Climbing the peak

Climbing the peak

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Scenario

In your usual sizing efforts you need to know the peak usage% for a certain workload and server(s). What is the right averaging time to capture this peak? Let’s see possible choices.

Too long averaging time

Averaging Time = 500 min. Peak usage% = 50%.

Total loss of finer details. Does this really mean that the usage% has been the same for the 500 min? You, like me, don’t believe that!

Too short averaging time

Averaging Time =  10 s. Peak usage% = 100%.

Too much detail. This may be good for performance analysis, but it is confusing for sizing. Spikes goes up to usage%=100%, meaning that for 10 s -the averaging time-  in a row the server is 100% busy. But I wouldn’t consider that the server usage% is 100% for sizing purposes. If you do so you most probably are oversizing, a common (and safe) strategy by the way.

The right averaging time?

Averaging Time =  10 min. Peak usage% = 68%.

Eureka! This is the right amount of detail. In my point of view the right averaging time for OLTP lies somewhere between 10 min and 1 hour, depending on the workload, on the available data, and on the degree of tolerance to a high usage%.

The upgrade sizing pitfall

The upgrade sizing pitfall

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The art of sizing is not exempt of pitfalls, and you must be aware of them if you want your sizing to be accurate and adequate. Let us talk about a typical scenario: a server upgrade.

All the metrics in sizing are measures of throughput, and this has an implication you must take into account: not always the service center (the server, here) with higher throughput capacity is better. What are you saying man?

Let's consider two servers, the base one and its intended upgrade:

1. Base: single core server with a capacity (maximum throughput = bandwidth) of 1 tps (transaction per second). Therefore the transaction service time is 1 second.
2. Upgrade: four core server with a capacity of 2 tps. Therefore the transaction service time is 2 seconds.

If you exclusively look at the throughput, B (2 tps) is better than A (1 tps). Period.

But from the response time perspective such a superiority must be revised. Let us graph the response time versus the number of users:

Figure: Best response time (average)  versus the number of users, with a transaction think time of 30 seconds. Server A (base) in blue. Server B (upgrade) in red.

In the light load zone, that is, when there are no or few queued transactions, A is better than B. This is consequence of a better (lower) service time for server A. In the high load zone B is better than A. consequence of a better (higher) capacity (throughput). If the workload wanders in the light zone such an upgrade would be a bad idea.

So when you perform a sizing you must know wich point of view is relevant to your sizing exercise: the throughput or the response time. Don't fall in the trap. A higher capacity (throughput) server is not unconditionally better. For an upgrade server to be unconditionally better its capacity (throughput) must be higher and its service time lower.

Phases of the response time with variability

Phases of the response time with variability

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Let's go to the response time versus the number of users signature (graph below) in the simple system described in "Phases of the Response Time". We made two simplifying assumptions: the service time is constant, and the interarrival time is constant (the the think time is constant). These assumptions allowed us to distill the essence of the response time dependencies, providing us with very useful insights regarding the response time behaviour, the primary parameters it depends on, how it depends on them, and what are its trends and its limits.

Figure 1: The response time versus the number of users for the simple model.

In the real world... variability!

Now let's go a step further introducing the variability. Customers seldom arrive to a service center at uniform intervals (arrivals side variability). Customers seldom demand the same service time (service side variability). Both magnitudes are essentially variable.

The analysis of the response time with variability is usually done using a powerful mathematical tool called probability analysis. Every time you hit into a queueing theory textbook or article, you'll find probabilities. Our constant values are transformed in something like this:  "it's twice more probable to have a service time of 2 s than 1 s", "there's a probability of 80% that service time lies in the interval (1 s, 2 s)", “the average response time is 2 s”, and so on. We enter the probabilistic world, where the raw material is random variables, on which we can only state probabilistic facts.

But, for now, I'm interested in highlighting the main consequences of the variability, not in performing an analytical in-depth analysis.

Variability Effects

Look at the figures 2 and 3.

Figure 2: No variability case. Uniform arrivals + Uniform service --> No waits --> Best and uniform response time.

This "no variability" figure corresponds to our simple all-constant case (Figure 1). Uniform arrivals and uniform service time result in no waits and the best and uniform response time.

