Who invented queueing?

The concept of waiting for service is so fundamentally woven into the fabric of modern life—from the grocery checkout line to logging into a popular website—that asking who invented it feels almost like asking who invented breathing. Waiting, in its most basic form, is ancient; whenever resources were scarce or access was limited, people had to wait their turn. ^[4][8] However, the transition from a chaotic, potentially violent scrum for a limited resource to the structured, orderly line we recognize today is a more recent development, one heavily influenced by social norms, architecture, and eventually, advanced mathematics. ^[5][7]

# Ancient Practices

Long before Sir Thomas Beecham declared that "the English are the only nation in the world that treats waiting as a pleasure," people were organizing themselves to receive goods or access services. ^[5] Historical accounts suggest that queues, or at least the concept of waiting in sequence, existed in various ancient and historical contexts, often driven by religious or civic necessity. For instance, access to certain holy sites or public amenities would naturally lead to some form of sequencing, even if it lacked the rigid rules of a modern line. ^[4][8] In early marketplaces or at public water sources, while a formal queue might not have been enforced by law, the more patient or physically imposing individuals often established a de facto order of service. ^[4] The need for an orderly approach arose when the stakes of not waiting got too high, or when the physical space itself demanded a linear progression, such as passing through a narrow gate or presenting goods to an official. ^[5]

# Organizing Space

The move toward the recognizable, single-file line seems to be less about a single inventor and more about social evolution and architectural constraint. The rise of large-scale retail and public services in the 18th and 19th centuries necessitated a more efficient and less conflict-ridden method of handling customer flow than sheer brute force or random opportunity. ^[5][7] As societies urbanized and people began interacting more frequently in dense public settings, the negative externalities of disorganized waiting—wasted time, public disorder, and potential injury—became too costly to ignore. ^[4] The shift to orderly queuing often coincided with developing civic infrastructure and a cultural move toward valuing individual fairness over pure dominance in access. ^[5] It is fascinating to consider that while the ancient world certainly saw people waiting in proximity, the social contract to wait in a specific, non-random sequence, often marked by physical barriers or defined pathways, appears to solidify much later, perhaps only truly embedding itself in Western culture around the time of the Industrial Revolution's later stages. ^[4][5]

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# Mathematical Foundations

While the physical act of queuing evolved organically, the science of understanding and predicting the behavior of those lines—Queueing Theory—has a very specific and traceable origin point tied to technological advancement at the turn of the 20th century. ^[3][9] The true "inventor" of queueing analysis is widely recognized as the Danish engineer Agner Krarup Erlang. ^[1][3] Erlang was not contemplating how to keep people calm in a post office line; his work was rooted in the practical needs of telecommunications engineering. ^[1][9]

Erlang was employed by the Copenhagen Telephone Company, and his initial task was to solve problems related to the efficiency and capacity of telephone exchange systems. ^[1][3] He needed to determine how many operators were required to handle the incoming call volume so that customers would experience an acceptable amount of waiting time, or, conversely, how much waiting time was inevitable given a certain number of staff. ^[1][9] His early work, dating back to around 1909, established the mathematical frameworks necessary to model service systems where random arrivals meet finite service capacity. ^[3] This mathematical modeling, which treats arrivals as random variables and service times as stochastic processes, formed the bedrock of the entire field of Operations Research (O.R.) as it relates to waiting lines. ^[3][9]

# Developing Models

Erlang’s initial findings were foundational, but the theory quickly expanded beyond simple telephony. ^[3] His early models, often involving the exponential distribution for arrival and service times, provided the first quantitative tools to analyze these systems. ^[9] For general readers, it is helpful to see the conceptual evolution: Erlang provided the initial link between arrival rate and service rate. ^[1][9] Subsequent researchers, building on Erlang’s work, developed more complex models to represent diverse real-world scenarios, such as multiple servers (like several checkout lanes) or queues where customers might abandon the line if waiting too long (balking or reneging). ^[3]

The formal notation used today, often referred to as Kendall's notation (e.g., M/M/1, M/M/c), categorizes these systems based on the distribution of arrivals, the distribution of service times, and the number of servers. ^[9] This formalization allowed engineers and managers to move from educated guesses to scientifically grounded predictions about performance metrics like average wait time or server utilization. ^[9] It’s interesting to observe the contrast here: the physical act of queuing was a social necessity solved by cultural adaptation over centuries, whereas the predictability of queuing was a mathematical invention required for the efficiency of new technologies like the telephone network. ^[1][3]

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# Digital Delays

The principles established by Erlang remain relevant, but the digital age has introduced complexities that challenge the neatness of classical queueing models. ^[2] In a physical queue, the line itself is a visible, tangible representation of the wait, which manages expectations to a degree, even if poorly designed. ^[7] However, online queuing systems, such as those used for virtual ticket sales or high-demand digital service rollouts, often operate differently. ^[2]

Traditional queue theory often assumes a known population and predictable physical space. ^[2] Online systems, however, can experience massive, unpredictable surges from a global user base—a situation far exceeding the typical scope Erlang modeled with local telephone traffic. ^[2] Furthermore, when a digital queue breaks down, the user experience is often worse than a physical one. In a physical line, a person is doing something—perhaps window shopping or talking to another person. ^[7] In a digital queue, users are often stuck staring at a static loading screen, leading to higher frustration and abandonment rates. ^[2] This highlights a divergence: the mathematical invention excels at optimizing throughput when the system is functioning as designed, but it struggles with the psychological impact of waiting in a purely abstract, non-corporeal space. ^[2][7]

# Designing Experience

Because the purely mathematical model sometimes fails to capture the human element of waiting, there has been a parallel evolution in the design of waiting environments. ^[7] This goes beyond simply forming an orderly line. ^[5] Modern designers, whether creating physical airport security checkpoints or digital interfaces, recognize that the perception of time is as important as the actual elapsed time. ^[7]

In physical spaces, this means incorporating elements that distract or engage the waiting customer—music, art, or interesting retail displays—effectively making the wait feel shorter or more valuable. ^[7] The invention of the queue, in its final form, is therefore a negotiation between efficiency and psychology. While Erlang provided the efficiency blueprint for the server, architects and UX designers now work to manage the customer's subjective experience of being on the waiting list, treating the waiting area itself as a temporary environment. ^[7] Thinking about this from a management perspective, an organization that focuses only on reducing the average wait time using Erlang’s formulas might still see high customer dissatisfaction if the waiting environment is stressful or boring. A truly successful system balances high throughput (the math) with low perceived friction (the design). ^[2][7] The ancient need for order and the modern need for engagement are now married in the successful management of any queuing system, digital or physical.

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# The Dual Invention

Ultimately, the question of who invented queueing has two very different answers. The practice of forming an orderly line is a gradual social and architectural invention, born from the necessity of managing public interaction in increasingly dense societies, replacing chaos with simple, sequential fairness. ^[4][5] This was an organic solution to a social problem.

The science of queueing, however, has a singular, brilliant inventor: Agner Krarup Erlang, who mathematically modeled the stochastic processes of waiting to make essential infrastructure like telephone networks functional. ^[1][3] His work provided the quantitative tools that allowed for engineering efficiency in service systems. ^[9] Modern challenges, particularly in the digital realm, continue to test the limits of Erlang’s initial insights, forcing new considerations about user psychology and system robustness when dealing with massive, instantaneous demand spikes. ^[2] The history of the queue is thus a layered story: first, the human instinct to line up; second, the social agreement to respect that line; and finally, the mathematical genius required to predict and manage that line at scale. ^[1][5][9]