Question 1. A single-server queuing system with an infinite calling population and a first-come

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:
? = 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 hewas busy all the time. On an average, an entrant arrives at his station at every 5 minutes. Theagent can be replaced by a more efficient specialist. The specialist can process 20 entrants in onehour. The specialist is paid $35 per hour whereas the current agent is paid $22 per hour. If anentrant’s time is considered to be worth $10 per hour, is it worth to replace the agent with thespecialist?
Note: Do hand calculations to answer this question.
3. A grocery store has four check-out counters. The average service rate for each check-outcounter is 22 customers per hour. The average arrival rate is 82 customers per hour. Assuming itis a multiple-server waiting line model; determine the average number of customers waiting for acheck-out counter and the average time a customer must wait for a check-out counter. What is theprobability that there will be more than 4 customers in the system?
Note: Use QM for Windows to answer this question.

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