Everyday Queueing #3: Why Airplane Boarding Feels So Inefficient

I used to pay little attention on boarding at the airport because of my elite status with various airlines. But retirement has kept me grounded and almost swiped my record clean in recent years. Recent trips, including one to Colombia with an infamous American airline, had me thinking more about the science behind plane boarding.  

Anyone who has boarded an airplane enough times has likely experienced the strange choreography that unfolds before takeoff. Passengers stand up almost immediately when boarding begins, lines begin forming long before their assigned group is called, and eventually a slow procession starts moving toward the aircraft. For a few moments the line appears to flow smoothly. Then everything stops. Someone is lifting luggage into an overhead compartment. Another passenger realizes they are seated twenty rows further back. A family begins negotiating seating arrangements while the rest of the line quietly waits. Movement resumes briefly before another interruption appears several rows ahead.

The experience often feels surprisingly inefficient. Modern airlines optimize routes across continents, calculate fuel consumption with extraordinary precision, and coordinate flights involving thousands of moving parts. Yet boarding an aircraft sometimes feels less like an engineering process and more like an elaborate experiment in organized congestion.

Readers of Everyday Queueing may recognize a familiar pattern here. In earlier articles, we saw how similar dynamics appear in both supermarket checkout lines and traffic systems. In Why the Shortest Checkout Line Is Sometimes the Wrong Choice, we saw that visible structure often hides the true driver of waiting time, which is not queue length but stochastic service rates and utilization. In Why the Fastest Lane Often Becomes the Slowest, we saw how feedback effects in traffic systems cause perceived advantages to disappear once enough participants respond to them. Airplane boarding behaves according to the same underlying principle: what looks like a simple line is actually a system with interacting constraints.

At first glance, boarding appears straightforward. Passengers arrive, enter the aircraft, locate seats, and sit down. One might naturally assume that efficiency depends mainly on processing people quickly. However, queueing systems involving physical movement often behave differently because movement itself introduces interference.

Unlike a supermarket checkout line where customers simply wait their turn, passengers boarding an aircraft interact continuously with one another. Every passenger occupies space, competes for overhead storage, and temporarily blocks movement behind them. The result is a queue with dependencies. One person's delay does not remain isolated; it propagates through the system.

Queueing theorists often model such systems using service times and blocking effects. If $S_i$ represents the time passenger $i$ requires to reach their seat and settle in, and $B_i$ represents additional delays caused by aisle interference, then total boarding time can be approximated as:

$$T=\sum S_i+\sum B_i$$

The first term represents ordinary service time. The second term represents interference created by interactions among passengers.

This distinction turns out to matter enormously. Airlines frequently attempt to improve efficiency through boarding groups: rows 1–10 first, then rows 11–20, and so on. Some airlines board from the back of the plane first to avoid blockades at the front of the plane -- so as to delay the delay. The logic seems intuitive because order feels efficient. However, mathematical simulations suggest something unexpected. Strict ordering can sometimes create more congestion rather than less.

Suppose several passengers assigned to neighboring rows board together. They all arrive at approximately the same location simultaneously and attempt to place luggage overhead. Suddenly, a localized bottleneck forms. Since aircraft aisles function essentially as single-lane channels, movement behind the bottleneck immediately stops.

Researchers studying boarding processes have modeled passengers using stochastic agent-based simulations. Rather than treating people as identical particles, these models assign probabilities to walking speed, luggage loading time, seat location, and behavioral variation. Surprisingly, some simulations found that randomized boarding strategies occasionally outperform carefully structured boarding zones.

This result initially feels counterintuitive. We tend to associate greater organization with greater efficiency. Yet queueing systems repeatedly demonstrate that order alone is not sufficient. What matters is reducing interference between interacting components.

This idea may sound familiar because it mirrors what we saw in both supermarket checkout lines and traffic flow systems. In checkout lines, variability in service time dominates visible queue length. In traffic systems, small disturbances propagate backward as shockwaves. In boarding systems, spatial constraints transform small delays into cascading blockages. Across all three systems, the same mathematical structure appears in different forms.

The next time boarding pauses several rows ahead and the line mysteriously freezes, it may be worth remembering that the delay is not necessarily caused by poor planning or inconsiderate passengers. You may simply be witnessing another example of Everyday Queueing: a shared mathematical pattern that connects supermarkets, roads, and airplanes under one underlying framework of stochastic systems and interacting constraints.

- PTS