The Cross-Industry Universal Laws of Exponential Booking Curves

Abstract

In recent years, the e-commerce market has grown with the spread of the internet worldwide every year. Accordingly, in service industries, purchasing products with reservations has become common. With the spread of online reservations, the booking curve, which is the concept of the time series in the cumulative number of reservations and has been used for sales optimization in the airline ticket and hotel industries, has been used in various industries. Booking curves in specific industries have been studied, but a universally applicable model across various industries has not been developed. In this study, we show that booking curves can be modeled universally by the exponential decay function, and we also show that the model is valid by using real data from some industries before and after the COVID-19 pandemic, that is, under completely different market conditions. The cross-industry exponential laws of booking curves constitute an important discovery in regard to mathematical laws in the social sciences and can be applied to give leading microeconomic indicators.

Time-Rescaling Regression Method for Exponential Decay Time Series Predictions

“…We predicted the reservation demand forecast on the usage days of each facility, where the data can be regressed in the interval t * ≤ t. Then, we used t * = 30 and the division constant N = 13. We prepared a full-year reservation data set in 2019 based on the previous study [7] and divided it into two periods. One is the first half year, that is, from January 1 to June 30, and the second is the latter half year, that is, from July 1 to December 31, 2019.…”

“…In the service industry, it is found that the booking curve universally follows an exponential decay function [7]. Here, the booking curve represents the cumulative sum of the number of reservations toward the usage day, which is used in many industries, including hotels and rental cars.…”

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The exponential law has been discovered in various systems around the world [1][2][3][4][5][6][7]. In this study, we introduce two existing and one proposed analytical method for exponential decay time-series predictions.

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