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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[Queuing Theory - Operation research] The take-out counter at an ice-cream parlor is serviced by one attendant. Customers arrive according to a Poisson process, at a mean arrival rate of 30 per hour. They are serviced on a FCFS basis, and because of the quality of the ice cream, they are willing to wait if necessary. The service time per customer appears to be exponentially distributed, with a mean of 1.5 minutes. Determine the following: (a) probability that the system is idle (b) average number of customers in the system (c) amount of time a customer should expect to wait before service (d) probability that a customer will have to spend more than 15 minutes in the queue
In an M/MA queueing system, the arrival rate is 5 customers per hour and the service rate is 9 customers per hour. If the service process is automated (resulting in no varlation in service times but the same service rate), what will be the resulting performance measurements? (Round your answers to 3 decimal places.) a. What is the utilization? Ubization b. What is the expected number of customers in the system (L)? Number of customers c. What is the expected walting time (in hours) for the system (W? Waiting timetin nours)
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?
The state operates a weigh station for trucks traveling on the highway. Every truck must pull off the highway, enter the weigh station, and undergo state inspection procedures before counting on. Trucks arrive at this station at a poisson rate of seven per hour. The time to inspect/weigh a truck varies, having an exponential probability density with a mean of 7 minutes.A. How many trucks are detained at the station on the average? B. How long can a truck expect to be detained?C. How many trucks are lined up in front of the station on the average?D. How long on the average does a truck driver have to wait in line for the truck to beinspected?
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
Christmas Airlines is reviewing its check-in procedures in anticipation of college students celebrating being done with finals.It takes an average of three minutes per passenger to check luggage and issue boarding passes.During flight operations, a passenger arrives, on average, every 5 minutes. Service times and interarrival times both have an exponential distribution. a.Define the states of this queuing systems. b.If there is a single clerk, provide the balance equation for state 3 for this queuing system. c.If there is a single clerk, what is the probability that the clerk will be idle?

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