How much do I have to wait?

Wait time is lost time

I suppose everyone agrees with the sentence: wait time is lost time. Nobody likes or wants to wait. From the customer (requester) point of view wait time is, in general, badly tolerated.

But the service provider point of view is different. In general it would not provide ample capacity to eliminate any waits, given that the capacity has a cost and probably will remain idle out of peak times. An agreement/equilibrium must be reached.

How much do you have to wait?

Suppose you are a customer, arrive to a service center that has one worker, and find Q customers waiting in the queue ahead of you, and one customer being serviced. How much do you have to wait?

The response is simple: the remaining service time for the customer being serviced, plus the service time of the 1st customer in the queue, plus the service time for the 2nd customer in the queue,..., and so on until the last customer  queued (the number Q). This results in the following expression for the waiting time (W) ():

S1 + S2 + ... + SQ  <=  W  <=  S0 + S1 + S2 + ... + SQ

If we make the simplifying assumption that the service time (S) is constant, that is, every customer spends the same amount of time receiving service, we have this simpler expression

Q · S  <=  W  <= (Q+1) · S

and being the response time equal to the sum of the waiting time and the service time (R = W + S) we have

(Q+1) · S  <=  R  <= (Q+2) · S

In the case of a service center that has m workers, and S constant, the bounds to the waiting and the response time are

S*INT(Q /m)  <=   W   <=  S+S*INT(Q /m)

and

S + S*INT(Q /m)  <=   R   <=  2S + S*INT(Q /m)

where INT() is the integer part function.

So the waiting time depends on:

• The Service Time  (S):  If the service time, mine or of the customers ahead in the line, increases (decreases) the response time will increase (decrease) as well.
• The Number of Workers  (m): If the number of workers increases (decreases) the wait time will decrease (increase) as the line will advance faster (slower).
• The number of queued customers (Q), that is, the number of waiting (queued) customers ahead of you. The bigger Q is the bigger the wait time is.

Practical cases

Hairdresser’s:

My hairdresser’s has the following performance values: a service time of 1 hour (S=1 h), and four hairdressers at work (m=4). When I arrive there, willing to get an haircut, there are 4 customers in the waiting room (Q=4).

I can easily derive that I'll have to wait between 1 and 2 hours,  as  1*int(4/4)=1  and 1+1*int(4/4)=2. That is, the response time I will experience will be between 2 h and 3 h.

Here is the plot of the response time (R)  interval against the number in the queue (Q):

Company Department:

In my company department jobs take one working day to be completed (S=1 day), and there are three equally qualified professionals working there  (m=3). So when a new job arrives and "finds" a queue of 6 (Q=6), it may be concluded that the job requester must have to wait between 3 and 4 days to get his request serviced, as 1 + INT(6/3) <= R <= 2 + INT(6/3).

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Introducing the Response Time

Introducing the Response Time

The response time is the loser in the set of all performance metrics. It's systematically ignored in almost every sizing, it’s neither measured nor accounted in most cases, and it's only marginally referenced in certain benchmark definitions. Clearly, the throughput is the winner: SAPS, IOPS, transactions per second are throughput metrics, not response time ones.

But from the end user point of view the response time is the king. Any service center performs very well or very poorly according to the response time perceived by its users. When the response time is bad It doesn't matter to the customers if the system administrator proclaims they are working with a many-oooops-per-second system. Just the system is slow and, consequently, bad. Period.

The Service Center

Look at the following picture, an idealization of any service center. A service center is a place, logical or physical,  where customers or users enter, are given a certain service by a worker (or a server), and exit. There's a line (queue) where arriving customers can queue and wait if all the workers are busy.

Figure: Service center with server(s), queue, and arriving  and departing customers.

You interact with service centers everywhere, as it is very general concept. For example:

Service Center	Service Given	Customer	Worker
Hairdresser’s	A haircut	People needing a haircut	Hairdresser
Our Company department	A step in an opportunity forward path	Company customers	Yourself
OLTP IT Server	CPU time	Users entering transactions at their terminals	CPU cores
Supermarket checkout	The checkout payment	Supermarket customers	Cashier
Bus Transport	A transport from place A to place B	Passengers	The driver and the bus
Public office desk	A request to the public administration.	Citizens	Public servant
Machine Repair Center	Fixing the malfunctioning machine	Machines	Repairman

A service center is fully characterized by the following magnitudes:

• The service time (S): the elapsed time a service takes,
• The number of servers (m):  the number of customers that can receive service simultaneously.

The Response Time

The Response Time (R) is the time elapsed from the arrival of a customer to the service center to its departure after receiving service.

The response time has two contributions: the service time (S)  and the wait time (W), resulting in this fundamental relationship:

R = W + S

To illustrate this look at the following scenario where we have depicted the flow of several customers through a very simple service center (m=1, S=cte)

• Customer #1  arrives a t=0, finds the worker/server idle, spends no time at all at waiting, is given a certain service taking S units of time, and exits the center of service at t=S. The wait time is 0. The response time is S.
• Customer #2  arrives a t=S, spends no time at all waiting, is given a certain service taking S units of time, and exits the center of service at t=2S. The wait time is 0. The response time is S.
• Customer #3  arrives a t=2S, spends no time at all waiting, is given a certain service taking S units of time, and exits the center of service at t=3S. The wait time is 0. The response time is S.

In this scenario none of its customers must wait for service, and so the response time is equal to the service time. The wait time contribution is zero.

Now look at the following scenario differing from the previous one in the way customers arrive.

