A firm is engaged in both shipping and receiving activities. The management is alwaysinterested 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 perThe 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?

Let me state the given data, As per the instruction, the first three sub-parts are taken for…

Answered: A firm is engaged in both shipping and…

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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Customers arrive randomly to an airport shoe-shine stand with only ONE attendant at a rate of 8 per hour. The average length of a shoe shine is 12 minutes. Assume that service times are exponentially distributed and that the queuing system model is (M/M/1):(GD/infinity/infinity). Does this queuing system have a steady state? It cannot be determined. Yes none of the other choices No
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?
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Please do not give solution in image formate thanku. A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Required: (g) Assume that the information desk employee earns $10 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day.
A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What is the expected average number of snowplows in the garage (waiting for repair and being repaired)? 5 1.04 1.67 8
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?
Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5 What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hours
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At the British Grand Prix’s Silverstone Circuit’s 3 July 2022 race, it was another battle royal of sorts as the Formula 1 drivers battled for maximum points in the series. The fans seeking to purchase tickets started arriving from 10:00 am running all through 1:30 pm, when the gates closed in readiness for the race. The fans were observed to arrive at an average of 2,048 each hour, and were being served at a rate of 533 every fourteen minutes. Some fans had already purchased their tickets earlier via the ticket sales agency e-commerce portal. The Silverstone gallery has a 150,000 seating capacity. The gallery was 95% full for this grace. Given the enthusiasm of the fans that were trickling in, this was going to be the race of the month. required; iv). On average, how long does a fan spend in the circuit ticketing system? v). What is the probability of having more than 5 but less than 12 fans in the circuit ticketing system? Determine the efficiency of the Silverstone circuit…
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
Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean oftwo hours per call. Requests for copier repairs come in at a mean rate of three per eight-hour day(assume Poisson). Determine the following: ( l) The average number of customers awaiting repairs (2) System utilization (3) The amount of time during an eight-hour day that the repairman is not out on a call (4) The probability of two or more customers in the system

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