Priority doesn't remove waiting from a system — it reallocates it between classes of people, and what that reallocation does depends on facts a published policy rarely tells you.
Imagine a supermarket with an ordinary checkout and an express lane for customers with only a few items. This is a hypothetical, not a documented case — but it’s a familiar enough shape to think with. Nobody in the ordinary line breaks a rule. The store simply decides, in advance, that people needing less checkout time will wait less. The person still standing in the ordinary line doesn’t get any of their time back — someone else’s wait gets shorter, while theirs stays the same or grows relative to what it would have been in a single shared line.
That’s what a priority rule actually is: not a feature added on top of a queue, but a decision about whose waiting a system will reduce, and whose it won’t. Last week asked whether you could verify a queue’s rule at all. This week keeps the rule fully visible and asks a different question: once a system has decided to treat two classes differently, what does that decision change about who gets served sooner, and who is left under the ordinary rule regardless?
A formal way of asking the same question#
A group of queueing researchers — Raz, Avi-Itzhak and Levy — built a precise, mathematical version of this question (Raz, Avi-Itzhak & Levy, 2004; detailed claims below are drawn from the fuller technical report underlying that extended abstract). They start from a simple baseline: at any moment, everyone currently waiting could be said to deserve an equal share of whatever service capacity the system is granting right then. How far a customer’s actual treatment departs from that equal share, added up over their time in the system, is what they call discrimination — their technical term, meaning only “distance from an equal share,” not anything about identity or bias.
Applying this baseline to an ordinary first-come-first-served system, they find that customers needing more service are already structurally worse off relative to it, even with no priority rule at all. Giving shorter-service customers priority — like the express lane — can improve this formal fairness measure. But it doesn’t always: their own result is conditional on how different the two classes’ typical service needs actually are. Below a certain point, giving one class priority can make the measure worse, not better.
Two things follow, and both matter more than any equation. First, this measure describes an allocation, not a feeling — it says nothing about whether the person still in the ordinary line notices, minds, or resents the difference. Second, whether priority even helps by this measure depends on facts — how much service time each class typically needs — that a policy posted on a sign essentially never tells you. You can read “5 items or fewer.” You cannot read off whether the underlying numbers make that rule formally favourable.
Where Maister fits, and where it doesn’t#
That’s exactly the gap Maister’s older, unproven idea sits in, deliberately unmerged with Raz et al.’s result rather than folded into it: Maister proposed that waits people read as inequitable are experienced as worse than waits they read as equitable, regardless of length. Nobody has tested this the way Raz et al. tested their formal claim — it’s a practitioner’s proposition, not evidence. But it names what the fairness measure can’t: what redistributing waiting might mean to the person who didn’t get the shorter version of it. Two separate, honest answers to two different questions, not one strengthened by two citations.
What this doesn’t establish#
Raz et al. show that the redistribution itself is a structural consequence of priority rules; that is a different claim from how the resulting wait is experienced. Their result comes from a mathematical model with its own assumptions, not from an observed system, and it holds only under specific conditions on the classes’ service-time difference — not universally. Maister’s proposition, meanwhile, has not been tested here or anywhere in this course’s sources; it’s included as a named framework, not as confirmation of anything Raz et al. calculated.
Why this matters#
Waiting is an experience, not merely a duration — and priority is one of the clearest ways a system can make two people’s experience of “the same queue” diverge on purpose. Raz et al. show that divergence has a real, structural shape, describable before anyone’s feelings even enter the picture. Maister is the reminder that the structural fact and the felt one are not the same claim, and this course won’t treat one as proof of the other.
Once you can see how a system distributes the right to wait less, the next question is what it’s trading for that. That’s next week.
Teaching team
- Marisol Quaye — convenor