Figure 3: With variability case (arrivals side). Non-uniform arrivals + Uniform service --> Waits --> Worse and variable response time

The "with variability" diagram illustrates the arrivals side variability, in particular batch arrival of users. Non-uniform arrivals result in waits, and the response time seen by users is worse and variable (or volatile).

Ideas to take -->  Variability effects are:

The response time is variable: the response time varies from user to user and from successive visits from the same customer. The average response time is worse: waits show up due to the lack of uniformity. increasing the response time.

An analysis of the same simple model but allowing  random -exponentially distributed- variation of the service time and the think time results in the graph in figure 4.

Figure 4: Average response time for the all-constant (blue) and the random (red) cases..

We can see, for example, that when the user population reaches  80% of the saturation value the average response time for the random model is 4 times the one for the all-constant model, and for 100% of the saturation population the ratio increases to 8 times!

By the way. don’t underestimate the effects of the variability, as it is one of the causes of unacceptable performance from the customer point of view: in general a customer is willing to accept higher but uniform response times than lower but highly variable ones.

Data Tiering: a simple performance analysis

A certain transaction uses 1 ms of cpu time and 20 ms of IO time. With a think time of 10 s the system supports 550 users with a response time R below 1 s. Now the same system is equipped with a faster storage where part of the data is placed. When this data replacement is automatic, the faster storage is acting as a cache. If the transaction finds the data in the cache the IO time is reduced to 5 ms. Otherwise the IO time remains to be 20 ms.   With a hit ratio of 10%, that is, one in ten IO accesses are served from the cache, the performance of the system improves in the following ways: With the same customer population (550 users) now the average response time drops from 1 s to 0.20 s! The user population may increase from 550 to 611 users to reach again the limit of 1 s of average response time.

Let us build a reasonably simplified performance model for the caching in data tiering, a model suitable for a simple but illustrative performance analysis. A transaction "visits" the CPU, using C units of time (1 ms in the scenario), and "visits" the storage, using S units of time (20 ms in the scenario).

With a cache in place the same transaction may find the data in the cache -this is called a (cache) hit-, and in such fortunate case it doesn't have to visit the storage. This fast IO takes F units of time (5 ms in the scenario)

Two parameters to describe the cache effect:

• α - efficiency  (0 <= α <= 1), defined as α=(S-F)/S or, equivalently  F=S(1-α).
• h - hit ratio: (0 <= h <= 1), ratio of transactions that get their required data from the cache, typically proportional to its capacity.

KPI #1: Best Latency

Without the cache the best latency (response time) a transaction may achieve is Rmin=C+S units of time. With the cache in place, the best achievable latency reduces to R'min=C+F, corresponding to the transactions that get their IO from the cache.

In our scenario, the best latency with cache miss is 21 ms, and with cache hit is 6 ms.

KPI	No cache	With cache
Best Latency	C+S	hit:     C+S(1-α) miss:           C+S

KPI #2: Bandwidth

Without the cache the bandwidth (best throughput) the system delivers is B=1/S, limited by the bottleneck device, the slow storage. With the cache in place the system is able to sustain a peak throughput of  B'=B/(1-h) for h<α and B'=B/(h·(1-α)) for h>α .

In our scenario, the bandwidth without cache is 1/20 ms-1, that is 50 transactions per second. With cache the bandwidth increases 11% for a hit ratio h=10%,  25% for h=20%, and 100% for h=50%.

KPI	No cache	With cache
Bandwidth	B=1/S	B'=B/(1-h)      if  h<=1/(2-α) B'=B/[h·(1-α)]   if h>1/(2-α)

Here is a plot of the bandwidth gain with cache versus the hit ratio. The hit ratio that achieves the maximum bandwidth gain is h=1/(2-α), and the corresponding maximum gain is B'/B=(2-α)/(1-α).

Graph: bandwidth gain with cache (α=75%) versus the hit ratio

KPI #3: Response Time

The impact of the presence of the cache in the response time signature of the system, that is, the graph response time versus the number of users interacting with the system, is twofold:

• a displacement to the right due to the increase of the saturation population, the point that marks the change of phase, and
• a decrease in the high load slope.

Graph: response time versus the number of users

The consequence of these is that the the cache reduces the response time, a reduction that  is stronger in the high load zone. We must speak of averages here, as there are two response times now: one for transactions with IO is served from cache, and other for transactions with IO served from the slow storage.

