Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. On average, how long (in minutes) does it take to service each student?

Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take, on average, 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. What percentage of time is Judy idle? Note: Round your answer to 1 decimal place.   How much time, on average, does a student spend waiting in line? Note: Do not round intermediate calculations. Round your answer to the nearest whole number.   How long is the (waiting) line on average? Note: Round your answer to 2 decimal places.   What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? Note: Do not round the intermediate calculations. Round your answer to 2 decimal places.

Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to nine. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.06 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.5 machines per hour.   Compute the operating characteristics if the company retains the single-employee repair operation. If required, round your answers to four decimal places.   P0 = fill in the blank 1   Lq = fill in the blank 2   L = fill in the blank 3   Wq = fill in the blank 4 hours   W = fill in the blank 5 hours Compute the operating characteristics if a second employee is added to the machine repair operation. If required, round your answers to four decimal places.   P0 = fill in the blank 6   Lq = fill in the blank 7   L = fill in the blank 8   Wq = fill…

Customers arrive at the lobby of the exclusive and expensive Ritz Hotel at the rate of 40 per hour (Poisson distributed) to check in. The hotel normally has three clerksavailable at the desk to check guests in. The average timefor a clerk to check in a guest is four minutes (exponentially distributed). Clerks at the Regency are paid $12 perhour and the hotel assigns a goodwill cost of $2 per minutefor the time a guest must wait in line. Determine if the present check-in system is cost effective; if it is not, recommend what hotel management should do

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?