In this online article Dr. Gunther digs down into the UNIX kernel to find out how load averages (the “LA Triplets”) are calculated and how appropriate they are as capacity planning metrics. With apologies to Jules Verne and his novel “20,000 Leagues Under the Sea,” I might equally have entitled this piece, “20,000 Lines Under the Shell.”

Have you ever wondered how those three little numbers that appear in the UNIX® load average (LA) report are calculated?

This TeamQuest paper explains how and how the load average (LA) can be reorganized to do better capacity planning. But first, try testing your knowledge with the “LA Triplets” Quiz.

In this two part-series I want to explore the use of averages in performance analysis and capacity planning. There are many manifestations of averages e.g., arithmetic average (the usual one), moving average (often used in financial planning), geometric average (used in the SPEC CPU benchmarks), harmonic average (not used enough), to name a few.

More importantly, we will be looking at averages over time or time-dependent averages. A particular example of such a time-dependent average is the load average metric that appears in certain UNIX commands. In Part 1 I shall look at what the load average is and how it gets calculated. In Part 2 I’ll compare it with other averaging techniques as they apply in capacity planning and performance analysis. This article does not assume you are a familiar with UNIX commands, so I will begin by reviewing those commands which display the load average metric. By Section 4, however, I’ll be submerging into the UNIX kernel code that does all the work.

1. UNIX Commands

Actually, load average is not a UNIX command in the conventional sense. Rather it’s an embedded metric that appears in the output of other UNIX commands like uptime and procinfo. These commands are commonly used by UNIX sysadmin’s to observe system resource consumption.

Let’s look at some of them in more detail.

1.1 Classic Output

The generic ASCII textual format appears in a variety of UNIX shell commands. Here are some common examples.

Uptime

The uptime shell command produces the following output:

[pax:~]% procinfo

9:40am up 9 days, 10:36, 4 users, load average: 0.02, 0.01, 0.00

It shows the time since the system was last booted, the number of active user processes and something called the load average.

Procinfo

On Linux systems, the procinfo command produces the following output:

[pax:~]% procinfo

Linux 2.0.36 (root@pax) (gcc 2.7.2.3) #1 Wed Jul 25 21:40:16 EST 2001 [pax]

Memory: Total Used Free Shared Buffers Cached

Mem: 95564 90252 5312 31412 33104 26412

Swap: 68508 0 68508

Bootup: Sun Jul 21 15:21:15 2002 Load average: 0.15 0.03 0.01 2/58 8557

...

The load average appears in the lower left corner of this output.

W

The w(ho) command produces the following output:

[pax:~]% w

9:40am up 9 days, 10:35, 4 users, load average: 0.02, 0.01, 0.00

USER TTY FROM LOGIN@ IDLE JCPU PCPU WHAT

mir ttyp0 :0.0 Fri10pm 3days 0.09s 0.09s bash

neil ttyp2 12-35-86-1.ea.co 9:40am 0.00s 0.29s 0.15s w

...

Notice that the first line of the output is identical to the output of the uptime command.

Top

The top command is a more recent addition to the UNIX command set that ranks processes according to the amount of CPU time they consume. It produces the following output:

4:09am up 12:48, 1 user, load average: 0.02, 0.27, 0.17

58 processes: 57 sleeping, 1 running, 0 zombie, 0 stopped

CPU states: 0.5% user, 0.9% system, 0.0% nice, 98.5% idle

Mem: 95564K av, 78704K used, 16860K free, 32836K shrd, 40132K buff

Swap: 68508K av, 0K used, 68508K free, 14508K cched

PID USER PRI NI SIZE RSS SHARE STAT LIB %CPU %MEM TIME COMMAND

5909 neil 13 0 720 720 552 R 0 1.5 0.7 0.01 top

1 root 0 0 396 396 328 S 0 0.0 0.4 0.02 init

2 root 0 0 0 0 0 SW 0 0.0 0.0 0.00 kflushd

3 root -12 -12 0 0 0 SW< 0 0.0 0.0 0.00 kswapd

…

In each of these commands, note that there are three numbers reported as part of the load average output. Quite commonly, these numbers show a descending order from left to right. Occasionally, however, an ascending order appears e.g., like that shown in the top output above.

1.2 GUI Output

The load average can also be displayed as a time series like that shown here in some output from a tool called ORCA.

Although such visual aids help us to see that the green curve is more spikey and has more variability than the red curve, and it allows us to see a complete day’s worth of data, it’s not clear how useful this is for capacity planning or performance analysis. We need to understand more about how the load average metric is defined and calculated.

2. So what is it?

So, exactly what is this thing called load average that is reported by all these various commands?

Let’s look at the official UNIX documentation.

