Erlang’s Queuing theory applied to Capacity planning for a Development House

Any development shop has multiple functions or verticals, separately staffed and having individual capacity and service profiles. For example, a typical SW development shop will have Requirements analysts, Designers, Developers, Testers, Release and configuration management people, and support people. Each of these will have their individual service times with respect to a standard project sizing unit, and individual capacities.

Traditionally, the capacity planning of staff and equipment is done on the basis of typical gut feel and qualitative weighing of various factors such as peak loads and acceptable wait times. However, a gut feel is retrospective and there is very little opportunity for predictive and quantitative understanding of how the resources can be shuffled and optimally reallocated.

Enter a mathematical tool that is often used in various other applications such as networking and service industry design, Erlang’s Queuing Theory.

A very nice writeup on the same appears here:

The average wait time for a new customer (any job that comes from downstream to upstream)


the time between customer arrivals is random with mean time λ. The Service time of each customer is exponentially distributed with mean time 1/μ. The number of servers is s. Server utilization is ρ.

This is the standard canonical form that is a part of most modern spreadsheet programs. The assumption of a Poisson Distribution can be borne out by past data, and the expressions re-derived. This, coupled by some off the shelf optimization software can throw out capacity numbers that minimize wait times at every stage. This approach is worth exploring.

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Enlightenment Now, Steven Pinker’s Magnum Opus- a review

One of the authors that I have taken to like a duck to water has been Steven Pinker. He has a style of writing where he breaks down complex issues and erects a data and evidence based structure to address the parts before knitting it back up. That makes for an exhilarating experience to read and ponder.

The latest book that he has come up with is “Enlightenment Now- A case for Reason, Science, Humanism and Progress”. The essential thesis is that we are much better off due to these enlightenment values irrespective of what the doom’s day prophets of the mainstream media would have us believe.

The table of contents of the book reveals the intellectual courage of Pinker to take on a expansive swath of topics with a range of impact that is almost unprecedented. You could have had a book written on each of these topics ( and many exist); but still none of the topics feel shortchanged for detail and hurried. The style of the author is that he very carefully lists all arguments that any detractor could make and addresses each one of them in great detail. This gets tiring in a (very) few places, but overall it makes the points bullet proof. Another evidence for the importance of the metaphorical Brakes in the vehicle of civilization.

Photo by Danka & Peter on Unsplash


  • LIFE

The essential take away from this is that problems are solvable. That requires that we look at the data to inform our opinions rather than preconceived notions. That does not mean that they will solve themselves, but it does mean that we can solve them if we sustain the benevolent forces of modernity that have allowed us to solve problems so far, including societal prosperity, wisely regulated markets, international governance, and investments in science and technology. That’s a solid message to keep in mind in these times of doom’s day prophets.

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Is Human Intelligence somehow special?


The artificial Intelligence community is in the news now-a-days, mostly for the right reasons. The resurgence of research in this area has been explosive, and that is not an exaggeration.

A proxy for the uptick in research is the number of cites some pioneers of the field have gathered over the years.

Citation count for Geoffrey Hinton

Citations for Yann LeCun

With such rapid progress, there are obvious concerns over AI safety and our future as a species with these technologies, which is a valid and pertinent area of concern. There is some fabulous work going on there, and you should check out the research around the alignment problem.

However, there is another faction that is dismissive of intelligence coming out of “mere” machines.

The argument goes thus: The modern machine learning and AI is just….. something, and will never be as good as human intelligence. Let us try to understand this argument, assuming that it *IS* a valid argument, not an argument from incredulity.

Arguments from incredulity can take the form:

I cannot imagine how P could be true; therefore P must be false.

I cannot imagine how P could be false; therefore P must be true.

Arguments from incredulity happen when people make their inability to comprehend or make sense of a concept the content of their argument.

This is just a bunch of matrix multiplications, how can it ever achieve human intelligence level?

It can, and it has, in several areas. The image recognition capabilities of modern AI far outstrip human performance. So does the chess playing ability. So do many other areas. When you really get into it, your actual neurons are also a bunch of electrical impulses calculating some mathematical function, phenomenologically speaking.


Machines and AI can never do X, where X is your favorite thing that AI can’t do.

Agreed, that it can’t do X *yet*. Maybe it can, maybe it can’t. There is no way to know unless you try. Unless you believe that the robots made of meat are somehow fundamentally and irreconcilably different than robots made out of silicon and steel, this argument seems untenable. Also, funnily enough, if you define AI as something computers haven’t figured out how to do, you are of course correct. Computers can’t do what they can’t do, because if they do, it’s not AI.

Is intelligence substrate dependent? Is there something special in carbon atoms that silicon atoms can not do, even in theory? The jury is still out one way or another, and I will be surprised if the narcissistic viewpoint that human intelligence is somehow special, turns out to be true.

The reductionist viewpoint (just a matrix multiplication, just an electrical impulse, just glorified curve fitting, just… you get the point) assumes that things are more complex on the larger scale than the smaller one, whereas the physical reality is often the opposite of that. Understanding something enough to make use of it is often simpler than understanding every last detail.

