Intuitive Explanation for the Wait time of 2 Queuing Models with 1 server vs 2 with equal rate

79 Views Asked by At

So I'm having a hard time understanding intuitively why the bottom queuing model behaves the way it does

The arrival rate of both systems is exponentially distributed with a rate of 3 customers per minute

$\text{Model 1:}$ $$M/M/1 \text{ , serving time} \sim Ex(4)$$ 4 as in 4 customers per minute.

$\text{Model 2:}$ $$M/M/2 \text{ , serving times for both are }\sim Ex(2)$$

In other words, the 2 servers in Model 2 are as efficient as the 1 server in Model 1.

So the wait time for the arriving customer is $1$ minute in Model 1 vs $1.22$ minutes in Model 2.

The wait time in the queue is $.75$ minutes in Model 1 vs $.72$ minutes for Model 2.

I can do the math behind it, but I have no idea why logically it works this way