Queues with no-show customers

Excerpt

There are different ways of modeling appointments made for a service facility. One useful way is to view them as jobs in a queue. This may seem unnatural at first. After all, an appointment implies a commitment made by the service provider to serve a particular customer at some specific time in the future, and if service times are stochastic it is not possible to know, at the time of the “arrival of an appointment,” when exactly the service associated with that appointment will start. However, one can assume deterministic service times, in which case customers would be told exactly when their services will start at the time they make their appointments, or allow stochastic service times, but assume that customers somehow show up at their random appointment times (see, e.g., [1]). One particular approach would be by viewing the appointment queue as a time-slotted batch-service system where a single service period in the model corresponds to a predetermined time period, say a single day, during which multiple customers are served (see, e.g., [2]). For example, such a model would be a good fit for appointments made for a healthcare clinic, which has the capacity to see some fixed number of patients on each day. In this system, batch size would correspond to the daily capacity of the clinic and each service period would last exactly one day. In this model, patients can be told exactly which day their services would take place at the time they schedule their appointments (i.e., the appointment’s arrival at the queue). They could presumably be also told the time of their appointment since the queueing model does not need to capture the times of individual services within one service period. …