On the Economics of Queuing and its Impact on Blockchain Technology
The act of queuing is a ubiquitous feature of modern life, and applies also to user’s interactions with blockchain networks. From the familiar wait for the cashier at the supermarket, a journey through rush-hour traffic or the submission of transactions to a blockchain, the feature that these situations have in common is that the flow of some objects, which could be people or information or energy, is limited by the maximum capacity of a channel. When this capacity is exceeded the traffic backs-up and slows down the objects progress.
In many cases, these queuing problems have economic elements that apply, for example, to how expensive it is to add new capacity or how costly it is for people to wait to reach the end of the queue. An example that can help us get a feel for the economics of these scenarios is to imagine a large city that decides to install public water fountains. To begin with, the city government decides that, since access to water is a human right, the fountain’s water must be freely-available. At first glance, this seems like a worthy goal and on the first morning of operation this policy might seem to work well, with water available to all citizens. Yet after several hours have passed, a queue of people has formed that continues to grow throughout the day.
As the queue increases in length, an increasing proportion of people that might wish to use the fountain instead choose not to join the queue. This arises from their perceived cost of waiting outweighing the benefit of obtaining water. This type of trade-off can be understood by a concept, developed by economists, known as utility. This involves aggregating the positive benefits and negative costs of an action to a common value that often has a monetary equivalent. In the water fountain example, people make the decision on whether to enter the queue on the basis of whether it benefits them or not. This corresponds to a utility that is either negative (costly) or positive (beneficial).
The utility value of an action can vary between people and for a single person at different times and under different conditions. Water is a good example of an essential resource that can have widely different utility values depending on its availability. The willingness of citizens to queue would, for example, be much higher if the fountains were the only source of drinking water. In rich countries, water is cheap and easily available but this often does not apply in poorer parts of the world. Different people will also assign different costs to waiting in the queue. Factors that contribute to these differences include income and a person’s situation at a particular moment in time. For example, someone might be more willing to queue when vacation than on their way to work.
If a resource, such as water, has a limited capacity and excess demand then a queue will form with an associated waiting cost. In the fountain example this means the city has not achieved its goal of free water provision. Worse still, the benefit of free water is absorbed by the wasteful act of queuing. This means that fountains may deliver little benefit or utility to the city’s residents.
One improvement that could make the system somewhat more efficient would be to introduce a flat price for using the fountain. This has the advantage that some of the cost of maintaining the resource is recovered. The city government can use this revenue to build more fountains to reduce congestion. However, for a fixed number of fountains, users will continue to waste time waiting in a queue. These queues will be shorter since the potential pay-off for queuing (and receiving subsidized water) is lower than when the water is free. Although, this occurs at the cost of excluding some people who cannot or are unwilling to pay the price for water.
This system is also inefficient but in a slightly different way. Users who value the water highly but have a strong aversion to queuing do not make use of the fountain despite being willing to pay higher prices. A similar argument applies to users who are willing to queue for longer but in exchange for low- or zero-price access to the resource. The efficiency can be increased by allowing financial exchanges between these different people. This allows those who are willing to pay more to “jump” places in the queue ahead of those who are prepared to wait longer.
Direct payments between queuers are unlikely to occur in reality as the sums are too small to justify the effort of bargaining. An alternative would be to grant access to the resource in rounds. The users would then submit public bids to gain access in the next available round [1]. This mechanism would allow high bidders to use the fountain after a smaller number of rounds than those who submitted lower bids. This type of mechanism is efficient as it accommodates the different urgency (and willingness to pay for it) of different people.
Anyone familiar with the Bitcoin or Ethereum blockchains will note the similarity of this process to submitting transactions to the blockchain. In that case, users bid to enter their transaction in the next block. A recent paper [2] showed that this payment system is one of a class of Vickery-Clark-Groves (VCG) mechanisms. This means that it also possesses two other important characteristics. The first of these is that transactors have an incentive to propose a fee that reflects the true cost that they associate with waiting. The second property is that VCG mechanisms are socially optimal. This means the fees cover the social cost that users impose on others through creating a delay on their transactions being entered into a block.
An advantage of this mechanism is that the fees for entering a transaction into the chain adjust automatically to changes in demand. However, the limited throughput of existing cryptocurrencies leads to other issues. In particular, it is possible for an attacker to submit a large number of transactions with high fees. This forces all other users to either accept similarly high fees or be “locked-out” of the system.
Records of transaction fees on the Ethereum suggest that an attack of this type occurred in early July 2018. During this time, the average transaction fee rose from $0.22 on the 29th of June to a peak of $5.53 on the 2nd of July. This was dismissed as a somewhat irrational occurrence by one eminent Ethereum developer:
Events in the market suggest otherwise. In the three months following the attack, Ethereum’s market cap collapsed by more than one-half, falling from $49bn dollars to $22bn. It is possible that other factors played a part in the decline of the Ethereum price. But it is clear that a leveraged short position on the value of Ether could have generated an enormous profit for the attacker. The many applications running on Ethereum such as exchanges and prediction markets provide other opportunities for an attacker to profit from denying access to other users. Whatever the reason behind it, the attack highlights the need for greater throughput if cryptocurrencies are to become widely adopted.
This raises the question of the economic impact of scalable ledgers on users and operators of nodes (also known as miners). The water fountain analogy is also useful for understanding this situation. This corresponds to access to the water fountain being completely unlimited. In this case, the cost of waiting would fall to zero to the obvious benefit of user. For miners or water fountain operators, this would be a less appealing prospect. The reason for this being that they would have to bear the potentially infinite cost of supplying water without any means of raising revenue.
One of the main advantages of blockchains is that they are free from centralized control. This prevents a single authority from extracting rents from its users. Existing payment systems, such as Visa or PayPal, charge transaction fees in the range of 1–5%. While these corporations profit from economies of scale, they are to some extent in competition with each other. It is difficult to see how replacing centralised payment schemes with a cartel that has control over assets provides any substantial benefit to consumers.
This raises the question of how to design incentives that both compensate miners and ensure truly low operating costs for users. A second question is how these incentives influence the design of scalable decentralized ledgers. While there are likely to be several different solutions to these problems. We propose two general guiding principles that we anticipate would promote more widespread adoption of blockchain technology:
- Fairness. Fees should reflect the costs that users impose on miners and other users.
- Transparency. The fee structure should be open and straightforward for users to understand.
Another possibility is for node operators to earn revenue from other sources. These could include services such as transaction execution and verification or more complex services such as search queries. If we return to the water fountain example, the fountains could be operated as franchises. In exchange for providing free or low-cost water, the operators would receive rights to some other profitable activity. This could, for example, involve selling snacks or soft drinks. In the context of blockchains, this could be achieved by encouraging corporations to operate nodes, which would allow them to achieve low-cost and trustless financial exchange. They would then be able to profit from providing services such as returning search queries or machine learning predictions.