2.1 The man Page

[pax:~]% man “load average”

No manual entry for load average

Oops! There is no man page! The load average metric is an output embedded in other commands so it doesn’t get its own man entry. Alright, let’s look at the man page for uptime, for example, and see if we can learn more that way.

...

DESCRIPTION

uptime gives a one line display of the following information. The current time, how

long the system has been running, how many users are currently logged on, and the

system load averages for the past 1, 5, and 15 minutes.

...

So, that explains the three metrics. They are the “... load averages for the past 1, 5, and 15 minutes.” Which are the GREEN, BLUE and RED curves, respectively, in Figure 1 above. Unfortunately, that still begs the question “What is the load?

2.2 What the Gurus Have to Say

Let’s turn to some UNIX hot-shots for more enlightenment.

Tim O’Reilly and Crew

The book UNIX Power Tools [POL97], tell us on p.726 The CPU:

The load average tries to measure the number of active processes at any time. As a measure of CPU utilization, the load average is simplistic, poorly defined, but far from useless.

That’s encouraging! Anyway, it does help to explain what is being measured: the number of active processes. On p.720 39.07 Checking System Load: uptime it continues ...

... High load averages usually mean that the system is being used heavily and the response

time is correspondingly slow.

What’s high? ... Ideally, you’d like a load average under, say, 3, ... Ultimately, ‘high’ means high enough so that you don’t need uptime to tell you that the system is overloaded.

Hmmm ... where did that number “3” come from? And which of the three averages (1, 5, 15 minutes) are they referring to?

Adrian Cockcroft on Solaris

In Sun Performance and Tuning [Coc95] in the section on p.97 entitled: Understanding and Using the Load Average, Adrian Cockcroft states:

The load average is the sum of the run queue length and the number of jobs currently running on the CPUs. In Solaris 2.0 and 2.2 the load average did not include the running jobs but this bug was fixed in Solaris 2.3.

So, even the “big boys” at Sun can get it wrong. Nonetheless, the idea that the load average is associated with the CPU run queue is an important point.

O’Reilly et al. also note some potential gotchas with using load average ...

...different systems will behave differently under the same load average. ... running a single cpu-bound background job .... can bring response to a crawl even though the load avg remains quite low.

As I will demonstrate, this depends on when you look. If the CPU-bound process runs long enough, it will drive the load average up because its always either running or runable. The obscurities stem from the fact that the load average is not your average kind of average. As we alluded to in the above introduction, it’s a time-dependentaverage. Not only that, but it’s a damped time-dependent average. To find out more, let’s do some controlled experiments.

3. Performance Experiments

The experiments described in this section involved running some workloads in background on single-CPU Linux box. There were two phases in the test which has a duration of 1 hour:

CPU was pegged for 2100 seconds and then the processes were killed.

CPU was quiescent for the remaining 1500 seconds.

A Perl script sampled the load average every 5 minutes using the uptime command. Here are the details.

3.1 Test Load

Two hot-loops were fired up as background tasks on a single CPU Linux box. There were two phases in the test:

The CPU is pegged by these tasks for 2,100 seconds. The CPU is (relatively) quiescent for the remaining 1,500 seconds.

The 1-minute average reaches a value of 2 around 300 seconds into the test. The 5-minute average reaches 2 around 1,200 seconds into the test and the 15-minute average would reach 2 at around 3,600 seconds but the processes are killed after 35 minutes (i.e., 2,100 seconds).

3.2 Process Sampling

As the authors [BC01] explain about the Linux kernel, because both of our test processes are CPU-bound they will be in a TASK_RUNNING state. This means they are either:

running i.e., currently executing on the CPU

runnable i.e., waiting in the run_queue for the CPU

The Linux kernel also checks to see if there are any tasks in a short-term sleep state called TASK_UNINTERRUPTIBLE. If there are, they are also included in the load average sample. There were none in our test load.

The following source fragment reveals more details about how this is done.

600 * Nr of active tasks - counted in fixed-point numbers

601 */

602 static unsigned long count_active_tasks (void)

603 {

604 struct task struct *p;

605 unsigned long nr = 0;

606

607 read_lock (&tasklist_lock);

608 for_each_task(p) {

609 if ( (p->state == TASK_RUNNING | |

610 (p->state & TASK_UNINTERRUPTIBLE ) ) )

611 nr += FIXED_1;

612 }

613 read_unlock(&tasklist_lock);

614 return nr;

615 }

So, uptime is sampled every 5 seconds which is the linux kernel’s intrinsic timebase for updating the load average calculations.

3.3 Test Results

The results of these experiments are plotted in Fig. 2. NOTE: These colors do not correspond to those used in the ORCA plots like Figure 1.

Although the workload starts up instantaneously and is abruptly stopped later at 2100 seconds, the load average values have to catch up with the instantaneous state. The 1-minute samples track the most quickly while the 15-minute samples lag the furthest.

