The average time customers spend waiting in line is also cut in half. Similar improvements can be realized by smoothing arrival times (e.g., by use of appointments). Wanda's Car Wash & dry is an automatic, five-minute operation with a single bay. On a typical Saturday morning. cars arrive at a mean rate of eight per hour, with arrivals tending to follow a Poisson distribution. Find a. The average number of cars in line. b. The average time cars spend in line and service. V14 Av. no. of cars waiting in line = 2000-2201212-8) -0.667 +12=0. Arrive Rate = = 8 cars per hour Service Rate = = 1 per 5 minutes, or 12 per hour 8 = 0.667 car 2u (A Av. time cars spend in line and service = W, 3+ 1.0.667 = 0.167 hours, or 10 minutes H 8 A departmental store has one cashier. During the rush hours, customers arrive at a rate of 20 per hour. The average number of customers that can be handled by the cashier is 24 per hour. Assume the conditions for use of the single channel queuing model. Find out average time a customer spends in the system. The usual notations are given: Arrival Rate = 1 = 20 customers/hour and service rate == 24 customers/hour Average no. of customers in the system = L - - 2220 - 20 = 5 customers customer spends in the system = W, = = 0.25 hour = 15 mins. Average time Illustration 11. As a tool service centre the arrival rate is two per hour and the service potential is three per hour. Simple queue conditions exist. The hourly wage paid to the attendant at the service centre is 21.50 per hour and the hourly cost of a machinist away from his work is 4 Calculate: (0) The average number of machinists being served or waiting to be served at any given time. () The average time a machinist spends waiting for service. (iii) The total cost of operating the system for an eight-hour day. (iv) The cost of the system if there were two attendants working together as a team, each paid 1.50 per hour and each able to service on average 2 per hour