates and the adjustment, an amount of the resource to allocated to the entity by applying an algorithm with respect to the adjusted estimates and the predetermined maximum available amount of the resources.

Abstract: A method for preserving privacy with respect to modeling event sequence data is provided. The method includes: receiving information about a sequence of events; modeling the event sequence by a Hawkes process that has an intensity that includes an exogenous base intensity rate and an indigenous component that has an excitation rate and a decay rate; analyzing the received information; and determining estimated values of the exogenous base intensity rate and the excitation rate, such that an accuracy of the estimates corresponds to a length of time over which the sequence of events is observed. Differential privacy is introduced by adding noise to the sequence of events in order to preserve the privacy of individuals associated with the events, and a cost of the differential privacy is expressible as an additional length of observation time required to ensure the accuracy of the estimates.