Inferring from the classis queueing theory and its impact on server utilization, this article tries to drive home the point how professional services company can never attain a high utilization of 90% and above

1. Queueing theory and Utilization factor in Services Company
I recently read an interesting article on Queueing theory and the analysis of server utilization.
This theory has been there for a long time and properly researched mostly from the hardware angle.
An idea struck my mind – why not I extend this theory to the utilization and billability concept that
every professional services company talks about and see if it makes real sense for them to achieve
greater than 90% utilization of people resources.
Let me introduce you to the common referred graph for server utilization. Every company has a
Human Resources department which means that all employees are treated like resources. This very
concept is so appalling to me as I prefer to use “Talent Office” because every employee is a talent for
the organization – we live in the days of Knowledge management. But let me not digress and let me
introduce you to the concept on which I would make some inferences later. This graph denotes that
the wait time just goes up badly as the server utilization goes beyond 80%.
The X Axis is server utilization and Y axis is the average wait time. At a utilization of 1, the average
time is actually infinity. Wait time here means that the jobs that arrive at the server have to wait
that much longer to be processed. You can even apply it to any retail store format regarding people
wait time where when the numbers of customers arrive faster in the line than the cashier can
actually serve and be done with each customer, the line becomes longer. The same logic applies to
fine dine-in restaurants – you see a line outside because all the tables and the waiters inside are
complete engaged with present customers who take a significant amount of time to get served and
eat. I will not get into the semantics of how to classify these types of time.
Now let us split the total amount of time to two segments – the actual wait time to get served, and
the actual service time where your job gets executed. Both of them together are the response time
– actually this would include a variability effect as well. To highlight the impact of the wait time, let
us assume the service time remains the same for all jobs or customers which may be incorrect but
let us do so for this article. And we are talking averages here throughout. The response time
degrades the busier the resource is. There would always be a safety capacity plan to support in
excess of expected demand to cover for the variability effect.
Some observations here:
- If you are the first job or the first customer, your response time is equal to the service time.

2. - If your resources are utilized at 50%, you can see the response time doubles!
- At 75% utilization, the response time quadruples and at 87%, it becomes eight times.
- At 94% utilization, the response time is 16 times and at 97% utilization, the response time is
32 times.
- When you go from 75% to 90% utilization, your response time increases by 225%!
So it is obvious that if the machine or the resources are busy, there would be lot of jobs waiting
in the queue. Now let us correlate it to what every professional services company uses as a key
objective – its billability and utilization. Without going too much into details, billability rate is
usually less than the utilization rate – meaning not all what a resource does for a project can be
billed. Utilization is just how long a resource gets occupied with a chartered project and
billability is how much of that can the service company bill the actual customer. Ideally they
would try to make them equal which is a fallacy and hence usually it is anywhere between 80%
and 90% of utilized time becomes billable to the customer.
What are the usual metrics that the services company would go after?
- Billability ratio of 90% and utilization of 100% ideally.
- Lots of customers and new clients added per quarter which necessitates adding capacity
(more resources) but to keep the cost down, they would maximize hiring freshers and
manage every project with a hierarchy of varied-experienced employees.
Now let us prove how these metrics may not be the right ones to use. Let us analyze from the
bottom and try to see how much of time does an average employee have for a project. Since this is
a high level view, with each company having their own way of operation, let us just use this as an
example for our story here:
1. There are 52 weeks in a year.
2. The vacation days (holidays and vacation put together) can be anywhere between 4 to 6
weeks depending on which geography you are in. So, effectively one would work for only 46
to 48 weeks in a year.
3. Let us assume a barest minimum of 1 week set aside for training each employee with new
skills. Usually this is more. Now we are left with 45 to 47 weeks of possible project work
time. In all honesty, most of the employees do not even get trained for a new skill ever!
4. There are months where there are more orders and there are some with the normal orders.
Hence these employees would be dragged to more critical projects for a week or two, on a
high priority need basis. So, we have about 43 to 45 weeks left. Again, these are minimal
numbers estimated. So, this 5% (~ 2 weeks) is to adjust for the variability effect.
5. Let us assume we work on projects 4 days a week of five official days. Meaning, your
billability is only 80% of utilization. You may be attending some process meetings, some
team meetings to make the project work, some lectures and talks, some business meetings
etc. which cannot be directly billed to the customer. Assume now that we have taken off 9
weeks for non-billable work, out of 43 to 45 weeks. One is left with only 34 to 36 weeks of
project work.
6. 34 weeks out of 52 weeks total is about 65% (36 weeks would make it 69%). Let us assume
it about 2/3rd
for calculation purposes. The employer still has to pay you for the 1/3rd
that

