Dean Smith is dissatisfied with the time it takes to get a new faculty ID made and believes more servers will speed up service and reduce costs thanks to shorter lines. Prof. Karen is tasked to study the situation. Prof. Karen observes an average of 20 customers/hr arriving and each technician (service window) serves 5 customer/hr, on average. Assume an M/M/s queue system. Prof. Karen calculates the operational cost of each server as $20/hr, and assumes a cost of waiting in the SYSTEM as $25/hr per customer. What is the optimal number of service windows to minimize total cost?
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- The check-out area of a grocery store has the average customer interarrival time = 2 minutes, the average processing time of each cashier = 6 minutes, and in total 4 cashiers. The average waiting time for each customer is 8 minutes. What is the average number of customers in the system (including waiting and using the service)? a 3 b 7 c 6 d 4One 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)In an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. If the service process is automated (resulting in no variation in service times but the same service rate), what will be the resulting performance measurements? (Round all answers to three decimals.) What is the utilization? What is the expected number of customers in the system (L)? What is the expected waiting time (in hours) for the system (W)? What is the expected number of customers in the queue (Lq)? What is the expected waiting time (in hours) in the queue (Wq)?
- On average, how much time would a server need to spend on a customer to achieve a service rate μ, with 30 customers per hour?During the recent pandemic, the seaport in Savannah Georgia, the third busiest in the United States, averaged loading or unloading 5.5 cargo ships per week. The average time to unload a ship is 1.95 days. Multiple cranes to load and unload the ship operate six days a week. Do not round intermediate calculations. a. How many ships are waiting to be unloaded on average using Little's Law? Round your answer up to the nearest whole number. ship(s) b. During the pandemic, at times, demand doubled, how many ships are waiting to be unloaded on average using Little's Law? Round your answer up to the nearest whole number. ship(s) C. If demand remains at 5.5 cargo ships per week and through better scheduling, training, and crane operations, the average time to unload a ship lowers to 1.05 days, how many ships are waiting? Round your answer up to the nearest whole number. ship(s)A call center has been serving 900 customers per day, with a 10% capacity cushion. There have been complaints about the length of time customers have to wait before their call is answered. If the manager of the call center wants to double the capacity cushion, how much extra capacity is needed?
- Eat Well is a tiny drive-through quick food restaurant in a shopping malltown, manned by an efficient employee named John. Customers arrive at the counter at a rate of one per 15 minutes on average, with a Poisson delivery for customer entry. Each food order takes John no more than ten minutes to process. a) How many customers are handled on average at any given time? b) The anticipated amount of clients that would be represented. c) Determine the average consumer wait time in the scheme. d) How much of the day is John Idle idle?If Melanie adds an additional server at Clean Machine carwash, the service rate changes to an average of 16 cars per hour.Th e customer arrival rate is 10 cars per hour. Melanie has askedyou to calculate the following system characteristics:(a) Average system utilization(b) Average number of customers in the system(c) Average number of customers waiting in linePlease 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?
- Determining the Number of ServersIn the service department of the Glenn-Mark Auto Agency, mechanics requiring parts for auto repair or service present their request forms at the parts department counter. The parts clerk fills a request while the mechanic waits. Mechanics arrive in a random (Poisson) fashion at the rate of 40 per hour, and a clerk can fill requests at the rate of 20 per hour (exponential).If the cost for a parts clerk is $30 per hour and the cost for a mechanic is $60 per hour, determine the optimum number of clerks to staff the counter. (Because of the high arrival rate, an infinite source may be assumed.)Saved Help Save & Exit Su In an M/MA queueing system, the arrival rate is 3 customers per hour and the service rate is 5 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 time d. What is the expected number of customers in the queue(Lq)? (Round your answer to 3 decimal places.) Mc Graw Hill Prev 1 of 5 Next >A post office clerk operates with 75% utilization. The coefficient of variation for the service process is 0.6 and the coefficient of variation of the arrival process is 0.9. The average processing time is 4 minutes. What is the average time a customer spends in the system according to the single-server queue model? Multiple Choice ○ 7.02 minutes 4 minutes 11.02 minutes О 3.51 minutes