(a) For task_1: Utilization = Arrival rate x Service time = 20 x (2⁄60) = 0.67 or 67%
For task_2 (before selective execution): Utilization = Arrival rate x Service time = 20 x (2.5⁄60) = 0.83 or 83%
For task_2 (after selective execution): Utilization = Arrival rate x Service time x Selective execution percentage = 20 x (6⁄60) x 0.25 = 0.50 or 50%
(b) Average WIP: Average WIP = (Utilization / (1 - Utilization)) x (1 - (Arrival rate / Resource capacity)) = (0.67 / (1 - 0.67)) x (1 - (20 / 1)) = 6.18 for task_1 = (0.83 / (1 - 0.83)) x (1 - (20 / 1)) = 4.94 for task_2 (before selective execution) = (0.50 / (1 - 0.50)) x (1 - (20 / 1)) = 1.00 for task_2 (after selective execution)
© Average flow time: Assuming that each case goes through both tasks, the average flow time can be calculated as follows:
Average flow time = Average waiting time + Average service time
For task_1: Average service time = 2 minutes Average waiting time = Average WIP / Arrival rate = 6.18 / 20 = 0.31 minutes Average flow time = 2 + 0.31 = 2.31 minutes
For task_2 (before selective execution): Average service time = 2.5 minutes Average waiting time = Average WIP / Arrival rate = 4.94 / 20 = 0.25 minutes Average flow time = 2.5 + 0.25 = 2.75 minutes
For task_2 (after selective execution): Average service time = 6 minutes Average waiting time = Average WIP / Arrival rate = 1.00 / 20 = 0.05 minutes Average flow time = 6 + 0.05 = 6.05 minutes
(d) Average waiting time for each task: Assuming that the cases are equally distributed between the tasks, the average waiting time for each task can be calculated as follows:
For task_1: Average waiting time = (Average WIP / 2) / Arrival rate = (6.18 / 2) / 20 = 0.155 minutes
For task_2 (before selective execution): Average waiting time = (Average WIP / 2) / Arrival rate = (4.94 / 2) / 20 = 0.1235 minutes
For task_2 (after selective execution): Average waiting time = (Average WIP / 2) / Arrival rate = (1.00 / 2) / 20 = 0.025 minutes