3. has to be accounted for in terms of salary. The other way of saying this is that a services
company takes a loss of a third of the total salary paid which they have to recover.
7. For our calculation again, let us assume 35% instead of 33.3% for this loss. If one take’s more
than a week for training, and if one gets dragged into other projects more than the two
weeks allotted, then this number actually increases to 40% and more. So, to recover that
35% of your salary, the company bills the customer 35% more than the salary (let us say this
is the average salary for the company). This amortized over the 260 working days possible
would give the company the contract rate to the customers. Of course, this would differ
from small to big based on the experience of the employee but again, we are talking
averages.
8. No services company runs for charity – they would try everything to make money. Not only
it does not want to take a loss, they have to make profit. This is a commercial venture. So, let
us assume 20% as a profit margin a company would expect. So, the services company would
charge 1.55x average salary and derive the per day or hour contract rate! Again, if you are
an accountant trying to read this, sorry, I may have simplified it a lot to give brevity.
9. Now the company has lots of overhead that they cannot bill. These could be support
functions, enabling functions and even managerial cadres. Let us assume for every 10
employees there is a manager who cannot be billed. Now his salary has to be amortized over
10 employees. His or her average salary would be 2 x employee salary. Now this salary has
to be added to the contract rate which makes it 1.75 x average salary! Yes, there are
differences you would see in these calculations (albeit minor) if you are mathematician and
can definitely pick holes in my derivation but this is close enough. Close enough is good
enough for an engineer! So, if the company is paying $10 for any BILLABLE employee on an
average, they would charge a minimum of $17.5 to the customer!
I pointed out these calculations to make the audience understand at a high level how the
accounting works (but there is more to this than what I have written) but may not directly
relate to what I am driving at.
I am assuming 34 weeks of 100% utilization for every employee based on the above analysis.
Now the expectation for all the employees to be 100% efficient in these 34 weeks with no
slack whatsoever. Borrowing from the machine utilization analogy, the following things can
be inferred:
o The slowest resource is going to derail the project – this is the critical path ideology
that every project manager would practice because of Theory of Constraints. Given
this is the scenario, the slowest resource efficiency cannot be equated to the normal
or faster resource efficiency. Yes, the slowest resources are working 100% of his 34
weeks but his output is lower than the others! So, as a project manager, add
resource to compensate for this thus adding cost, or push schedule and eat your
TIME buffers to meet the customer milestones. If the slowest resource is the long
pole in the tent, it does not matter if others finish faster – they all need to wait for
this resource to complete! Plan for lower utilization to address this factor.
o If something goes wrong in between, there is no slack to compensate now. Since
employees are on the edge with 100% utilization, this automatically means nothing

4. wrong is allowed to happen nor all risks are naturally mitigated so that there are no
surprises. Living on the edge can never be right. It causes stress and stress leads to
lower quality of work. So, even in those 34 weeks, it is quite natural for the project
managers to add a safety cushion for a said demand (remember, this is NOT a
variability effect cushion which is based on demand)
o Not all customers are alike nor all projects the same. Some customers are more
demanding than others, and some projects are more complex than others. So, the
response time of execution of any project is going to increase based on higher
demands of a customer or due to more customers, if the capacity of resources
remains the same! Service level agreements are likely to suffer.
With all the above factors, it is extremely difficult to get to a consistent long-term
utilization of 90% and above, which would automatically means the best billability would be
in the range of 75% to 80%. For the services company to stay competitive on rates, they
need to reduce their operational costs and develop a decent hierarchy of experience that
can still deliver high quality solutions. It is always about quality assurance during design
rather than quality control after design! Continuously improve the process but understand
there is an upper limit in utilization for your highest efficiency and this is not even close to
100%. Even if you are pushing the envelop, the incremental benefits in revenue you may get
from pushing the utilization (and hence billability) from 90% to 95% or more would be
definitely negated by the impact it would have on quality and customer relationships.
Remember, there would be penalty clauses at high as 20% from every customer if the
deliverables are not achieved within the specified time.
Remember, we have been just talking about averages here and not even maximum
which would be worst case. Also I have not even accounted for attrition which is usually
between 8-20% for any services company which would translate to delays in response
directly. Going from 85% to 90% and beyond does have a bigger impact on response time.
For a services company to deliver with good quality at all times, the target thus has to be
preferably defined between 80 to 90% only. Nothing more. If someone is saying they have
a 100% utilization, it is high time we do a due diligence audit on the calculation!