Software service time

The software service time per I/O operation which the user sees mainly comprises:

• the wait time ahead of the volume concerned and

• the hardware service time for performing the physical I/O operation (see DISK report group of openSM2: SOFTWARE-DURATION and HARDWARE-DURATION).

The wait time W ahead of the volume is derived according to the rules for queue formation depending on:

• the distribution of the times between the I/O requests (interim arrival times),

• the distribution of hardware service times and

• the volume utilization.

Without delving further into queue theory, the following two formulas can be used to estimate the average wait time W:

1. When assuming the prerequisite "M/M/1" (worst-case scenario):

   M: Exponential distribution of interim arrival times
   M: Exponential distribution of hardware service times
   1: one console

2. W = S * U / (1-U)

   S: Average hardware service time
   U: Volume utilization

   Example

   S = 6 ms; U = 30%
   W = 6 ms * 0,3 / (1 - 0,3) = 2,6 ms

   When the volume utilization is 30%, the I/O requests must wait an average of 2.6 ms before the volume is released.

3. When assuming the prerequisite "M/D/1" (best-case scenario):

   M: Exponential distribution of interim arrival times
   D...: Constant hardware service time
   1: 1 console

   W = S * U / (2 * (1-U))

A comparison of the two formulas shows that, given a constant hardware service time (M/D/1), the average wait time W is only half as long as with exponential distribution of the hardware service time (M/M/1).
In practice neither a strictly exponential distribution of hardware service times nor a constant service time occurs. The wait times which occur as a result of the volume utilization are around the average of the results of the two formulas.

The table below illustrates the factor by which the hardware service time is dilated irrespective of the volume utilization.

Volume utilization (%)	dilation factor M/M/1	dilation factor M/D/1
10	1.11	1.06
20	1.25	1.13
30	1.43	1.21
40	1.67	1.33
50	2.00	1.50
60	2.50	1.75
70	3.33	2.17
80	5.00	3.00
90	10.00	5.50

The wait time ahead of the volume constitutes a major part of the I/O time. The utilization of volumes which are shared by multiple users should not exceed 30%.