3. Operations Research

Queuing Theory — Quiz

Test your understanding of queuing theory with 5 practice questions.

Practice Questions

Question 1

In an M/M/c queuing system, what is the probability that an arriving customer will find all 'c' servers busy and thus have to wait in the queue?

Question 2

For an M/M/1 queuing system, if the arrival rate is $\lambda$ and the service rate is $\mu$, what is the average waiting time in the system ($W$)?

Question 3

In a birth-death process, if $\lambda_n$ is the birth rate and $\mu_n$ is the death rate when there are $n$ customers in the system, what is the steady-state probability $P_n$?

Question 4

Consider a queuing system where the arrival process is Poisson with rate $\lambda$ and the service times are exponentially distributed with rate $\mu$. If there are $c$ servers, what is the probability that a customer is being served by a specific server, assuming all servers are identical and equally utilized?

Question 5

In a queuing system, what is the primary implication of the 'PASTA' property (Poisson Arrivals See Time Averages)?