• Customer #1  arrives a t=0, spends no time at all at the queue, is given a certain service taking S units of time, and exits the center of service at t=S. The wait time is 0. The response time is S.
• Customer #2  arrives a t=0, has to wait in queue S units of time, is given a service taking S units of time, and exits at t=2S. The wait time is S. The response time is 2S.
• Customer #3  arrives a t=0, has to wait in queue 2S units of time, is given a service taking S units of time, and exits at t=3S. The wait time is 2S. The response time is 3S.

Some of the customers must wait for service and, consequently the response time has the two contributions: the service time (grey) and the wait time (blue),

Waiting for the SAPS

Looking at a SAPS benchmark report, may you tell which contribution to the response time is bigger: the wait or the service time?

Remember this first: SAPS is a performance metric measuring throughput: 1 SAPS is 1 customer service per minute, or 1 dialog step per minute (dialog step is an SAP term). The benchmark is essentially performed by progressively increasing the customer population, and monitoring the response time.  When the response time reaches 1 second (R=1 s), the measured throughput, as expressed in dialog steps per minute, is the SAPS value.

A SAP server in essence is a service center for SAP dialog steps. And according to the certification report these are its measured numbers:

• There are 128 workers, corresponding to 128 HW threads executing dialog steps, so m=128.
• The average response time is measured to be 0.98 s. R=0.98 s.
• 5113000 dialog steps are executed (serviced) in an hour.

And from the above the following values can be easily derived:

• The service time is S=0.090 s , as every worker processes (5113000/128) ds per hour, and then  ( 1 h / (5113000/128) ds ) · ( 3600 s/h) = 0.0901 s.
• The wait time is W= 0.89 s  (W = R - S).

The dialog step response time is decomposed into 0.89 s of wait time and 0.09 s of service time:

Wow!  W >> S, in fact W ~ 10·S. So it’s sure there is a queue of dialog steps waiting  to be processed. If you scale this to, for example, a supermarket checkout counter that spends  5 minutes per customer, W=10·S means a 50 minutes waiting in the line!

Coming Soon

This is the first blog entry of the Demystifying the Response Time series, an exploration into the response time jungle. There are very interesting facts and analysis ahead. Stay tuned.

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How much capacity does a virtual cpu guarantee?

The rapid answer to the question how much capacity does a virtual cpu guarantee? is as much as one core can deliver (PowerVM VP), or as much as one thread can deliver (ESX vCPU). This is the best case, and so has been In the two previous entries ( “Don’t put in the same bag Xeon and POWER virtual CPUs”, “More on ESX vCPU versus PowerVM VP” ). But the best case is not necessarily the most common case.

Two typical non-best cases in the real world:

• For a good technical reason, trying to leverage the “sharing” capability that virtualization technologies enable,
• For a bad economic reason, reselling the same underlying physical capacity to more than one customer.

Independently of the true reason, you should be aware of a parameter, assigned to a VM, that helps a lot in specifying how much capacity does your particular VP (vCPU) guarantee. It’s called Entitlement in PowerVM, and Reservation in ESX. These parameters have a very interesting property: they cannot be overcommitted, that is, you cannot distribute among the VMs more Entitled (Reserved) capacity than is available in the physical machine. On the contrary, you can create and distribute more VPs (vCPUs) than existing cores (threads). If you simply divide the VM Entitlement (Reservation) by the number of VP (vCPU) in the VM you will have how much a virtual cpu guarantees.

Let us illustrate this with a very simple scenario, a reasonable setup for two VMs, the Red VM and the Blue VM, with the same importance. This situation may arise, i.e.,  when two productive environments share the same PM.

Physical Machine	IBM POWER S824 2s/24c/192t POWER8 @3.52GHz
Cores	24
SAPS	115870
SAPS/core	4828

Red VM		Blue VM
12	Entitlement (cores)	12
24	Virtual Processors	24
Uncapped	Cap/Uncap	Uncapped

The reason for 24 VP per VM, instead of 12 VP, is for the VM to be able to reach the 100% capacity of the PM.

In the best case (for the Red VM) the Blue VM remains idle, and under such a circumstance the 24 Red VPs can use the 24 cores, giving the equivalence 1 VP = 1 core = 4280 SAPS. To simplify we are not taking into account capacity reductions due to virtualization.

In the worst case (for the Red VM), the Blue VM is fully loaded and then the 24 Red VPs can use 12 cores at most, the Entitlement, giving the equivalence 1 VP = 0.5 core = 2140 SAPS.

So the actual Red VP capacity will be somewhere in the interval [2140, 4280] SAPS, depending on the Blue VM usage. Never will be less than 2140 SAPS, the guaranteed or worst case. Never will be more than 4280 SAPS, the underlying core capacity.

By the way, this is a good illustration of the good technical reason for overcommitting VP (vCPU) mentioned above. But may also be an example of the bad economic reason: just imagine that the owner of the physical machine sells the 24 VPs to the red customer, and 24 VPs to the blue customer, promising 1 VP = 4280 SAPS to everyone!

Summarizing

If you only know the number of VP (vCPU) that your VM has been assigned, you don’t have enough information to establish its precise capacity point. At least you should be informed of its Entitlement (Reservation) to derive the guaranteed capacity.

	PowerVM	ESX
Best Case	1 VP = 1 core	1 vCPU = 1 thread
Guaranteed / Worst Case	1 VP = Entitlement/NumberofVP	1 vCPU = Reservation/NumberofvCPU

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