The (relative) cost of the customer’s waiting time has long been used as a key parameter in queuing models, but it can be difficult to estimate. A recent study introduced a new queue characteristic, the value of the customer’s waiting time, which measures how an increase in the total customer waiting time reduces the servers’ idle time. This paper connects and contrasts these two fundamental concepts in the queuing literature. In particular, we show that the value can be equal to the cost of waiting when the queue is operated at optimal. In this case, we can use the observed queue length to compute the value of waiting, which helps infer the cost of waiting. Nevertheless, these two measures have very different economic interpretations, and in general, they are not equal. For nonoptimal queues, comparing the value with the cost helps shed light on the underlying causes of the customer’s waiting. Although it is tempting to conclude that customers in a queue with a lower value of waiting expect to wait longer, we find that the value of waiting in general does not have a monotonic relationship with the expected waiting time, nor with the expected queue length.
Decomposition of M/M/1 With Unreliable Service and a Working Vacation