Realtime crowdsourcing with payment of idle workers in the Retainer Model

The realtime applications of crowdsourcing are a very promising topic, due to its high potentialities, for example in marketing, security or telecommunication applications. Realtime crowdsourcing ensures that solutions to a given problem are obtained in the shortest possible time using collective intelligence. In order to be ready to carry out any requested task in realtime, crowdworkers must be available at any time. Here we focus on the payment of crowdworkers and on the trade-off between the expected waiting time for a task to be carried out and the number of workers in the pool that should not become too large otherwise the total cost increases. In particular we consider the, so called, Retainer Model in which crowdworkers are paid in order to be ready to carry out any requested task in realtime. The Retainer Model considers an expected total cost which takes into account both the amount paid to a crowdworker to be in idle-state and the loss when the task is not completed in realtime. After checking the existence of a minimum cost we characterize the optimal number of crowdworkers, and suggest a practical and quick way to obtain it. Moreover, we analyse the sensitivity of the optimal number of crowdworkers with respect to different task intensities