Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 12.5, Problem 14P
Summary Introduction
To determine: The change L, W, LQ, and WQ if L and W is doubled in formula.
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.
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suppose tht a queueing system has two identical servers, and an exponential service-time distribution with a mean of 1/u=10minutes. furthermore, a customer has just arrived to find two in the system. how long would you expect him to wait before being able to start service?
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Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism.
Answer completely.
You will get up vote for sure.
An emergency room (ER) at a Prisma Health Hospital has 10 total
beds it can hold patients, i.e., the capacity of the queueing system of this ER is 10. Patients
arrive to the ER at a rate of 5 per hour. Therefore, we have that λn = 6 for n = 0, 1, . . . , 9
and λ10 = 0 for this queueing system. A patient is seen by an ER doctor as the ‘service’
of this queueing system. The amount of time required for an ER doctor to treat a patient
is exponentially distributed with a mean of .4 hours. We seek the minimum number of ER
doctors so that the expected time of a patient waiting to be seen (so the Wq) is less than
or equal to 15 minutes (.25 hours). You should begin by analyzing s = 1 and show any
calculations that were used to determine Wq for each number of servers that you considered
until you meet the target metric.
An M/M/1 queueing system has that customers arrive to it at a
rate of 5 per hour, i.e., its interarrival times between two consecutive arrivals follows an
exponential distribution with parameter 5 per hour. This question will ask you to evaluate
two options for designing the server in the system. Both options for the single server provide
the same service for the customers in the queueing system but they cost different amounts to
implement. In addition, the total costs of the queuing system are the implementation costs
plus the customer costs. Currently, the customer costs are $100 per hour per customer in the
queueing system.
In comparing these options, it costs us $100 per hour per customer in the queueing system.
(a) The first option for the server is one that has a service time that follows an
exponential distribution with mean 10 minutes. Determine L, W, Lq, and Wq for this
system.
(b) The second option for the server is one that has a service time that follows
an…
Chapter 12 Solutions
Practical Management Science
Ch. 12.3 - Prob. 1PCh. 12.3 - Explain the basic relationship between the...Ch. 12.3 - Prob. 3PCh. 12.3 - Prob. 4PCh. 12.4 - Prob. 5PCh. 12.4 - Prob. 6PCh. 12.4 - Prob. 7PCh. 12.4 - Prob. 8PCh. 12.5 - Prob. 9PCh. 12.5 - Prob. 10P
Ch. 12.5 - Prob. 11PCh. 12.5 - Prob. 12PCh. 12.5 - Prob. 13PCh. 12.5 - Prob. 14PCh. 12.5 - Prob. 15PCh. 12.5 - Prob. 16PCh. 12.5 - Prob. 17PCh. 12.5 - Prob. 18PCh. 12.5 - Prob. 19PCh. 12.5 - Prob. 20PCh. 12.5 - Prob. 21PCh. 12.5 - Prob. 22PCh. 12.5 - On average, 100 customers arrive per hour at the...Ch. 12.5 - Prob. 24PCh. 12.5 - Prob. 25PCh. 12.5 - Prob. 26PCh. 12.5 - Prob. 27PCh. 12.5 - Prob. 28PCh. 12.5 - Prob. 29PCh. 12.5 - Prob. 30PCh. 12.5 - Prob. 31PCh. 12.5 - Prob. 32PCh. 12.5 - Prob. 33PCh. 12.5 - Prob. 34PCh. 12.5 - Prob. 35PCh. 12.5 - Two one-barber shops sit side by side in Dunkirk...Ch. 12.5 - Prob. 37PCh. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Prob. 52PCh. 12 - Prob. 54PCh. 12 - Prob. 56PCh. 12 - Prob. 57PCh. 12 - Prob. 58PCh. 12 - Prob. 59PCh. 12 - Prob. 60PCh. 12 - Prob. 61P
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- Consider a Poisson queue with the following steady-state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and pn = for n = 3,4,5, ... . What is the minimum number of stools that would accommodate all customers in the system at least 75% of the time in steady state? 3 stools O 2 stools none of the other choices O 1 stoolarrow_forward8 customers per hour 7. Suppose that the queueing system under consideration fits the M/M/s model with = and μ 10 customers per hour. Use the Excel template to find the optimal number of servers for each of the following cases. (a) Cs = = $100 and Cw = $10. (b) Cs = $100 and Cw = $100. 'W (c) C = $10 and Cw = $100. - For each part, please list the results in a table like below. You just need to submit one Excel file (the one with the optimal number of servers) for each part. E(SC) = Cçs E(WC) = CwL P E(TC)=E(SC) + E (WC) S 1 2 3 4arrow_forwardThe QRS Trucking Services, has one warehouse servicing its 4 clients within the area. The warehouse hasonly one loading harbor with 3 service crews. The manager has observed that there are certain timeswherein their delivery vans are waiting in the harbor to be loaded. Also, there are instances whereintheir three service crews are idle. Thinking about the situation of their business , the manager noticedthat it follows the Single-Channel Queueing Model.Analyzing the record book, he noticed that the customers’ arrival rate is 3 delivery vans per hour, and onthe average service rate is 5 delivery vans per hour. What advise can you give to the manager about theimplication of adding another service crew, or even two or more crews to increase and improve theservice rate of his loading harbor?If the manager adds one or more service crew(s), the loading harbor can still be considered as a single-channel system, because only one delivery truck ( the customer) can be served at any one time.…arrow_forward
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- Consider a base case where a customer arrives every 52 seconds and the Customer Service Champion can handle 115 customers per hour. There are two Food Champions, each capable of handling 100 orders per hour. On average, how many cars do you expect to have in the drive-thru line? (Include those waiting to place orders and those waiting for food.) (Use the Excel spreadsheet Queue Models.). (Do not round intermediate calculations. Round "Lg" value and final answers to 4 decimal places.) Average total customers waiting in line Average number of customers in the systemarrow_forwardCompute the expected queueing time in an M/G/1 queue with an arrival rate of 10 per hour and the following service time distributions, all with mean 5 minutes: (1) exponential;(2) uniform over (0,a);(3) deterministic. Which distribution produces the smallest Wq and which the largest?arrow_forwardOn a toll road, there are 5 lanes for drivers to pay their toll. Customer arrival times are random, with a general independent distribution. Service times are constant, with a degenerate distribution. What is the proper description for this queueing system?arrow_forward
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