QUESTION 5A post office has a counter for customers' drive-through to get the services. The design of thedrive-through lane allows for unlimited queue length. The arrival and service rate are Poissondistributed with A= 20 customers per hour arriving on average and u=25 customers per hour canbe served on average.a) Compute the average number of arrivals.b) Compute the average time a customer waits.c) Compute the average number of arrivals in the system.d) Compute the average time a customer is in the system.e) Compute the probability that less than or equal to 3 customers are in the system.f) If the single counter for the customer drive-through has been replaced with the automaticoperation, service rates are constant with A= 20 and u =25. Compute (a), (b), (c) and (d).

Let, Arrival rate, λ = 20 per hour Service rate, μ = 25 customers per hour The average number of…

Answered: A post office has a counter for…

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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Question #4: 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.)
Question 3) Waiting Line Analysis Helen runs a small shop where she provides a service. She is able to process an average of 8 customers per hour. An average of 5 customers per hour seek this service at her shop. What is: a) the probability that Helen will not be working with a customer (no customers) when the shop phone rings? b) the probability of 4 customers in the system? c) the average time a customer spends waiting in line (in minutes)?
Question 4 CWD Business systems maintains a successful Telecom sales department for Top up call credit in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the department are answered automatically by an answering machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 15 per hour. The clerk is capable of taking an order in an average of 3 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $15 per hour, but because of lost goodwill and sales, CWD loses about $30 per hour of customer time spent waiting for the clerk to take an order. Part A a. What is the probability that no customers are in the system (Po)? b. What is the average number of customers waiting for service ( Lq)? c. What is the average number of customers in the system (L)?d. What is the average time a…
Which of the following departments would be responsible for approving a bill-to-master account-credit to an organization? Question 15 options: a) Front desk b) Security c) Controller d) Sales
Question #5: If the restaurant runs a sale and the customer arrival rate increases by 20%, how would this change the total time expected to serve a customer? How would this change the average number of cars in the drive thru-line?
Question 4Consider a birth death model with birth rates in states n = 0, 1, . . . and death rates in states n = 1, 2, . . (a) Give the detailed balance conditions for the equilibrium probability of being in state n, for n = 0, 1, . . . and explain how they are derived. (b) Using the detailed balance conditions derive an expression and state any condition needed to ensure that the equilibrium distribution exists. (c) i Now consider the M/M/1 queue with arrival rate λ and service rate µ and explain how it can be modelled as a birth death model. ii. For the M/M/1 queue derive the form of , the equilibrium distribution of the number of customers present, and give any conditions needed to ensure the existence of the equilibrium distribution. Derive the mean value of the equilibrium distribution
QUESTION 14 Requiring employees to wear safety glasses is an example of a A. procedure. B. policy. C. rule. D. strategy.
Question The new accounts loan officer of the Millennium Commercial Bank interviews all customers for new accounts. The customers desiring to open new accounts arrive at the rate of 4 per hour, according to a Poisson distribution, and the accounts officer spends an average of 12 minutes with each customer, setting up a new account. Required A. Determine the operating characteristics (P0, L, Lq, W, Wq and Pw) for this system. B. Add an additional accounts officer to the system described in this problem so that it is now a multiple-server queuing system with two channels and determine the operating characteristics required in part A.
Question The new accounts loan officer of the Millennium Commercial Bank interviews all customers for new accounts. The customers desiring to open new accounts arrive at the rate of 4 per hour, according to a Poisson distribution, and the accounts officer spends an average of 12 minutes with each customer, setting up a new account. Required 1. Determine the operating characteristics (P0, L, Lq, W, Wq and Pw) for this system. 2. Add an additional accounts officer to the system described in this problem so that it is now a multiple-server queuing system with two channels and determine the operating characteristics required in part A.
Question 2 A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N ) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by c(N) = a+bN, for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver uses the road at most once. the number of drivers that join the road is Ne = (v−a)/b (iv) Suppose that the government charges a toll t (a congestion charge) for each journey. Find the optimum toll. Interpret your answer in terms of the externality that each driver imposes on others.
Operating Systems Question 15 What is the main disadvantage of busy waits?
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