Saturday, May 13, 2023

A Queuing Problem

 Queues are waiting lines. For example boarding a plane or buying coffee. Now if one has a gas powered car, the typical queues at a gas station is zero, namely you pull up to a pump and fill the tank. Why? Simple, the arrival rates are low, cars can drive long distances between fills, the number of servers or gas pumps is very large and the holding time or time to fill a tank is at best a couple of minutes.

Now if we move to electrical vehicles we have the following problem:

1. The arrival rate is high due to low distance capacity of batteries. Namely a gas vehicle goes say 400 miles on a tank, 18 gallons and say 25 mpg.

2. The holding time is at least an order of magnitude longer. Typically 45 minutes with a fast charger or 8 hours if a slow charger.

3. Thus having the arrival rate, holding time we can find the number of servers needed for zero queue length. 

The answer is staggering. We need millions of charging stations to assure an available one for every car without any delay. 

It is clear that no one has analyzed this simple problem. The DC characters are totally clueless and have not even examined the simple ones. This also opens up the need for a dramatically expanded grid, redundancy, security etc. 

For those of us who lived through the oil embargoes of the 70s they will seem like the good old days!