Suppose a theme park has a roller coaster has a train with six carriages. Each carriage takes eight customers. A train arrives at the loading point every 30 seconds. However, each hour, on the hour, the roller coaster is shut down for 3 minutes to check the system. 1. What is the capacity of the roller coaster? We suppose the customers arrive at the ride at a rate of 90 customers per minute and all customers wait for the service. 2. What is the average utilization rate of the roller coaster? We recall that a useful service metric is the probability that a customer is delayed. Hitotaka Sagasegawa (1977) developed a useful and simple approximation for the probability of delay pd , where pd is approximately equal to a with a = - 1 + [2 (s+1)]1/2 3. Compute the probability of delay.

Suppose a theme park has a roller coaster has a train with six carriages. Each carriage takes eight customers. A train arrives at the loading point every 30 seconds. However, each hour, on the hour, the roller coaster is shut down for 3 minutes to check the system. 1. What is the capacity of the roller coaster? We suppose the customers arrive at the ride at a rate of 90 customers per minute and all customers wait for the service. 2. What is the average utilization rate of the roller coaster? We recall that a useful service metric is the probability that a customer is delayed. Hitotaka Sagasegawa (1977) developed a useful and simple approximation for the probability of delay pd, where pd is approximately equal to 2 with a=1+[2(s+1)]1/2 3. Compute the probability of delay