3 The M/M/1 QueueDuring peak time, customers arrive at a bank teller window (with a single teller) at a rate of 23per hour, where the teller can serve 25 per hour. This problem will allow you to investigate (via asimple extension of the mean queue size formula) the effect of highly-variable service times on ourfamiliar queuing metrics. The diagram below stylizes the queuing system:WaitingServiceCalculate the marginal probability P (T > oT).a.O b. 0.25O c. 0.63O d. 0.75Calculate the mean time a customer spends at the bank (waiting time plus service time) inminutes.O a. 30 minutesO b. 27.6 minutesO c. 2.4 minutesO d. 7 minutes

λ = Arrival rate = 23 customers/hrμ = Service rate = 25 customers/hr1λ=a = Inter arrival time

Answered: 3 The M/M/1 Queue During peak time,…

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...

See similar textbooks

Similar questions

A proposal has been presented to the government of Newfoundland and Labrador that would build a new section of highway which would provide improved access for residents of a remote coastal area near Bonavista. The highway would be 16 kilometres in length. The initial proposal called for 7 toll booths, each staffed by an employee. But a subsequent proposal recommended replacing the employees with machines. Many factors must be considered because the intended employees are unionized. However, one of the government's concerns is the effect that replacing the employees with machines will have on the times the drivers spend in the system. Customers will arrive to any one toll booth at a rate of 9 per minute. In the exact-change lanes with employees, the service time is essentially constant at 5 seconds for each driver. With machines, the average service time would still be 5 seconds, but it would be exponential rather than constant, because it takes time for the coins to rattle around in…
A horologist (watchmaker) is typically able to service a mechanical watch in about 120 minutes (exponential distribution). Assuming an 8 hour work-day, the watchmaker averages 3 customers arriving at his shop every day following a poisson distribution. The watchmaker just purchased a new machine that will polish the dial and crystal reducing his service time by 20 minutes per watch. How much will the line for a watch waiting to be serviced be reduced by the watchmaker using this new machine, assuming no increase in customer demand? O 2.25 watches waiting for service O The number waiting to be serviced will be reduced by about 1.2 watches O The number waiting to be serviced will be reduced by about 0.4 watches The number waiting to be serviced will be reduced by about 1.45 watches
Customers in a small retail store arrive at the single cashier on average every 6 minutes. The average service time for the cashier is 5 minutes.Arrivals tend to follow a Poisson distribution, and service times follow anexponential distribution. We need to analyze this waiting-line system. (g) Should the retail store consider creating a second cashier lane?(h) A cash machine manufacturer has offered an advanced system that willreduce service time to 2 minutes per customer. The cost of the newmachine would be the same as opening a second cashier lane, so theowner has decided to buy the new system only if it reduces wait timesover the two-cash option. Evaluate the two options (advanced cash or atwo-cash system) and suggest which option you would choose.
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?
Let a queuing system have the Kendall model (M/M/1) : (GD/infinity/infinity). Assume A < µ. Does W, for the service discipline FIFO equal W, for the service discipline SIRO? O I have no idea. no yes It cannot be determined.
Customers arrive at a bank counter at an average rate of 3customers per hour.a) Suggest a suitable distribution to model the number ofcustomers arriving at the counter, X, per minute.b) State clearly any assumptions you have made by suggestingthis model.c) Using your model,I. Find the probability that no customer arrive in a givenminute.II. Find the probability that at most 4 customers arrive in agiven minute.III. In any given 4 minutes period, find ? such that?(? > ?) = 0.0487.IV. Check the answer of part I and part ii using RStudio.
Customers arrive at a one window drive according to a poison distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced ones. Other vehicles are have to wait outside this space. Calculate:a. A. probability that an arriving customer can drive directly to the space in front of the windowb. Probability that an arriving customer will have to wait outside the directed space c. How long an arriving customer is expected to wait before getting the service?
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 the corresponding 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 is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
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. 15.What is the average time in minutes that a customer spends in the system? 3.8 mins 7 mins 4.8 mins 8.9 mins
A firm is engaged in both shipping and receiving activities. The management is always interested in improving the efficiency of new innovations in loading and unloading procedures. The arrival distribution of trucks is found to be Poisson with arrival rate of 3 trucks per The service time distribution is exponential with unloading rate of 4 trucks per hour. Determine (i) expected number of trucks in the queue, hour. (ii) expected waiting time of the truck in the queue, (iii) probability that the loading and unloading dock and workers will be idle, (iv) what reductions in waiting time are possible if loading and unloading is standardised?
please dont answer in image format. Do type Thnks
Ali Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a.Compute the average number of cars in line. b.Calculate the value of probability that there are no car in the system. c.Compute the average time that a car spends in the system.

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Operations Management

ISBN:

9781259667473

Author:

William J Stevenson

Publisher:

McGraw-Hill Education

Operations and Supply Chain Management (Mcgraw-hi…

Operations Management

ISBN:

9781259666100

Author:

F. Robert Jacobs, Richard B Chase

Publisher:

McGraw-Hill Education

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Operations Management

ISBN:

9781259667473

Author:

William J Stevenson

Publisher:

McGraw-Hill Education

Operations and Supply Chain Management (Mcgraw-hi…

Operations Management

ISBN:

9781259666100

Author:

F. Robert Jacobs, Richard B Chase

Publisher:

McGraw-Hill Education

Business in Action

Operations Management

ISBN:

9780135198100

Author:

BOVEE

Publisher:

PEARSON CO

Purchasing and Supply Chain Management

Operations Management

ISBN:

9781285869681

Author:

Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson

Publisher:

Cengage Learning

Production and Operations Analysis, Seventh Editi…

Operations Management

ISBN:

9781478623069

Author:

Steven Nahmias, Tava Lennon Olsen

Publisher:

Waveland Press, Inc.

SEE MORE TEXTBOOKS