Might randomization in queue discipline be useful when waiting cost is a concave function of waiting time?
This paper suggests that introducing randomization in queue discipline might be welfare enhancing in certain queues for which the cost of waiting is a concave function of waiting time. Concavity can make increased variability in waiting times good not bad for aggregate customer welfare. Such concavity may occur if the costs of waiting asymptotically approach some maximum or if the customer incurs a fixed cost if there is any wait at all. As examples, cost might asymptotically approach a maximum for patients seeking organ transplants who will not live beyond a certain threshold time, and fixed costs could pertain for knowledge workers seeking a piece of information that is required to proceed with their current task, so any delay creates a "set up charge" associated with switching tasks.
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