Gursoy Car Wash will wash a car in exponential amount of time with mean 10 minutes. Arrivals occur as a Poisson process with rate 5 per hour. a) What is percent of the time the car wash is idle? b) On the average how many cars are in the system? c) On the average how many cars are waiting in line? d) On the average how long does a car spends in the system? e) What fraction of times there are more than 3 cars in the system? f) What is the probability that a car spends more than 30 minutes in the system?
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- In queuing system 1.- What is the average Queue lenght ? What is the expected waiting time ? 2.-Customers in LineWestern National Bank is considering opening a drive-thru window for customer service. Management estimates that customers will arrive at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of one every three minutes.Part 1 Assuming Poisson arrivals and exponential service, find1. Utilization of the teller.2. The average number in the waiting line.3. The average number in the system.4. The average waiting time in line.5. The average waiting time in the system, including service.Fantasy Park has two service desks, one at each entrance of the park. Customers arrive at each service desk at an average of one every six minutes. The service rate at each service desk is four minutes per customer.
- 38) Daisy's Shop Daisy runs a shop where she is able to serve an average of 9 customers per hour. An average of 5 customers per hour arrive at her shop. What is the average number of customers at the shop (either waiting in line or being served)? Group of answer choices a) 1.8 b) 2.67 c) 1.25 d) 0.56 e) 0.69 f) 3.00Using the Queuing Theory principles, a) List Lq, and Wq for all of the stations in a table b) Determine the performance measure (L,W) of the system. 0.25 S2 S4 0.6 Hz=15 H4=13 2=15 S1 S5 H=20 0.9 Hs=15 S3 H3=840) Burger Cart April has a popular burger cart where an average of 12 customers per hour arrive to buy a burger. April can serve an average of 20 customers per hour. What is the average time a person spends waiting in line? Group of answer choices a) 16.0 minutes b) 2.25 minutes c) 3.0 minutes d) 12.0 minutes e) 7.0 minutes f) 4.5 minutes g) 9.0 minutes h) 1.2 minutes
- 13. Movie Tonight is a typical video and DVD movie rental outlet for home viewing customers. During the weeknight evening, customers arrive at Movies Tonight at the average rate of 1.25 customers per minute. The checkout clerk can serve an average of two customers per minute. Assume Poisson arrivals and exponential service times.What is the probability that no customers are in the system?What is the average number of customers waiting services?What is the average time a customer waits for service to begin?Do the operating characteristics indicate that the one-clerk check out system provides an acceptable level of service?13. Suppose AirOM passengers arrive to the check-in desk every 100 seconds (on average). The desk is staffed by a single ticketing agent, who takes 1.4 minutes (on average) to process a passenger. The arrivals follow a Poisson process and the service time is distributed exponentially. What is a passenger’s average waiting time (in seconds)? Enter a single number as your answer. If your final number is not integer, keep two decimal places in your answer.Please do not give solution in image formate thanku. λ= 4 customers per hour; μ = 5 customers per hour; M= 1 An average of 20 customers arrive at a service center each hour. There are two servers on duty, and each can process 12 customers per hour. a) What is the system utilization? b) What is the average waiting time for customers who actually have to wait? c) What is the average time customers wait in line for service?
- Identify 10 real-life examples of queuing systems withwhich you are familiar.c. An average of 18 customers arrive at a service center each hour. There are two servers on duty,and each server can process 12 customers per hour.(1) What is the system utilization?(2) What is the average number of customers in the system (waiting plus being served)?(3) What is the average time customers wait in line for service?(4) What is the average waiting time for customers who actually have to wait?Give 3 interesting real-life empirical studies about queuing theory and provide some short information.