Might Randomization in Queue Discipline Be Useful When Waiting Cost is a Concave Function of Waiting Time?

This paper raises the question of whether some degree of randomization in queue discipline might be welfare enhancing in certain queues for which the cost of waiting is a concave function of waiting time, so that increased variability in waiting times may be good not bad for aggregate customer welfare. Such concavity may occur if the costs of waiting asymptotically approach some maximum (e.g., for patients seeking organ transplants who will not live beyond a certain threshold time) or if the customer incurs a fixed cost if there is any wait at all (e.g., for knowledge workers seeking a service or piece of information that is required to proceed with their current task, so any delay forces them to incur the “set up charge” associated with switching tasks).