Homework SourseBlank parts arrive in the FIFO firstin firstout queue and be
Blank parts arrive in the FIFO (first-in first-out) queue and being processed by a single machine with the arrival and service times below.
a) Compute the average waiting time in queue (give the numerical answer below).
b) Compute the maximum number of parts in queue (give the numerical answer below).
c) Compute the time-average resource-busy number (give the numerical answer below).
d) Compute the minimum total time in system for parts. Give the numerical answer below.
| Part Number: | 1; | 2; | 3; | 4; | 5 |
| Arrival Time: | 0; | 3; | 4; | 7; | 10 |
| Service Time: | 4; | 2; | 1; | 1; | 2 |
Solution
Minimum total time in system for parts = 12
part 2 and part 3 have to wait for 1 unit time and 2 unit time respectively
Total waiting time in queue = 1+2 = 3
average waiting time in queue = Total waiting time / number of parts in the system
average waiting time in queue = 3/6 = 0.5
maximum number of parts in queue = 2 ( part 2 and part 3 )
total idle time = 2
total busy time = total time in system - total idle time = 12 - 2 = 10
time-average resource-busy number = total busy time / total time in system = 10/12 = 0.833
time-average resource-busy number = 0.833
| part number | arival time | time service starts | service time | time service ends | waiting time in queue | machine idle time |
| 1 | 0 | 0 | 4 | 4 | 0 | 0 |
| 2 | 3 | 4 | 2 | 6 | 1 | 0 |
| 3 | 4 | 6 | 1 | 7 | 2 | 0 |
| 4 | 7 | 7 | 1 | 8 | 0 | 0 |
| 5 | 10 | 10 | 2 | 12 | 0 | 2 |
