Operations Management
17th Edition
ISBN: 9781259142208
Author: CACHON, Gérard, Terwiesch, Christian
Publisher: Mcgraw-hill Education,
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Chapter 17, Problem 6PA
Summary Introduction
To determine: The interarrival time for combined lot.
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- Explain how waiting lines can develop even when the service time is a constant.arrow_forwardThe Taj Service Station has five mechanics each of whom can service a scooter in two hours on an average. The scooters are registered at a single counter and then sent for servicing to different mechanics. Scooters arrive at the service station at an average rate of two scooters per hour. Assuming that the scooter arrivals are Poisson distributed and the servicing times are distributed exponentially, determine a. Utilisation factor b. The probability that the system shall be idle. c. The probability that there shall be three scooters in the service centre d. The probability that there shall be eight scooters in the service centre e. The expected number of scooters waiting in the queue f. The expected number of scooters waiting in the service centre g. The average waiting time in the queue h. The average time spent by a scooter in waiting and getting servicearrow_forwardAuto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with anaverage of 10 units per hour. The service time is distributed exponentially with a mean of3 minutes. Find the following:i. Average number of units in the systemii. Average waiting timeiii. Average length of queueiv. Probability that a customer arriving at the pump will have to waitv. The utilization factor for the pump unitvi. Probability that the number of customers in the system is 2.arrow_forward
- State the assumptions of the basic single channel queuing model.(Model A or M/M/I)?arrow_forward5.12. For each of the following queuing systems, indicate if it is a single- or multiple-server model, the queue discipline, and if its calling population is infinite or finite: Hair salon Bank Laundromat Doctor’s office Adviser’s office Airport runway Service station Copy center Team trainer Mainframe computerarrow_forwardTop Cutz International Barbershop is a popular haircutting and styling salon . Four barbers work full-time and spend an average of 15 minutes on each customer. Customers arrive all day long at an average rate of 12 per hour. When they enter, they take a number to wait for the first available barber. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed. REQUIRED (e) What is the average number waiting to be served?arrow_forward
- 12-19 Juhn and Sons Wholesale Fruit Distributors employs one worker whose job is to load fruit on outgoing company trucks. Trucks arrive at the loading gate at an average of 24 per day, or 3 per hour, according to a Poisson distribution. The worker loads them at a rate of 4 per hour, following approximately the exponential distribution in service times. Determine the operating characteristics of this loading gate problem. What is the probability that there will be more than three trucks either being loaded or waiting? Discuss the results of your queuing model computation.arrow_forwardThe state operates a weigh station for trucks traveling on the highway. Every truck must pull off the highway, enter the weigh station, and undergo state inspection procedures before counting on. Trucks arrive at this station at a poisson rate of seven per hour. The time to inspect/weigh a truck varies, having an exponential probability density with a mean of 7 minutes.A. How many trucks are detained at the station on the average? B. How long can a truck expect to be detained?C. How many trucks are lined up in front of the station on the average?D. How long on the average does a truck driver have to wait in line for the truck to beinspected?arrow_forward
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