Practical Management Science
5th Edition
ISBN: 9781305734845
Author: WINSTON
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 13.5, Problem 22P
Summary Introduction
To determine: The number of servers that would minimize the sum of delay and service cost per hour.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A radio repairer notes that the time he spends on his job has an exponential distribution with a mean of 4 minutes. He follows the first come first serve principle. The arrival time of clients takes a Poisson distribution with an average rate of 8 clients every 1 hour.Determine the arrival rate value , service rate value to be used,time taken by aclient waiting in the queue
Determine the client’s average waiting time in the system and Compute the probability that the system is idle; P (idle)
Zimmerman’s Bank is the only bank in the small town of St. Thomas. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find:
The average time in the line.
The average number in the line.
The average time in the system.
The average number in the system.
The probability that the bank is empty.
A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 3. The average waiting time in the system is
Chapter 13 Solutions
Practical Management Science
Ch. 13.3 - Prob. 1PCh. 13.3 - Prob. 2PCh. 13.3 - Prob. 3PCh. 13.3 - Prob. 4PCh. 13.4 - Prob. 5PCh. 13.4 - Prob. 6PCh. 13.4 - Prob. 7PCh. 13.4 - Prob. 8PCh. 13.5 - Prob. 9PCh. 13.5 - Prob. 10P
Ch. 13.5 - Prob. 11PCh. 13.5 - Prob. 12PCh. 13.5 - Prob. 13PCh. 13.5 - Prob. 14PCh. 13.5 - Prob. 15PCh. 13.5 - Prob. 16PCh. 13.5 - Prob. 17PCh. 13.5 - Prob. 18PCh. 13.5 - Prob. 19PCh. 13.5 - Prob. 20PCh. 13.5 - Prob. 21PCh. 13.5 - Prob. 22PCh. 13.5 - Prob. 23PCh. 13.5 - Prob. 24PCh. 13.5 - Prob. 25PCh. 13.5 - Prob. 26PCh. 13.5 - Prob. 27PCh. 13.5 - Prob. 28PCh. 13.5 - Prob. 29PCh. 13.5 - Prob. 30PCh. 13.5 - Prob. 31PCh. 13.5 - Prob. 32PCh. 13.5 - Prob. 33PCh. 13.5 - Prob. 34PCh. 13.5 - Prob. 35PCh. 13.5 - Prob. 36PCh. 13.5 - Prob. 37PCh. 13 - Prob. 46PCh. 13 - Prob. 47PCh. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 54PCh. 13 - Prob. 58PCh. 13 - Prob. 59P
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
- At a fashion retailer, there are three cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It is estimated that the customer arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 15 minutes. Suppose that customers form a single line. What is the average waiting time in minutes for a customer? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.arrow_forwardThe SFO airport branch of Hertz maintains a fleet of 50 SUVs. The interarrival time between requests for an SUV is 2.4 hours, on average, with a standard deviation of 2.4 hours. There is no indication of a systematic arrival pattern over the course of a day. Assume that, if all SUVs are rented, customers are willing to wait until there is an SUV available. An SUV is rented, on average, for 3 days, with a standard deviation of 1 day.arrow_forwardNeve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 12 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the negative exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find: 1. The average time in line 2. The average number in the line 3. The average time in the system 4. The average number in the system 5. The probability that the bank is empty 6. CEO Benjamin Neve is considering a second teller (who would work at the same rate as the first) to reduce waiting time for customers. A single line would be used, and the customer at the front of the line would go to the first available bank teller. He assumes that this will…arrow_forward
- A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. How long does the average person spend waiting for a clerk? 1.143 minutes 3.429 minutes 1.929 minutes 0.643 minutearrow_forwardTown Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 11. What percentage of time all dispatchers are idle? 25.58% 15.58% 45.75% 8.65%arrow_forwardTown Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 15.What is the average time in minutes that a customer spends in the system? 3.8 mins 7 mins 4.8 mins 8.9 minsarrow_forward
- Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 12. What percentage of time only one dispatcher is busy? ° 56.27% 27.27% 45.35% 15.89%arrow_forwardAn average of 36 customers per hour arrives at a bank branch office (Poisson arrival) and wait in a single line to be served by the first available teller. The average time for each teller to service a customer is 4 minutes (exponentially distributed). Each teller earns $160/day and the bank branch office assesses a waiting cost of $50/day that a customer waits in the system. How many tellers should be on duty in this bank branch office to minimize the total cost of this waiting line system? 2 4 5arrow_forwardMarty's Barber Shop has one barber. Customers have an arrival rate of 1.1 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? Round your answer to four decimal places.P3 = What is the probability that more than two customers are waiting? Round your answer to four decimal places.P(More than 2 waiting) = What is the average time a customer waits for service? Round your answer to four decimal places.Wq = minutesarrow_forward
- A horologist (watchmaker) is typically able to service a mechanical watch in about 120 minutes (exponential distribution). Assuming an 8 hour work-day, the watchmaker averages 3 customers arriving at his shop every day following a poisson distribution. The watchmaker just purchased a new machine that will polish the dial and crystal reducing his service time by 20 minutes per watch. How much will the line for a watch waiting to be serviced be reduced by the watchmaker using this new machine, assuming no increase in customer demand? O 2.25 watches waiting for service O The number waiting to be serviced will be reduced by about 1.2 watches O The number waiting to be serviced will be reduced by about 0.4 watches The number waiting to be serviced will be reduced by about 1.45 watchesarrow_forwardA firm is engaged in both shipping and receiving activities. The management is always interested in improving the efficiency of new innovations in loading and unloading procedures. The arrival distribution of trucks is found to be Poisson with arrival rate of 3 trucks per The service time distribution is exponential with unloading rate of 4 trucks per hour. Determine (i) expected number of trucks in the queue, hour. (ii) expected waiting time of the truck in the queue, (iii) probability that the loading and unloading dock and workers will be idle, (iv) what reductions in waiting time are possible if loading and unloading is standardised?arrow_forwardConsider a bank with two tellers. An average of 2 customers per hour arrive at the bank and wait in a single línea for an idle teller. The average time it takes to serve a customer is triangular (x1=1, y1=0), (x2=4, y2=2/3) Assume that inter-arrival times and services time is exponential. Develop the service (ST) equation? a. Y=2x-22/6B. Y=2x-22/3C. Y=22/3x-2/3D. Y=2x-3/22arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
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,