8 customers per hour7. Suppose that the queueing system under consideration fits the M/M/s model with=and μ10 customers per hour. Use the Excel template to find the optimal number of servers for each of thefollowing 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 onewith the optimal number of servers) for each part.E(SC) = CçsE(WC) = CwLPE(TC)=E(SC) + E (WC)S1234

Find the Calculation methods below: ρ (Single server) = λμρ (multiple server) = λ(μ*s)Total cost =…

Answered: Suppose that the queueing system under…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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In queueing theory, λ represents the mean arrival rate; for example, the number of peoplearriving at the service counter per hour. What does 1/λ represent?o Service rateo Interarrival timeo Service time None
The manager of a large group of employees must decideif she needs another photocopying machine. The cost of amachine is $40 per 8-hour day whether or not the machineis in use. An average of 4 people per hour need to use thecopying machine. Each person uses the copier for an averageof 10 minutes. Interarrival times and copying times areexponentially distributed. Employees are paid $8 per hour,and we assume that a waiting cost is incurred when a workeris waiting in line or is using the copying machine. Howmany copying machines should be rented?
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…
a)Resolution of issue pertaining to storage of steel plates. b)What objectives are to be planned to address the delays in up-gradation of facilities? c)Suggest a strategy to accomplish the objectives planned (in part b). d)How to manage orders those are queued for which it is confirmed that they will be delayed and penalty is inevitable?
In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. Note: Round your answers to 3 decimal places. What is the probability that the server will be idle? What is the probability of having exactly 4 customers in the system? What is the probability of having 4 or fewer customers in the system?
None
What is the difference between Maximum Foreseeable Loss(MFL), Probable Maximum Loss(PML), and Estimated Maximum Loss(EML)? Please use your own word :)
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 stool
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.
For a single-server queue of 10 customers whose arrival and service time is given below in the table. Complete the below given table. Customer Arrival Time ti Inter Arrival Time Ai=ti—ti-1 Service Begins (Sb) Delay Time (Di) Service Time (Si) Calculate Ci=ti+Di+Si 1 7:00 7:02 6 2 7:08 7:12 4 3 7:11 7:16 1 4 7:13 7:19 5 5 7:18 7:25 10 6 7:36 7:39 2 7 7:40 7:44 3 8 7:45 7:48 3 9 7:49 7:52 4 10 7:55 7:57 3 Find the average service time and average delay time. Average Service Time= Average Delay Time=
3 The M/M/1 Queue During peak time, customers arrive at a bank teller window (with a single teller) at a rate of 23 per hour, where the teller can serve 25 per hour. This problem will allow you to investigate (via a simple extension of the mean queue size formula) the effect of highly-variable service times on our familiar queuing metrics. The diagram below stylizes the queuing system: Waiting Service Calculate the marginal probability P (T > oT). a. O b. 0.25 O c. 0.63 O d. 0.75 Calculate the mean time a customer spends at the bank (waiting time plus service time) in minutes. O a. 30 minutes O b. 27.6 minutes O c. 2.4 minutes O d. 7 minutes

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