LambdaMuProbability system is emptyAverage number waiting for service in the queueAverage number in system (queue and in service)Average time waiting for service (time in queue)vaiting time in system (waiting time plus service time)Probability arrival has to waitn=bability of n units in the system (queue and in service)10120.1674.1675.0000.4170.5000.83330.096 Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is five trucks per hour, and themean service rate is seven trucks per hour. Use the Single Server Queue Excel template in MindTap to answer the following questions. Do not roundintermediate calculations. Round your answers to three decimal places.a. What is the probability that the truck dock will be idle?b. What is the average number of trucks in the queue?truck(s)c. What is the average number of trucks in the system?truck(s)d. What is the average time a truck spends in the queue waiting for service?hour(s)e. What is the average time a truck spends in the system?hour(s)f. What is the probability that an arriving truck will have to wait?g. What is the probability that more than two trucks are waiting for service?

Answered: Assume trucks arriving 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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In an M/MA queueing system, the arrival rate is 8 customers per hour and the service rate is 11 customers per hour. (Round your answers to 3 decimal places.) a. What is the probability that the server will be idle? Probability b. What is the probability of having exactly 4 customers in the system? Probability c. What is the probability of having 3 or fewer customers in the system? Probability
The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of two jobs per 8-hour day. The company's repair facility is a single-server system operated by a repair technician. The service time varies, with a mean repair time of 3.0 hours and a standard deviation of 2.1 hours. The company's cost of the repair operation is $26 per hour. In the economic analysis of the waiting line system, Robotics uses $37 per hour cost for customers waiting during the repair process. (a) What are the arrival rate and service rate in jobs per hour? (Round your answers to four decimal places.) λ = μ = (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) L = 9 L = W₁ = Wa W = h Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $ (c) The company is considering purchasing a computer-based equipment repair system that would…
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
Consider a system with Poisson distributed arrival rate with average of 10 clients per day. The service time is exponentially distributed with 8 clients per day. If the cost for operating each server is $20 per day and the cost of holding a client in the system is $200 per day, What is the total cost of operating with 5 servers? Answer is $350.65 please explain.
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?
The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 12 minutes to land and clear the runway (following an exponential distribution). Planes arrive at the airport at the rate of one every 15 minutes. The arrival rate follows a Poisson distribution. A plane is considered to have entered the “system” once it has notified the airport that it is in the vicinity and wants to land. For purposes of this analysis, you can ignore the planes taking off. a) Determine the average number of planes that are in the system waiting to land. b) Find the average time a plane is in the system either waiting to land or landing. c) What is the probability that a plane approaching the airport will find at least two other that are already in the “system” that is waiting to land? d) Suppose that the cost assigned to a plane while it is waiting to land (in the stack) is $1,000…
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
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