You would be forgiven for jumping to the conclusion that the “load” is the same thing as the CPU utilization. As the Linux results show, when two hot processes are running, the maximum load is two (not one) on a single CPU. So, load is not equivalent to CPU utilization.

From another perspective, Fig. 2 resembles the charging and discharging of a capacitive RC circuit.

4. Kernal Magic

Now let’s go inside the Linux kernel and see what it is doing to generate these load average numbers.

unsigned long avenrun[3];

624

625 static inline void calc_load(unsigned long ticks)

626 {

627 unsigned long active_tasks; /* fixed-point */

628 static int count = LOAD_FREQ;

629

630 count -= ticks;

631 if (count > 0) {

632 count += LOAD_FREQ;

633 active_tasks = count_active_tasks( );

634 CALC_LOAD(avenrun[0], EXP_1, active_tasks);

635 CALC_LOAD(avenrun[1], EXP_5, active_tasks);

636 CALC_LOAD(avenrun[2], EXP_15, active_tasks);

637 }

638 }

The countdown is over a LOAD_FREQ of 5 HZ. How often is that?

1 HZ = 100 ticks

5 HZ = 500 ticks

1 tick = 10 miliseconds

500 ticks = 5000 miliseconds (or 5 seconds)

So, 5 HZ means that CALC_LOAD is called every 5 seconds.

4.1 Magic Numbers

The function CALC_LOAD is a macro defined in sched.h

58 extern unsigned long avenrun[ ]; /* Load averages */

59

60 #define FSHIFT 11 /* nr of bits of precision */

61 #define FIXED_1 (1<<FSHIFT) /* 1.0 as fixed-point */

62 #define LOAD_FREQ (5*HZ) /* 5 sec intervals */

63 #define EXP_1 1884 /* 1/exp(5sec/1min) as fixed-point */

64 #define EXP_5 2014 /* 1/exp(5sec/5min) */

65 #define EXP_15 2037 /* 1/exp(5sec/15min) */

66

67 #define CALC_LOAD(load,exp,n) \

68 load *= exp; \

69 load += n*(FIXED_1-exp);\

70 load >>= FSHIFT;

A notable curiosity is the appearance of those magic numbers: 1884, 2014, 2037. What do they mean? If we look at the preamble to the code we learn,

/*

49 * These are the constant used to fake the fixed-point load-average

50 * counting. Some notes:

51 * — 11 bit fractions expand to 22 bits by the multiplies; this gives a

52 * load-average precision of 10 bits integer + 11 bits fractional

53 * — if you want to count load-averages more often, you need more

54 * precision, or rounding will get you. With 2-second counting freq,

55 * the EXP_n values would be 1981, 2034 and 2043 if still using only

56 * 11 bit fractions.

57 */

These magic numbers are a result of using a fixed-point (rather than a floating-point) representation.

Using the 1 minute sampling as an example, the conversion of exp(5/60) into base-2 with 11 bits of precision occurs like this:

These numbers are in complete agreement with those mentioned in the kernel comments above. The fixed-point representation is used presumably for efficiency reasons since these calculations are performed in kernel space rather than user space.

One question still remains, however. Where do the ratios like exp(5/60) come from?

4.2 Magic Revealed

Taking the 1-minute average as the example, CALC_LOAD is identical to the mathematical expression:

load(t) = load(t-1) e-5/60 + n (1 - e-5/60) (3)

If we consider the case n = 0, eqn.(3) becomes simply:

load(t) = load(t-1) e-5/60 (4)

If we iterate eqn.(4), between t = t0 and t = T we get:

load(t T ) = load(t 0 ) e-5t/60 (5)

which is pure exponential decay, just as we see in Fig. 2 for times between t 0 = 2100 and t T = 3600.

Conversely, when n = 2 as it was in our experiments, the load average is dominated by the second term such that:

load(t T ) = 2 load(t 0 ) (1 - e-5t/60) (6)

which is a monotonically increasing function just like that in Fig. 2 between t 0 = 0 and t T = 2100.

5. Summary

So, what have we learned? Those three innocuous looking numbers in the LA triplet have a surprising amount of depth behind them.

The triplet is intended to provide you with some kind of information about how much work has been done on the system in the recent past (1 minute), the past (5 minutes) and the distant past (15 minutes).

As you will have discovered if you tried the LA Triplets quiz, there are problems:

The “load” is not the utilization but the total queue length. They are point samples of three different time series. They are exponentially-damped moving averages. They are in the wrong order to represent trend information.

These inherited limitations are significant if you try to use them for capacity planning purposes. I’ll have more to say about all this in the next online column Load Average Part II: Not Your Average Average.