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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Wesley is having a busy afternoon working at the Cool ice cream shop. He is the only employee working because his co-worker for this shift has called in sick. It is a hot summer day and a customer arrives every five minutes on average. Wesley takes an average of four minutes to serve a customer. Assume M/M/1 and FIFO queuing system and no limits on queue size. Select the best choice. a. Since his average service capacity is greater than the average customer demand, Wesley is never busy at the Cool ice cream place. b. Wesley is busy about 85% of the time at the Cool ice cream place. c. Wesley is busy about 25% of the time at the Cool ice cream place. d. Wesley is idle (i.e., not busy) about 20% of the time at the Cool ice cream place.
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?
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
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)?
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.
The bank manager is concerned with its waiting line system in his bank. Currently bank uses a single-server, single-line, single-phase system. Based on historical evidence, the average number of customers arriving per hour is C1 and is described by a Poisson distribution. The service rate is <=15 >11 customers per hour with the service times following an exponential distribution. The customers are come from an infinite population. The manager of the bank would like calculate the operational characteristics of the waiting line system that:(a) What is the average system utilization?(b) What is the average number of customers in the system? (c) What is the average number of customers waiting in line?(d) What is the average time a customer spends in the system?(e) What is the average time a customer spends waiting in line?
Subject - account Please help me. Thankyou.
At a fashion retailer, there are three cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It is estimated that the customer arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 15 minutes. Suppose that customers form a single line. What is the average waiting time in minutes for a customer? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.
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
What is the answer in this number 2?

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