An average of 12 jobs per hour arrive at our departmentalprinter.a Use two different computations (one involving thePoisson and another the exponential random variable) todetermine the probability that no job will arrive duringthe next 15 minutes. b What is the probability that 5 or fewer jobs will ar-rive during the next 30 minutes?
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An average of 12 jobs per hour arrive at our departmental
printer.
a Use two different computations (one involving the
Poisson and another the exponential random variable) to
determine the probability that no job will arrive during
the next 15 minutes.
b What is the probability that 5 or fewer jobs will ar-
rive during the next 30 minutes?
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- The following data has been collected on the number of customers seen to arriveto a museum in a succession of 5-minute intervals: 5, 1, 3, 7, 5, 5, 6, 7, 5, 7, 4, 8, 1,5, 2, 3, and 5. Estimate the squared coefficient of variation of the arrival process. Ifthis data was known to come from a Poisson process, what would be your estimateof l, the rate of customer arrivals?A petrol station in the capital Kingstown has a single pump manned by one attendant.Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on anaverage. Assume the arrival rate is Poisson probability distribution and service rate isexponentially distributed. Arrivals tend to follow a Poisson distribution, and service timestend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill andsales, station loses about $15 per hour of customer time spent waiting for the attendant toservice and order. Part BThe Petrol station is considering adding a second pump with an attendant to servicecustomers. The station would pay that person the same $10 per hour.Using appropriate formula for the multiple channel model, answer the following questions: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…A petrol station in the capital Kingstown has a single pump manned by one attendant.Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on anaverage. Assume the arrival rate is Poisson probability distribution and service rate isexponentially distributed. Arrivals tend to follow a Poisson distribution, and service timestend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill andsales, station loses about $15 per hour of customer time spent waiting for the attendant toservice and order. 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 customer waits for service(Wq)? e. What is the average time in the system (W)?f. What is the probability that a customer will have to wait for service (Pw)?g What is the probability that there is exactly 2…
- Doña Blanca plans to open a small car wash and must decide how much space to allocate to waiting cars. She estimates that customers will arrive randomly (Poisson process) at an average rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers will take their car elsewhere. The total time attributable to washing a car has exponential distribution with mean 3 minutes. Compare the fraction of potential customers lost due to lack of waiting space if a) 2 and b) 4 spaces (in addition to the wash location) are provided.A new mall is considering the number of employees on desk dutyinformation, currently only one employee is employed. Based on the informationobtained, it is known that customers will come to the information desk with an average of 20people per hour. It takes an average of 3 minutes to answer the questions. Assumedthat the customer arrival rate follows the Poisson distribution and service timefollowing an exponential distribution. Assume that the employee at the information desk earns Rs50.000,- per hour. The cost of waiting time, if the customer is not satisfied, is IDR 35,000,-per hour of time spent in queue. a. The mall management has decided to consider using two peopleemployee at the information desk. Propose to mall management whether to use aor two employees at the information desk. Explain your answer.20. A small bank is trying to determine the number of tellersto employ. The total cost of employing a teller is $100per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day atthe bank, and both service times and interarrival times areexponentially distributed. If the delay cost per customerday is $200, how many tellers should the bank hire?
- Customers arriving at a service center are assigned to one of three categories, with category 1given the highest priority. Records indicate that an average of nine customers arrive per hour andthat one-third are assigned to each category. There are two servers, and each can process customers at the rate of five per hour. Arrival and service rates can be described by Poisson distributions.a. What is the utilization rate for this system?b. Determine the average waiting time for units in each class.c. Find the average number of customers in each class that are waiting for serviceChapter 5. (M/M/s/K Model). Leia is responsible for 13 data units in the IT offices in a small business called DataWish. Each data unit runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the “arrival” of each data unit for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (ρ) % Performance Measures P0 (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the system) weeks Wq (average time in the queue) weeks c. If we assign a cost of waiting as $400 per week per data unit and $800 per…The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of l = 3 per day (approximately Poisson in nature). The crew can service an average of m = 8 machines per day, with a repair time distribution that resembles the exponential distribution. (a) What is the utilization rate of this service system? (b) What is the average downtime for a machine that is broken? (c) How many machines are waiting to be serviced at any given time? (d) What is the probability that more than one machine is in the system? Probability that more than two are broken and waiting to be repaired or being serviced? More than three? More than four?