Single-server queuing system

1. A single-server queuing system with an infinite calling population and a first-come, firstserved queue discipline has the following arrival and service rates:
λ = 36 customers per hour
µ = 50 customers per hour
Determine P0, P4, L, Lq, W, Wq, and U.
2. An immigration agent at an airport, on an average, could process 15 entrants in one hour, if he
was busy all the time. On an average, an entrant arrives at his station at every 5 minutes. The
agent can be replaced by a more efficient specialist. The specialist can process 20 entrants in one
hour. The specialist is paid $35 per hour whereas the current agent is paid $22 per hour. If an
entrant’s time is considered to be worth $10 per hour, is it worth to replace the agent with the
specialist?
Note: Do hand calculations to answer this question.
3. A grocery store has four check-out counters. The average service rate for each check-out
counter is 22 customers per hour. The average arrival rate is 82 customers per hour. Assuming it
is a multiple-server waiting line model; determine the average number of customers waiting for a
check-out counter and the average time a customer must wait for a check-out counter. What is the
probability that there will be more than 4 customers in the system?
Note: Use QM for Windows to answer this question.