Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 8 haircuts per hour. What is the number of average customers waiting for haircuts? (Round to two decimals) What is the average number of customers in the shop? (Round to two decimals) The average time a customer waits until it is his or her turn = minutes (Round to two decimals) The average time a customer spends in the shop = munites (Round to two decimals) The percentage of time that Rich is busy = percent (Roound to nearest whole number)

Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 8 haircuts per hour. What is the number of average customers waiting for haircuts? (Round to two decimals) What is the average number of customers in the shop? (Round to two decimals) The average time a customer waits until it is his or her turn = minutes (Round to two decimals) The average time a customer spends in the shop = munites (Round to two decimals) The percentage of time that Rich is busy = percent (Roound to nearest whole number)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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Customers arrive at Rich Dunn's Styling Shop at a rate of 4 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 8 haircuts per hour. a) The average number of customers waiting for haircuts = 0.500.50 customers (round your response to two decimal places). b) The average number of customers in the shop = nothing customers (round your response to two decimal places).
Customers arrive at the company's service office at an average of one every 20 minutes. Their requests take, on average, 15 minutes to be processed. The service counter is staffed by only one employee, who works six hours per day. Assume Poisson arrivals and exponential service times. What model should you use? What percentage of time is the employee idle? How long is the waiting line, on average? How much time, on average, does a customer spend waiting in line? What is the probability that an arriving customer, just before entering the office, will find at least one other customer waiting in line?
12-17 Automobiles arrive at the drive-through window at a post office at the rate of four every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. a. What is the average time a car is in the system? b. What is the average number of cars in the system? c. What is the average time cars spend waiting to receive service? d. What is the average number of cars in line behind the customer receiving service? e. What is the probability that there are no cars at the window? f. What percentage of the time is the postal clerk busy? g. What is the probability that there are exactly two cars in the system?
Customers arrive at Rich Dunn's Styling Shop at a rate of 2 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 6 haircuts per hour. a) The average number of customers waiting for haircuts = ? enter your response here customers (round your response to two decimal places). b) The average number of customers in the shop = ?customers (round your response to two decimal places). c) The average time a customer waits until it is his or her turn = ? enter your response here minutes (round your response to two decimal places).
One field representative services 5 customers for a computer manufacturer. Customers request assistance at an average (Poisson-distributed) rate of once every 3.1 working days. The field representative can handle an average (Poisson-distributed) of 1.0 call per day. Determine: Use Table 1. a. The expected number of customers waiting. (Round "X" value to 2 decimal places. Round your answer to 3 decimal places.) Expected number of customers waiting b. The average length of time customers must wait from the initial request for service until the service has been completed. (Round your answer to 2 decimal places.) Average length of time days c. The percentage of time the service rep will be idle. (Round your answer to 1 decimal place.) Percentage of Idle time d. By how much would your answer to part a be reduced if a second field rep were added? (Round your answer to 3 decimal places.) Reduced number of customer(s)
I ONLY NEED HELP WITH PARTS B,C,D PLEASE The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three 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 2.2 hours and a standard deviation of 1.4 hours. The company's cost of the repair operation is $27 per hour. In the economic analysis of the waiting line system, Robotics uses $36 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.) ?= 0.375 IS CORRECT ?= 0.4545 IS CORRECT (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) Lq= 1.4622 IS WRONG L= Wq= h W= h Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $…
At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 11 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? b. What is the average time that a vehicle must wait to get through the system? c. What is the utilization of the inspector? d. What is the probability that when you arrive there will be three or more vehicles ahead of you?
An average of 90 patrons per hour arrive at a hotel lobby(interarrival times are exponential), waiting to check in. At present, there are 5 clerks, and patrons are waiting in a singleline for the first available clerk. The average time for a clerkto service a patron is 3 minutes (exponentially distributed).Clerks earn $10 per hour, and the hotel assesses a waitingtime cost of $20 for each hour that a patron waits in line.a Compute the expected cost per hour of the currentsystem.b The hotel is considering replacing one clerk with an Automatic Clerk Machine (ACM). Management esti-mates that 20% of all patrons will use an ACM. An ACM takes an average of 1 minute to service a patron.It costs $48 per day (1 day 8 hours) to operate anACM. Should the hotel install the ACM? Assume thatall customers who are willing to use the ACM wait in asingle queue.
Please do not give solution in image format thanku Customers checking out at Food Mart arrive in a single-line queue served by two cashiers at a rate ofeight per hour according to a Poisson distribution. Each cashier processes customers at a rate of eightper hour according to an exponential distribution.1. If, on average, customers spend 30 minutes shopping before getting in the checkout line, what isthe average time a customer spends in the store?2. What is the average number of customers waiting for service in the checkout line?3. What is the probability that a customer must wait?4. What assumption did you make to answer this question? I need this in Excel format please. Can you also include a small interpretation with the answers ?