Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 7.3, Problem 16P
a)
Summary Introduction
Interpretation: the arrival rate
Concept introduction:sakasegawa is simple and intuitive, the actual probability of delay is dependent on both the staffing decisions made by the firms and the arrival and service processes
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A single Automated Teller Machine (ATM) is located on the ground floor of a popular shopping mall. Service time at this machine is exponentially distributed. On average, the ATM machine can serve a customer in 3 minutes. Customer arrivals at the machine are Poisson distributed, with an average of 15 customers an hour. Relevant formulas to analyze this M/M/1 model are available in your textbook.
What percent of the time is this machine idle?
25%
0%
75%
50%
100%
Consider a Poisson queue with random arrivals at the rate of 12 customers per hour and the following steady-
state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and p, = 0 for n = 3,4,5, ... . What is the mean (or effective) arrival
rate in customers per hour for this queuing system? Consider drawing a rate diagram to assist in your solution.
O 10
12
O none of the other choices
O 2
Consider a system with Poisson distributed arrival rate with average of 10 clients per day. The service time is exponentially distributed with 8 clients per day. If the cost for operating each server is $20 per day and the cost of holding a client in the system is $200 per day, What is the total cost of operating with 5 servers?
Answer is $350.65 please explain.
Chapter 7 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 7.1 - Prob. 1PCh. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Prob. 5PCh. 7.1 - Prob. 6PCh. 7.1 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10P
Ch. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - Prob. 14PCh. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 18PCh. 7.4 - Prob. 19PCh. 7.4 - Prob. 21PCh. 7.4 - Prob. 22PCh. 7.4 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - Prob. 27PCh. 7.8 - Prob. 28PCh. 7.8 - Prob. 29PCh. 7.8 - Prob. 30PCh. 7.8 - Prob. 32PCh. 7.8 - Prob. 34PCh. 7.8 - Prob. 35PCh. 7.8 - Prob. 36PCh. 7 - Prob. 38APCh. 7 - Prob. 39APCh. 7 - Prob. 40APCh. 7 - Prob. 41APCh. 7 - Prob. 42APCh. 7 - Prob. 43APCh. 7 - Prob. 44APCh. 7 - Prob. 45APCh. 7 - Prob. 46AP
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- In an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. What is the expected number of customers in the queue(Lq)? Note: Round your answer to 3 decimal places. What is the expected waiting time in the queue(Wq)?arrow_forwardA number of decision may be need to made when designing a queueing system . What are they explain?arrow_forwardThe manager of a bank wants to use an MyMys queueingmodel to weigh the costs of extra tellers against the costof having customers wait in line. The arrival rate is 60customers per hour, and the average service time is fourminutes. The cost of each teller is easy to gauge at the$11.50 per hour wage rate. However, because estimatingthe cost per minute of waiting time is difficult, the bankmanager decides to hire the minimum number of tellersso that a typical customer has probability 0.05 of waitingmore than five minutes in line.a. How many tellers will the manager use, given thiscriterion?b. By deciding on this many tellers as “optimal,” themanager is implicitly using some value (or some range of values) for the cost per minute of wait-ing time. That is, a certain cost (or cost range) would lead to the same number of tellers as sug-gested in part a. What is this implied cost (or cost range)?arrow_forward
- Why do queues arise at a service facility even though there is more than enough capacity to meet regular demand in the long run?arrow_forwardIn an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. What is the expected number of customers in the system (L)? (Round your answer to 3 decimal places.) What is the expected waiting time in the system (W)? (Express the waiting time in hours, round your answer to 3 decimal places.) What is the expected number of customers in the queue(Lq)? (Round your answer to 3 decimal places.) What is the expected waiting time in the queue(Wq)? (Express the waiting time in hours, round your answer to 3 decimal places.)arrow_forwardWhat is a single-channel queuing system?arrow_forward
- Below are the data of the gasoline station. Number of gas pumps = 1 Policy of the gasoline station is "If you want to wait, pay PhP45 per liter; if you do't want to wait, pay PhP55/liter." Service mean time (exponential distribution) = 5 minutes Arrival rate (Poisson distribution) = 10 per hour. Customers usually wait to buy gasoline. a) What is the probability (in decimal) that customer will wait? Answer in 4 decimal places.b) Determine the probability that the customer will not wait. Answer in 4 decimal places.c) How many customers are falling in line? Answer in integer value.d) Determine the expected price of gasoline per liter.arrow_forwardIn an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. What is the utilization? Note: Round your answer to 3 decimal places. What is the expected number of customers in the system (L)? Note: Round your answer to 3 decimal places. What is the expected waiting time in the system (W)? Note: Express the waiting time in hours, round your answer to 3 decimal places. What is the expected number of customers in the queue(Lq)? Note: Round your answer to 3 decimal places. What is the expected waiting time in the queue(Wq)?arrow_forwardNote: Formulas to solve the following problems are given in the class and example problems were solved in the class. Follow the examples described in the class and read the literature posted on blackboard. 1. Huntsville Bank (a fictitious one) has a drive-through teller window and observed that customers arrive for service one every three minute, on an average, and the average service time per customer is 2.4 minutes. Assume inter-arrival time and service time follow a negative Exponential distribution. The bank hires you as a consultant. You guess that this is an M|M|1 system and you are required to determine the following: a. Probability (teller is busy) b. Probability (teller is idle) c. Average number of customers waiting for service, that is, number of autos in the line excluding the one at the teller window. d. Average number of customers in the system, that is, number of autos in the line including the one at the teller window. e. Average time a customer spends in the waiting…arrow_forward
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