Mathias Brandewinder on .NET, F#, VSTO and Excel development, and quantitative analysis / machine learning.
7. January 2010 17:13

I am currently prototyping an application, which brought up some fun modeling questions.

Imagine the following situation: there are 2 products on the market. Customers use either of them, but not both. In each time period (we consider a discrete time model), new customers come on the market, and select one of the 2 products, with probability p and (1-p). At the end of each period, some existing customers stop using their product, and leave the market, with a rate of exit specific to the product.

Suppose that you knew p and the rates of exit for each product. If the size of the total market size was stable, what market share would you expect to see for each product?

Before tackling that question, let’s start with an easier problem: if you knew how many new customers were coming in each period, what would you expect the product shares to be?

Let’s illustrate with an example. You want to open the Awesome Bar & Restaurant, an Awesome place with a large bar and dining room. You expect that 100 customers will show up at the door every hour. A large majority of the customers (70%) head straight to the bar, but one the other hand, people who come for dinner stay for much longer. How many seats should you have in the bar and the restaurant so that no one has to wait to be seated?

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