Practical Operations Management
2nd Edition
ISBN: 9781939297136
Author: Simpson
Publisher: HERCHER PUBLISHING,INCORPORATED
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Question
Chapter 5, Problem 20P
Summary Introduction
Interpretation: Average number of customers in the system, considering 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.
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A supermarket has four girls ringing sales at the counters. If the service time for each customer is exponential with mean 4 minutes, and if people arrive in a Poisson fashion at the rate of 10 per hour, calculate
i.
The average number of customers in the system.
ii.
The average time a customer spends in the system.
iii.
The average queue length
iv.
The average waiting time for customers.
v.
The expected percentage of idle time for each girl
vi.
The probability that at least a girl is waiting for the customer.
Customers arrive at the lone check-out desk of a certain convenience store at the average rate of 0.23 per minute. If it takes on average four minutes for the store manager to serve each customer, how many customers will on average find themselves waiting in the queue?
A. 10.58
B. 0.00024
C. 3.20
D. 0.00351
The office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution.
b.) What proportion of time are both clerks idle?
c.) Counting each person being served and the people in line, on average, how many customers would be in this system?
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
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