(Not homework)
I'm doing some studying for an upcoming final, which includes material on queueing theory (the class is on design/analysis of computer networks, not queueing theory). I've worked through a couple prior questions that led me to this question.
Prior questions were:
- What is the probability that the server is idle?
This was simple. The probability that the server is idle is the probability that 0 customers are in the queue: $P_0 =1-\frac{λ}{μ}$
- What is the probability that the server is busy?
After calculating 1., this is simple $1 - P_0$
Now, onto my question.
EDIT: I probability should have noted that the probability of $n$ customers in the queue is $P_n = (\frac{λ}{μ})^i \cdot P_0$. I believe this equation will be needed to calculate the question below.
- What is the probability that the queue has less than 5 customers?
My first though it to simply sum up the probability $P_0$ to $P_4$. Is this correct? If not, could you lead me toward the correct answer?