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Artificial Intelligence and Deep Learning

Submitted for publication in a magazine for restricted circulation within the employing organisation, all rights reserved. ©

In the recent years, there have been phenomenal advances in the state of the art in Deep learning and Deep neural networks, one of the most promising directions for Artificial Intelligence. Most of you would have seen the Robot “Sophia” holding her own in conversations with humans. She (it?) was recently given citizenship in Saudi Arabia as well.

Less fancy but more useful applications have transformed our lives in many subtle but important ways.

Neural networks are one of the most beautiful programming paradigms ever invented. In the conventional approach to programming, we tell the computer what to do, breaking big problems up into many small, precisely defined tasks that the computer can easily perform. By contrast, in a neural network we don’t tell the computer how to solve our problem. Instead, it learns from observational data, figuring out its own solution to the problem at hand. So, in essence, instead of writing detailed instructions for the computer, you show it the output you want and let it figure out the instructions by itself. Isn’t that how you teach a human?

The power of a deep neural network comes from the possibility to learn very complex non-linear functions. For example, the following shows the impact on revenue from consumer churn.

Automatically learning from data sounds promising. However, until 2006 we didn’t know how to train neural networks to surpass more traditional approaches, except for a few specialized problems. What changed in 2006 was the discovery of techniques for learning in so-called deep neural networks. These techniques are now known as deep learning. They’ve been developed further, and today deep neural networks and deep learning achieve outstanding performance on many important problems in computer vision, speech recognition, and natural language processing. They’re being deployed on a large scale by companies such as Google, Microsoft, and Facebook.

What is a deep neural network? It is the name we use for “stacked neural networks”; that is, networks composed of several layers. The layers are made of nodes. A node is just a place where computation happens, loosely patterned on a neuron in the human brain, which fires when it encounters sufficient stimuli.


Deep neural networks have surpassed humans in many image and language processing tasks already but they are still narrow intelligence rather than general intelligence. The frontier of research in the field is moving extremely fast. Some beautiful examples of generalization can already be seen ( and
) but there is still a wide gap. The future is indeed exciting.


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Optimal for “me” may not be Optimal for “us”

Two criminals are apprehended by the police, suspected of armed robbery. Call them Alice and Bob. (Hey, women can be armed robbers as well!). Being hardened criminals, it is difficult to get a confession out of them. And we have hardly any other evidence to convict in an absence of an explicit confession.

Now the cop is a clever guy. He goes up to both the suspects and offers them the following deal:

  • If you both stay silent, you get 1 year in jail each.
  • If one of you stays silent and the other one betrays the silent person, the betrayer goes free and the betrayed gets 3 years in jail.
  • If both of you betray each other, both of you get 2 years in jail.

He then separates them and leaves them to think through their options for the night.

Alice thinks that – assuming that Bob Betrays – if she stays silent she gets 3 years. If she betrays she gets only 2 years in jail. Assuming that Bob Stays silent, If she stays silent as well, she gets one year in jail, whereas if she betrays, she goes home free. So in both cases, she is better off betraying Bob.

On the other hand, Bob’s thinking is also identical. He will also be better off betraying in all cases, irrespective of Alice’s behaviour.

So, being perfectly rational, they both betray each other and get 2 years in Jail each.

Take a moment thinking about this. As a group, the most beneficial outcome would have been that both stayed silent, getting one year in jail each. However, in ignorance of the other’s choice, the group settles for 2 years in Jail each.

The decision that the individuals took is the most optimal for them but is suboptimal for the group as a whole. This is the classic “Prisoner’s Dilemma”. This strategy (The Dominant Strategy) is the famous Nash Equilibrium, by John Nash. There is an excellent movie based on his life, “A beautiful Mind”, which you should watch. John Nash got a Nobel for his work on Game Theory, the field which deals with decision making under uncertainty.

Unfortunately, this is not far-fetched in the business world. We often have people working within the same organisation operate in conflict with one another.

Uncooperative behaviour can be further seen when unreasonable expectations, aggressive deadlines and inadequate measurement criteria cause undue stress and competition. Stress brings out the win-lose psyche in people and we’ve all seen this play out at work.

If this isn’t bad enough, local optimisations with complete disregard to any impact that such actions may have on other areas of the business cause the nastiest forms of such behaviour. Sales people selling products/services that their firm’s operations staff can’t produce or provide is a classic example of this in action.

Regardless of the cause, uncooperative conduct hinders an organisation’s performance. In fact, a steady diet of it leads to lingering, sub-optimal results – the consequences of which can be disastrous to the long-term health and prosperity of the enterprise.

Clearly, we as leaders must sniff this out and take the necessary steps to eradicate the behaviour.

We can do this by:

  • Being very clear and deliberate with our direction-setting;
  • Establishing appropriate expectations, deadlines and goals;
  • Aligning measurements and rewards with expected results;
  • Stressing “team” over “individual” performance, and;
  • Raising awareness and providing appropriate training, as needed.

In this way, we can reset our organisation’s group dynamics in a direction that enables success and help it avoid falling victim to the prisoner’s dilemma.



