Sar: why is %util for a multipathed device not the same as %util added up for all its paths?

Issue

• With multipath device and 8 paths, why doesn't the %util from each path added up correspond to the %util from the multipathed device?

  • For example from the following sar output, there are 4 active paths to the storage (dev8-16, dev8-48, dev8-80 and dev8-112) having 35.50, 34.19, 32.26 and 33.72 as their respective values for %util. Combining them would bring you a total of 135.67. The multipathed device dev253-12 (which is backed by the 8 paths) only has 97.48 % utilization. How can this be explained?

00:00:01       DEV       tps  rd_sec/s  wr_sec/s  avgrq-sz  avgqu-sz  await  svctm   %util     
12:35:01    dev8-0      0.00      0.00      0.00      0.00      0.00   0.00   0.00    0.00  
12:35:01   dev8-16    719.94  71100.04      0.11     98.76      0.66   0.92   0.49   35.50  
12:35:01   dev8-32      0.00      0.00      0.00      0.00      0.00   0.00   0.00    0.00  
12:35:01   dev8-48    717.35  71100.92      0.13     99.12      0.59   0.82   0.48   34.19  
12:35:01   dev8-64      0.00      0.00      0.00      0.00      0.00   0.00   0.00    0.00  
12:35:01   dev8-80    698.86  71102.33      0.21    101.74      0.59   0.85   0.46   32.26  
12:35:01   dev8-96      0.00      0.00      0.00      0.00      0.00   0.00   0.00    0.00  
12:35:01  dev8-112    662.44  71099.91      0.27    107.33      0.58   0.88   0.51   33.72  
12:35:01 dev253-12  35550.38 284402.35      0.72      8.00     46.35   1.30   0.03   97.48