Monte Carlo Shop

This is a simple shop simulation demonstrating the usage of random variates drawn from various statistical distributions (using packages from @stdlib/random/base) to model real world characteristics of the interactions. It simulates customers arriving at a shop, potentially making a purchase, and then leaving. The simulation speed and customer behavior can be adjusted through the user interface.

Inspiration

This simulation draws inspiration from the property ownership mechanics in games like Grand Theft Auto (GTA). In those games, some purchased properties (business) often generate a fixed amount of revenue over a certain period (daily). This simulation takes that idea one step ahead to explore how a probabilistic model of revenue generation would behave.

Features

• Simulates Customer Arrivals: Customers arrive at the shop based on a configurable rate (customers per hour) using an exponential distribution for arrival times.
• Purchase Probability: Each arriving customer has a chance to make a purchase, determined by a configurable probability.
• Random Purchase Price: If a customer makes a purchase, the price is randomly generated within a configurable range, following a Beta distribution to simulate a more natural distribution of prices.
• Adjustable Simulation Speed: Control how many simulated minutes pass per real second, allowing you to speed up or slow down the simulation.
• Real-time Updates: The UI displays the elapsed simulation time, the time until the next customer arrives, the total revenue, and the outcome of the last customer interaction.
• Interactive Parameters: Users can adjust the number of customers per hour, the purchase probability, the minimum and maximum purchase prices, and the simulation speed.
• Visual Representation: A simple visual representation shows a customer icon moving into and out of the shop area.

How to Run

1. A live preview of the project is available at https://impawstarlight.github.io/stdlib-showcase

2. Alternatively, to run locally:

   git clone https://github.com/impawstarlight/stdlib-showcase.git
   cd stdlib-showcase
   npm install
   npm run dev

How the simulation works:

The simulation is about a shop (or maybe a stall), selling only a single item (yeah, very small stall). Customer arrivals, purchase decisions and purchase prices are generated randomly with appropriate distributions.

• The Time passed counter will show the passed minutes in the simulation based on the simulation speed.
• The Next Customer indicator shows the time (in simulated minutes) until the next customer arrives. This is calculated by drawing a random variate from an exponential distribution (@stdlib/random/base/exponential) following a rate parameter defined by the Customer per Hour parameter. To be precise, lambda = Customer per Hour / 60 since we are using minutes as the unit of time so customer per minute is actually our lambda here.
• The Revenue will update whenever a customer makes a purchase, subject to an adjustable Purchase Probability. For this, an uniform random variate is drawn using @stdlib/random/base/uniform. The purchase price is derived from another random variate using a beta distribution (@stdlib/random/base/beta) to emulate a bounded normal distribution to model naturally varying prices within a certain range.
• The Last Customer field will display whether the last arriving customer made a purchase and, if so, the amount.

Libraries Used

• Vite + Svelte: JavaScript framework for the frontend design and building the website preview.
• @stdlib/random-base: A library providing various random number generators and distribution functions, used here for uniform, exponential, and beta distributions.

Notes

• The customer icon's transition duration is dynamically set based on the nextCustomerArrival and simulationSpeed to provide a visual cue related to the arrival time.
• The purchase price is generated using a Beta distribution (with alpha=20 and beta=20) scaled to the defined price range. This tends to produce values clustered around the middle of the range, providing a more realistic price distribution than a purely uniform random selection.
• The next customer arrival time is determined using an exponential distribution, which is commonly used to model the time between events in a Poisson process (like customer arrivals).

Enjoy experimenting with the simulation parameters to see how they affect the shop's performance!