4.The problem: In a queueing problem modelled as (M/M/2), if L (number of units in the system)0.75 units and service rate for each s (server) is 3 units per hour, what is the arrival rate?To answer the problem or question, you were given the following data/statements:=(1) The average time a unit spends in the queue is 2.5 mins.(2) The average time a unit spends in the system is 22.5 hours.Which of the following appropriately describes the data/statements provided? Select thecorresponding letter and support your answer.A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE issufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.

Queueing model: M/M/2 (Poisson arrival and exponential service rate, 2 servers) Service rate for…

Answered: 4. The problem: In a queueing problem…

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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Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.5per minute. The average time to handle each is 10seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation. a) The probability that the operator is busy = enter your response here (round your response to two decimal places). b) The average time that a caller must wait before reaching the operator = enter your response here minutes (round your response to two decimal places). c) The average number of calls waiting to be answered = enter your response here calls (round your response to two decimal places).
Customers enter the camera department of a store at an average rate of six per hour. The department is staffed by one employee, who takes an average of six minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. (Use the Excel spreadsheet Queue Models.) a-1. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? Note: Round your answer to 2 decimal places. a-2. How long would a customer expect to spend in the camera department (total time)? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. b. What is the utilization of the clerk? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. c. What is the probability that there are more than two people in the camera department (excluding the clerk)? Note: Round your intermediate calculations to 3 decimal places and final answer to 1…
A server operates with 70% utilization. The coefficient of variation for the service process is 0.6 and the coefficient of variation of the arrival process is 1. The average processing time is 3 minutes. What is the average time a customer spends in the system according to the single-server queue model? A. 9 minutes B. 6 minutes C. 3 minutes D. 7.5 minutes Consider an Erlang loss system. The average processing time is 6 minutes. The average interarrival time is 3 minutes. The number of servers is 9. What is the capacity of the system? A. 0.8 customers per minute B. 1.5 customers per minute C. 1.1 customers per minute D. 2.4 customers per minute
In a queueing system, customers arrive once every 5 minutes (standard deviation = 7) and services take 3 minutes (standard deviation = 6.8). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the system (in minutes)? minutes
Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 12. What percentage of time only one dispatcher is busy? ° 56.27% 27.27% 45.35% 15.89%
Consider a base case where a customer arrives every 40 seconds and the Customer Service Champion can handle 120 customers per hour. There are two Food Champions, each capable of handling 100 orders per hour How long should it take to be served by the restaurant (from the time a customer enters the kiosk queue until her food is delivered)? Use queuing models to estimate this.
On a toll road, there are 2 lanes for drivers to pay their toll. Customer arrival times are constant, with a degenerate distribution. Service times are random, with an exponential distribution. What is the proper description for this queueing system?
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?
48. Ships arrive at a port facility at an average rate of twoships every three days. On average, it takes a single crewone day to unload a ship. Assume that interarrival andservice times are exponential. The shipping companyowns the port facility as well as the ships using that facility. The companyestimates that it costs $1000 per dayfor each day that a ship spends in port. The crew servicing the ships consists of 100 workers, each of whom ispaid an average of $30 per day. A consultant has recommended that the shipping company hire an additional40 workers and split the employees into two equal-sizecrews of 70 each. This would give each crew an averageunloading or loading time of 1.5 days. Which crew arrangement would you recommend to the company?
A. Know some of the basic queue performance measure B. Identify the relationships between queues and some statistical distribution
8 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 4
Please do not give solution in image format thanku

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