Practical Operations Management
2nd Edition
ISBN: 9781939297136
Author: Simpson
Publisher: HERCHER PUBLISHING,INCORPORATED
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5, Problem 19P
Summary Introduction
Interpretation: Average length of the line, considering it M/M/1 model.
Concept introduction: The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in an FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further, if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise, it tends to be too variable of a distribution.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A bank has 1 enquiries staff and six tellers. Customers enter the system and walk up to the enquires counter for the enquiries queue or they go to the tellers station where they join a single queue for the 6 tellers.The arrival rate at the enquiry counter, lambda 8 customers per hour and the service rate at the enquiry counter, Mu 6 minutes per customer. The arrival rate at the tellers’stations, lambda 10 clients per hour and the service rate at the tellerstations, Mu 4 minutes per client.
Find the total time customers spend at the bank
At the stadium, there are seven lines for arriving customers, each staffed by a single worker. The arrival rate for customers is 180 per
minute and each customer takes (on average) 2.1 seconds for a worker to process. The coefficient of variation for arrival time is 1.3 and
the coefficient of variation for service time is 1.3.
(Round your answer to three decimal places)
On average, how many customers will be waiting in the queue?
customers
Customers arrive in a barber shop at an average rte of five per hour, the actual arrivals being Poisson distributed. There is one barber on duty at all times and there are four chairs for customers who arrive
when the barber is busy. Local fire ordinances limit the total number of customers in the shop at the same time to maximum of five. Customers who arrive when the shop is full are denied entrance and
their business is presumed lost. The barber's service time is exponentially distributed, but the mean changes with the number of customers in the shop. As the shop fills, the barber tries to speed service,
but actually becomes less efficient, as shown in the following table:
Number in Shop
Mean Service Time, minute
1
9
2
10
Determine:
a) the probability that the barber is idle. Answer in 4 decimal places.
b) the average number of people in the shop at the same time. Answer in 3 decimal places.
3
12
4
15
5
20
Chapter 5 Solutions
Practical Operations Management
Ch. 5 - Prob. 1DQCh. 5 - Prob. 2DQCh. 5 - Prob. 3DQCh. 5 - Prob. 4DQCh. 5 - Prob. 5DQCh. 5 - Prob. 6DQCh. 5 - Prob. 7DQCh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3P
Ch. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10PCh. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - Prob. 16PCh. 5 - Prob. 17PCh. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Prob. 21PCh. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - Prob. 26PCh. 5 - Prob. 27PCh. 5 - Prob. 28PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - Prob. 38PCh. 5 - Prob. 1.1QCh. 5 - Prob. 1.2QCh. 5 - Prob. 1.3QCh. 5 - Prob. 1.4QCh. 5 - Prob. 2.1QCh. 5 - Prob. 2.2QCh. 5 - Prob. 2.3QCh. 5 - Prob. 3.1QCh. 5 - Prob. 3.2QCh. 5 - Prob. 3.3QCh. 5 - Prob. 3.4Q
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. What is the approximate average time in minutes that truckers wait to be seated?arrow_forwardAt the Franklin Post Office, patrons wait in a single line for the first open window. On average, 100 patrons enter the post office per hour, and each window can serve an average of 45 patrons per hour. The post office estimates a cost of $0.10 for each minute a patron waits in line and believes that it costs $20 per hour to keep a window open. Interarrival times and service times are exponential. a. To minimize the total expected hourly cost, how many windows should be open? b. If the post office's goal is to ensure that at most 5% of all patrons will spend more than five minutes in line, how many windows should be open?arrow_forwardA road transport company has one reservation clerk on duty at a time. He handles information of bus schedules and makes reservations. Customers arrive at a rate of 8 per hour and the clerk can, on an average, serve a customer within 5 minutes. The company estimates that the arrival rate will be Poisson distributed whilst the service time is exponentially distributed. Use the information above to answer question 70 through to 75 70. What is the average number of customers waiting in line to be served? А. 1 В. 1.04 . С. 1.33 D. 2.666 71. What is the average number of customers in the system? А. 2 В. 3 С. 4 D. 5 72. What is the average time a customer has to wait before being served? A. 4 minutes B. 5 minutes C. 8 minutes D. 10 minutes 73. What is the average time a customer spends in the system? A. 0.2 hr B. 0.25 hr С. 12 hrs D. 15 hrs Page 11 of 16 Peu l'ell/ mideam!?/2-19/20 Scanned with CamScanner 74. What is the probability of not finding a customer in the system? A. 0 B. 0.33 C.…arrow_forward
Recommended textbooks for you
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,