3. (for all students) Jobs arrive to a single server queue according to a Poisson process with a rate of 2.5 jobs per hour. You have collected past data and determined that service times have a mean of 19.8 minutes and variance of 123.8 minutes squared.
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- Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.d. Calculate the probability a customer will spend more than an hour at the bakery(time in queue plus service time).In an M/MA queueing system, the arrival rate is 4 customers per hour and the service rate is 6 customers per hour. a. What is the utilization? (Round your answer to 3 decimal places.) Utilization b. What is the expected number of customers in the system (2)? (Round your answer to 3 decimal places.) Expected number of customers c. What is the expected waiting time in the system (W)? (Express the waiting time in hours, round your answer to 3 decimalCustomers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.c. How many customers are in the bakery on average?
- In an M/MA queueing system, the arrival rate is 6 customers per hour and the service rate is 8 customers per hour. a. What is the utilization? (Round your answer to 3 decimal places.) Utilization b. What is the expected number of customers in the system (L)? (Round your answer to 3 decimal places.) Expected number of customers c. What is the expected waiting time in the system (W? (Express the waiting time in hours, round your answer to 3 decimal places.) Expected waiting timeA single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service rate of 15 customers per hour. The average length of time customers will spend in the system is: O a. 2.667 minutes O b. 0.1111 minutes O c. 6.667 minutes O d. 0.04444 minutesIn an M/MA queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. 0. What is the utilization? (Round your answer to 3 decimal places.) Utilization b. What is the expected number of customers in the system (L)? (Round your answer to 3 decimal places.) Expected number of customers c. What is the expected waiting time in the system (W? (Express the waiting time in hours, round your answer to 3 decimal places.) Expected waitng time