How to model delayed flows due to unmet demand

[nzligul]

Hello,

In my model, I have a stock of patients who require medication. Some of them recover after receiving treatment and move to another stock (e.g., under treatment). However, when there is not enough medicine available, others stay in the stock for a certain period while waiting for medication. If they do not receive it in time, they may either recover without treatment or switch to an alternative therapy.

This is conceptually similar to a firm facing unmet demand: if a product is unavailable, some customers are willing to wait, but after a certain delay, they give up (lost sales).

I want to avoid modeling this as an immediate outflow from the stock. Instead, I would like individuals (or demand) to remain in the stock for a while before transitioning based on whether treatment becomes available or not. What is the best way to represent this relationship? Should I use an additional stock to represent this waiting period? Or is there a more suitable modeling approach for handling this?


Kind regards,
Nazli

[Administrator]

The simplest would be to introduce another stock to represent the waiting period.

[tomfid]

Something like this:

queue.png (53.36 KiB) Viewed 4090 times

In queuing theory there's also the concept of "balking" where arrivals decline to joint the queue, because they immediately perceive that the line is too long.