In our scenario with a hit ratio of 10% the response time of the system drops from 1 s to 0.20 s with the same customer population (550 users).

KPI #4:Supported users

Looking at the response time signature from another point of view is clear that  additional users may work in the system while keeping the same level of performance (response time limit).

In our scenario the user population may increase from 550 to 611 users to reach again the limit of 1 s of average response time (see above graph).

Side effects

These performance benefits of caching don't come for free. Apart from the evident monetary cost, think about the following

• The CPU usage increases: the cache alleviates the load on the storage but increase the load on the CPU, because if the CPU gets the data faster, it has more work to do. This may displace other cpu intensive work that may be competing for the CPU.

• The housekeeping burden: cache housekeeping tasks (data load, data discard...) may consume CPU cycles, unless this task is offloaded to the storage.

The scalability of the software

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The developers team in the ABC company has just built a five star transaction / program. The program code has a critical region. Basic performance tests with a few users result in a the total execution time of 1 s, with a residence time in the critical region of 0.05 s. These numbers are considered satisfactory by the management, so the deployment for general availability is scheduled for next weekend.

You, a performance analyst's apprentice, ask for the expected concurrency level, that is, the number of simultaneous executions of the  transaction / program. This concurrency results to be 100.

What do you think about this?

A suitable performance model

A very simple model to analyze and predict the performance of the system is a closed loop, with two stages and fixed / deterministic time in each stage, as depicted here:

The total execution time of the program is divided into:

• the time in the parallel region, where concurrency is allowed.
• the time in the serial (critical) region, where simultaneity is not allowed..

With only one user (one copy of the program/transaction in execution) the elapsed time is P + S, that is, 1 s ( = 0.95 + 0.05 ).

But what happens when the concurrency level is N? In particular, what happens when N=100?

And the model predicts...

Calculating as explained in "The Phases of the Response Time" the model predicts the saturation point at N*=20 (=1+0.95/0.05) users. This is the software scalability limit. More than 20 users or simultaneous executions will queue at the entry point of the critical region. The higher the concurrency level, the bigger the queue, and the more the waiting time. You can easily calculate that with the target concurrency level of 100 users, the idyllic 1 s time measured by the developers team (with few users) will increase to an unacceptable 5 s level. This means that the elapsed time of any program/transaction execution will be 5 s, distributed in the following way:

• 0.95 s in the parallel region,
• 4 s waiting to enter the critical (serial) region, and
• 0.05 s in the critical region.

Elapsed execution time for N=1 and N=100 concurrency level

The graph of the execution time against the number of concurrent users is the following:

Elapsed execution time against the concurrency level

And, in effect, when the program is released  the unacceptable response time shows up!

Corrective measures

The crisis committee hold an urgent meeting, and these are the different points of views:

• Developers Team: the problem is caused by a HW capacity insufficiency. Please, growth (assign more cores to) the VM supporting the application and the problem will disappear.
• Infrastructure Team: hardware undersized? No point. The CPU usage is barely 25%! We don't know what is happening.
• Performance Analyst Team (featuring YOU): more cores won't solve the problem as the hardware is not the bottleneck!  

Additional cores were assigned but, as you rightly predicted, things remained the same. The bottleneck here is not the hardware capacity. but the program itself. The right approach to improve the performance numbers is by reducing the residence time in the non parallelizable critical region. So the developers team should review the program code in a  performance aware manner.

You go a step further and expose more predictions: if the time in the critical region were reduced from the current 0.05 s to 0,02 s the new response time for a degree of simultaneity of 100 will be 1.5 s, and the new response time graph will be this one (blue 0.05 s, red 0.02 s):

Elapsed execution time against the concurrency level for S=0.05 ms (blue) and S=0.02 ms (red).

Lessons learnt

• Refrain to blame the hardware capacity by default. There are times, more than you think, in which the hardware capacity is not the limiting factor, but an innocent bystander that gets pointed as the culprit.
• Plan and execute true performance tests in the development phase, and specially a high load one, because with few users you probably will not hit the performance bottleneck.
• Definitively welcome the skills provided by a performance analyst. Have one in your team. You won't regret.

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