Quiz 9: The Impact of Variability on Process Performance: Throughput Losses

Business

In order to compute the probability of m resources being utilized and a newly arrived unit is rejected, the Erlang Loss Formula table has to be used. a. The average arrival rate is 55 units per hour. So, the average interarrival time, img The average processing time, img img The number of servers, m = 7 Look up the Erlang Loss Formula table for img So, the probability that all the seven servers are busy is img b. Compute the flow rate, R using the following formula: img So, the flow rate i.e. the customers served per hour is img c. Compute the customer lost customer per hour by subtracting the flow rate from the average arrival rate. So, img So, customers lost per hour is img

Consider the following information: Number of guards img = 5 Calls per hour = 12 calls Therefore, inter-arrival time img = 60/12 = 5 minutes Activity time img = 90 minutes a. Determine the fraction of time the incoming alarms are directed to the police as shown below: Initially determine the ratio of activity time to inter-arrival time img using given formula: img Now, use the Erlang loss table to find the probability that that all five servers are utilized. For the table it is found that for img = 5 and img the probability that all servers are busy is, img Hence, the fraction of time the incoming alarms are directed to the police is 0.7402 or 74.02%. b. Determine the total amount the home security has to pay the local police every month as shown below: Determine the lost customer using given formula: img The local police charges $5000 for every call. Therefore, the total amount that home security pays every month to local police is calculated as shown below: img Hence, the home security has to pay img to the local police.

The given information is shown below: Number of copies = 9 Arrival rate, A img Average Rental duration, P = 36 hours (a) Calculate the likelihood that a customer going to the video store would find the movie available as shown below : img Use "Erlang Loss" Table to find the probability with all utilized servers Probability of r (22.5) = 62.44% Thus, people going to video store would find the movie available with the probability of (100-62.44) = 37.56% (b) Calculate the revenue of the store per day as shown below: Flow rate = 0.235 customers per hour. The Revenue of the store img Thus, the Revenue of the store per day is $28.16 (c) The loss rate is 0.39 customers per hour and each of them get $1. Calculate the loss for the day as shown below: img Thus, loss for the day is $9.36 (d) Number of copies = 9 Arrival rate, A img Average Rental duration, P = 36 hours Calculate the revenue of the store per day as shown below : Flow rate = 0.259 customers per hour. The Revenue of the store img Thus, the Revenue of the store per day is $31.19 Thus, the Increased profit is (31.19 - 28.16) = $3.62