Queuing-theory-quiz.docx

Queuing Theory Name: 1. This is defined as the difference between the actual travel time on a given segment and some ideal travel time of that segment a. Arrival Rate b. Delay c. Service Rate d. Queue 2. Statement 1: Queuing theory is the mathematics of waiting lines. Statement 2: Queuing theory provides short term average values. a. Statement 1 is correct b. Statement 2 is correct c. Both statements are correct d. Neither of the statements are correct 3. This is usually expressed in flow (customers/hr) or time headway (seconds/customer) a. Mean arrival rate (λ) b. Mean service rate (𝜇) c. Mean service rate (λ) d. Mean arrival rate (𝜇) 4. Which is correct about the queue discipline? a. If customers are served according to arrival, this is known as LIFO. b. In FIFO, customers are served in the reverse order of their entry. c. In SIRO, every customer in the queue is equally likely to be selected. d. Customers are selected for service at random, irrespective of arrivals in FIFO.

Schedule: c. Both statements are correct d. Neither of the statements are correct 7. It is the rate which customers depart from a transportation facility. a. Mean arrival rate (λ) b. Mean service rate (𝜇) c. Mean service rate (λ) d. Mean arrival rate (𝜇) 8. This is defined as a parameter that explains how the customers arrive at a facility a. Queue Patterns b. Queue discipline c. Queuing theory d. None of the above 9. Statement 1: In a processor sharing, the server is switched between all the queues for a predefined slice of time in a round-robin manner. Statement 2: Treatment of VIPs in preference to other patients in a hospital is an example of processor sharing a. Only statement 1 is correct b. Only statement 2 is correct c. Both statements are correct d. Both statements are wrong 10. Which of the following statement is wrong? a. The M/M/1 Model uses Markovian Theory b. The M/M/N Model has multiple queues c. The M/M/N Model has multiple servers d. The M/M/1 Model has single server

5. Which of the following is not an assumption / feature of M/M/1 Model? a. Exponential service time distribution b. First In, Last Out c. Infinite population w/ independent arrivals d. Single waiting line with unlimited space

11. In a D/D/N model, the ff. are correct except a. Arrival and service rates are probabilistic b. Customers are assumed to be patient c. Users arrive from unlimited sources d. Arrival and service time are known

6. Statement 1: If arrival rate is higher than service rate, the queue has a never ending growth. Statement 2: If arrival rate is lower than service rate, there is no queue. a. Statement 1 is correct b. Statement 2 is correct

12. Which of the following is not an input parameter in the queuing theory? a. Mean arrival rate b. Mean service rate c. Standard deviation d. Number of services

13. The following are advantages of using the single server model except a. It guarantees fairness b. Avoids cutting-in problems c. Jockeying is avoided d. Labor specialization is possible 14. This refers to the number of servers and speed of service to be considered a. Queuing pattern b. Service pattern c. Arrival pattern d. Poisson distribution 15. This is defined as the time duration between each customers’ arrival a. Poisson distribution b. Inter-arrival time c. Service pattern d. Arrival pattern Problem Solving: In a health clinic, the average rate of arrival of patients is 12 patients per hour. On an average a doctor can serve patients at the rate of one patient every four minutes. Assume, the arrival of patients follows a Poisson distribution and service to patients follows an exponential distribution. Find the following: a. Average number of patients in the waiting line (Lq) b. Average number of patients in the clinic (L) c. Average waiting time in the waiting line (Wq): d. Average waiting time in the clinic (W): e. Utilization Factor:

ANSWERS: Theories 1. 2. 3. 4. 5.

___ ___ ___ ___ ___

Problem 1. 2. 3. 4. 5.

_____ _____ _____ _____ _____

6. ___ 7. ___ 8. ___ 9. ___ 10. ___

11. ___ 12. ___ 13. ___ 14. ___ 15. ___