Examples of Erlang C in action
Although Erlang C originally was developed for call centers it can be used in a lot of different settings. These settings vary from determining the number of cash registers that should be open in a supermarket to determining how much staff will be needed in a department store.
If you are the manager of a supermarket you need to make schedules for your employees and how many of them should operate a cash register.Erlang C can be perfectly used for this. If you determine the average time it takes for a customer to get all his products scanned and how much time it takes him to pay we can use that number as the ‘average calling time’ in the Erlang C form. Waiting time is the time the customer has to wait in line before being helped by the cashier.
Example: your supermarket receives 250 customers an hour and the average time it takes to help a customer is 1 and a half minute. You want a customer to wait a maximum of of 4 minutes in line and expect that 90% of the customers will not have to wait longer. Erlang C will tell you that you need 7 agents and that the average waiting time will be 1 minute and 24.2 seconds.
If you are the store manager of a big store like for instance Macy’s (a big department store) or Hennis & Mauritz (a big clothing store) you will need to make schedules for shop sales people. You can do this by using your experience but maybe calculating how much people you might need can result in a higher turnover and thus more profit. Often it is, in contrary of call centers, a good idea to let people browse the department store before helping them with a purchase. This is helpful in a way that some customers will ask for getting help but it is also possible to help customers who did not ask themselves. Therefor the average waiting time starts at the moment the customer enters the shop.
Example: your shop receives 50 customers an hour and you want them to browse for a maximum of 10 minutes before a shop employee asks them if they can use help. You want at least 90% of the customers to get this service within 10 minutes. A customer will need 5 minutes help on average. Erlang C will tell you that you need 10 employees in your shop and the average time a customer walks around without being helped will be 1 minute and 27.8 seconds.
A taxi company can predict the amount of customers they will get for a certain day. Also the average time it needs to bring a customer to her destination is known. If not too many customers share cabs we can easily use Erlang C to calculate the needed number of taxi’s and serve a customer within a fair amount of time.
Example: your taxi company gets called 35 times within the busiest hour of the day, it takes 15 minutes to take customer to her destination and it takes 7 minutes to get to the next customer. If we compute the numbers and add these to the calculator (as 35 calls, which take 22 minutes or 1320 seconds) and we set the service level to 80% and waiting time to 10 minutes we see that we need 15 taxi’s with drivers.
Festival or big event
Some of the most basic needs have to be fulfilled at festivals and big events. People need to eat and drink but also need to make use of restrooms. Yes, the Erlang C-formula can also be used for this. You need historic data about how often a festival visitor will visit a toilet, how long the average use is for hat toilet and how long the lines have to be to prevent people from abandoning the row. Input this data in the Erlang C Calculator and it will calculate the needed number of toilets. (Same can be applied towards how many food trucks you will need based upon how many customers can be served at once per food truck and how long it takes to serve one customer.)
Trunked radio systems
According to Wikipedia a trunked radio system is a complex type of computer-controlled two-way radio system that allows sharing of relatively few radio frequency channels among a large group of users. A trunked radio system is often used by fire-departments and police department. The technology is based on the fact that not all users communicate at the same time. Erlang C can be used to determine the number of frequencies to be used with a given communication load. For more information on trunked radio systems one can look at Radio Reference Trunking Forum .