4. Mom-and-Pop's Grocery Store has a small adjacent parking lot with three parking spaces reserved for thestore's customers. During store hours, cars enter the lot and use one of the spaces at a mean rate of 2 perhour. If there is no parking space available, the car just leaves without waiting. For n = 0, 1, 2, 3, the probabilityPn that exactly n spaces currently are being used is Po = 0.1, P₁ = 0.2, P₂ = 0.4, P3 = 0.3.(a) This parking lot can be interpreted as being a queueing system. Identify the customers and the servers.What constitutes a service time? What is the queue capacity?(b) Determine the basic measures of performance-L, Lq, W, and Wa-for this queueing system.(c) Use the results from part (b) to determine the average length of time that a car remains in a parking space.(d) Find p, the utilization factor.

NOTE: We are allowed to do the first three sub-parts only. Given: Arrival rate (lambda) = 2 per hr

Answered: Pn that exactly n spaces currently are…

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 an M/MA queueing system, the arrival rate is 3 customers per hour and the service rate is 5 customers per hour. If the service process is automated (resulting in no variation in service times but the same service rate), what will be the resulting performance measurements? (Round your answers to 3 decimal places.) a. What is the utilization? Utilization b. What is the expected number of customers in the system (L)? Number of customers c. What is the expected waiting time (in hours) for the system (W)? Waiting time(in hours)
Provide instead: 3 Positive and 3 negative outcomes for forecasting 3 Positive and 3 negative outcomes for queuing model
Answer the following questions. Answers are listed at the end of this section.1. The queuing models assume that customers are served in what order?2. Consider two identical queuing systems except for the service time distribution. In the first system, the service time is random and Poisson distributed. The service time is constant in the second system. How would the waiting time differ in the two systems?3. What is the average utilization of the servers in a system that has three servers? On average, 15 customers arrive every 15 minutes. It takes a server exactly three minutes to wait on each customer.4. What is the expected waiting time for the system described in question 3?5. Firms that desire high service levels where customers have short wait times should target server utilization levels at no more than this percentage.
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
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…
The 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)?
A fast-food restaurant offers a variety of products: from pre-made packaged sandwiches to milkshakes with different flavors. Many customers order one item time, other customers order multiple items. Sometimes customers buy the pre- made items, and some customers actually ask the restaurant to cook their food while they wait. The restaurant manager has kept careful records of some queuing statistics over several weeks. According to this data, the staff needs 4 minutes on average to serve a random customer. On average, the restaurant served 120 customers on a given day. This restaurant is open from 9 AM to 9 PM every day, and has a single service counter. If you want to help the manager measure this restaurant's waiting line performance, which of the following should you use? Exponential Service Rate Model The Finite Source Model Constant Service Rate Model O The multi phase single channel model
Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.
Subject - account Please help me. Thankyou.
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?
7

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