CHAPTER 9
QUEUEING MODELS
SOLUTIONS TO DISCUSSION QUESTIONS
9-2. The underlying assumptions are:
2. There is no balking or reneging.
4. Arrivals are Poisson.
6. Average service rate exceeds average arrival rate.
9-3. The seven operating characteristics are:
1. Average number of customers in the system (L)
3. Average number in the queue (Lq)
5. Utilization factor (ρ)
7. Probability there are exactly n customers in the system (Pn)
9-5. First-in, first-out (FIFO) is often not applicable. Some example are (1) hospital emergency rooms, (2)
an elevator, (3) an airplane trip, (4) a small store where the shopkeeper serves whoever can get his or her
9-6. Examples of finite queuing situations include (1) a firm that has only 3 or 4 machines that need
servicing, (2) a small airport at which only 10 or 15 flights land each day, (3) a classroom that seats only
9-7.
(a) Barbershop: usually a multiple-server system (if there is more than one barber).
Arrivals Customers wanting haircuts
Waiting line Seated customers who informally recognize who arrived first among them
Service Shampoo, haircut, style, and so forth; if service involves shampooist, then barber,
(b) Car wash: usually either a single-server system, or else a system with each service bay having its own
queue.
Arrivals Dirty cars or trucks
9-8. Doctors’ offices generally have either “grouped” arrivals or uniform arrivals, unless they extensively
treat emergency cases (which tend to be Poisson arrivals). Grouped arrival means that 10 patients may be
scheduled for 9 A.M., 10 for 10 A.M., 10 more for 11 A.M., and so on. Theoretically, patients all arrive at
9-9. Appropriate to use Poisson to describe arrivals:
(a) Cafeteria: probably not. Most people arrive in groups and eat at the same time.
(b) Barbershop: probably acceptable, especially on a weekend, in which case people arrive at the same