Why are there waiting lists?

A common complaint has to do with the delay in days, weeks or even months, to get an appointment with a primary physician, a specialist or a test. The problem is so widespread, that we may think that it's inevitable that it be so and that patients and providers have to live with it. However, it shouldn't be that way and the mathematical models and ways to programme services better do exist, to the extent of offering same-day access (also called open access) or at least a significant shortening of wait times to reasonable levels.

One of the reasons for long waiting lists, has to do with the reactive response to a long waiting list: the supply is gradually tweaked to catch up with demand, when counter-intuitively an apparently inverse approach would be best. There exist many mathematical models for waiting lists but one of the simplest may help understand why queues get longer and longer, in spite of efforts to the contrary. If we divide demand by supply, we obtain an index which is called saturation. The length of a waiting list (analogous to the number of automobiles waiting at a red traffic light) is calculated by (saturation squared)/(1-saturation). As saturation is a number between 0 (zero demand) and 1 (demand = supply) we can easily see that when we're close to full saturation (eg >0.9) the queue grows geometrically longer until it's infinite. In a nutshell: to maximise profit, it pays off to have a very long waiting list, as this assures coverage of future operating expenses, especially overhead.

In other words, to have a short waiting list and provide an excellent service, we need to supply services well in excess of the expected demand. For example, in primary care medicine, the daily demand for an appointment is less than 1% of the covered population. Therefore, if a physician has a defined population base of 1000 persons, the daily demand for appointments would average less than 10 (or 50 per workweek). A common temptation would be to have 10 slots per day, but as we have seen, this would result in a waiting list of several days. If 12 slots are offered, the queue would be a lot shorter: 1-2 days.

Therefore, long waiting lists are the result of 2 factors. Firstly, the population base may saturate or flood supply. Secondly, there exists a restrictive policy of supply, due to lack of time, personnel or costs. The result of this is work-related stress, pressures to overbook and labelling test requests as pseudo-urgent to queue-skip the waiting list and get an earlier slot. Most of the time, both factors are present to a great extent.

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