Econometrica: May 1972, Volume 40, Issue 3

Individual and Social Optimization in a Multiserver Queue with a General Cost-Benefit Structure

https://doi.org/0012-9682(197205)40:3<515:IASOIA>2.0.CO;2-G
p. 515-528

Niels Chr. Knudsen

This paper considers an M/M/s queuing model in which customers who arrive when k customers are present in the queuing system obtain a net benefit of a?k. The a?-sequence is assumed to be a decreasing one. If it is left to the individual customer to decide whether to join the queue or not, he will balk whenever the queue length is greater than some number, say n1. It is shown that if a balking level n2 < n1 is enforced, then the customers as a group can generally expect a larger net benefit per time unit than when the balking level n1 is applied. One way to ensure social optimality is to impose a toll on the customers who join the queue. In the discussion of a possible economic interpretation of the model we point out the similarities between such a toll and a shadow price in a more conventional optimization model. It is also demonstrated that in a stochastic optimization model capacity utilization is not a sufficient price criterion.

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