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There is a spring in my step

“Hope springs eternal in the human breast;
Man never Is, but always To be blest.
The soul, uneasy, and confin’d from home,
Rests and expatiates in a life to come.”

-Alexander Pope

The triumph of the human thought, that has brought us so much progress over the millennia, gets a new shot in the arm every Spring Season. Spring heralds new beginnings, the rejuvenation of the spirit that seeks to conquer new heights of achievement and glory and to shed the baggage of failed promises and missed opportunities.
Let us all bask in the glory of this Spring season. Let us celebrate the bonds that bind us, and strive towards the synergies that are distinctly individual- but at the same time decidedly targeted towards a common goal. Let us connect and contribute to our common causes and efforts in our own individual way and seek to attain the goal in sight.


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Book Review- The Fountainhead by Ayn Rand

There are—a few times in your life— experiences that shape your psyche and leave an indelible mark on your world-view. Reading Ayn Rand’s masterpieces ‘The Fountainhead’ and ‘Atlas Shrugged’ was one of those experiences for me.

I have never been too fond of fiction and novels, with non-fiction having a place of pride in my set of preferences. The Fountainhead was on my radar for a very long time (think years!), but I could never get around to it. In a discussion we were having with some like-minded colleagues, someone brought the topic up and I picked up the book in curiosity. Boy, what a ride!

Ayn Rand weaves the motifs of the triumph of the human spirit, with intrigues of love and sex to politics in the corridors of power effortlessly and in a cohesive whole. Her philosophy of ‘Objectivism’ and ‘individualism’ are recurring themes that are evident throughout the novel. The book in notoriously difficult to begin and taxes your patience in the first few pages. However, if you endure the arduous climb atop the cliff, the view is exhilarating.

Rand has an unmatched ability to make her characters so life-like that they almost dance in front of your eyes. The protagonist ‘Howard Raork’ in particular is someone who is an outlier and hence is scorned and shunned by the society. The overarching theme is that the collective wisdom of the society thrives on averages and those beyond those averages are given a hard time by the society. It is also true that these outliers that struggle their way through to the top of the world are the ones that shape society and move the average ahead. As it is often said, an idea progresses from preposterous, to acceptable to obvious in due course, if the one proposing the ‘preposterous’ idea perseveres.

Man cannot survive except through his mind. He comes on earth unarmed. His brain is his only weapon. Animals obtain food by force. man had no claws, no fangs, no horns, no great strength of muscle. He must plant his food or hunt it. To plant, he needs a process of thought. To hunt, he needs weapons, and to make weapons – a process of thought. From this simplest necessity to the highest religious abstraction, from the wheel to the skyscraper, everything we are and we have comes from a single attribute of man -the function of his reasoning mind.

What is defining about this book is the unique perspective each character brings to the table. Roark ignores the world, Dominique mocks it, Wynand is out to destroy it. Toohey, the antagonist, is a parasite who loves playing games to thwart greatness and Keating is a bumbling fool who thrives on his mediocrity and is destroyed by it.

When you sit and read this book, you are giving a gift to yourself. The gift of your own life, that is yours to live and enjoy, the one where you can and do what you think is the best for your own happiness. Of course, if you happen to agree with the book 100%, you have not understood it. The author wants you to be an individual and form your own opinion and be superlatively selfish in the quest. As she herself says:

The Fountainhead’s is a confirmation of the spirit of youth, proclaiming man’s glory, showing how much is possible. It does not matter that only a few in each generation will grasp and achieve the full reality of man’s proper stature–and that the rest will betray it. It is those few that move the world and give life its meaning–and it is those few that I have always sought to address. The rest are no concern of mine; it is not me or The Fountainhead that they will betray: it is their own souls.

Though best read in context, here are some of the defining quotes from the novel:


On being followers of ideas rather than their proponents:

“Listen to what is being preached today. Look at everyone around us. You’ve wondered why they suffer, why they seek happiness and never find it. If any man stopped and asked himself whether he’s ever held a truly personal desire, he’d find the answer. He’d see that all his wishes, his efforts, his dreams, his ambitions are motivated by other men. He’s not really struggling even for material wealth, but for the second-hander’s delusion – prestige. A stamp of approval, not his own. He can find no joy in the struggle and no joy when he has succeeded. He can’t say about a single thing: ‘This is what I wanted because I wanted it, not because it made my neighbors gape at me’. Then he wonders why he’s unhappy.”


On selfishness being a virtue and competence being the only thing worthy of worship

“It’s easy to run to others. It’s so hard to stand on one’s own record. You can fake virtue for an audience. You can’t fake it in your own eyes. Your ego is your strictest judge. They run from it. They spend their lives running. It’s easier to donate a few thousand to charity and think oneself noble than to base self-respect on personal standards of personal achievement. It’s simple to seek substitutes for competence–such easy substitutes: love, charm, kindness, charity. But there is no substitute for competence.”


On being true to your convictions in the face of adversity, a trait personified by the protagonist – Howard Roark

“Integrity is the ability to stand by an idea.”

“Self-sacrifice? But it is precisely the self that cannot and must not be sacrificed.”


On being pioneers of an idea; on persevering in the face of mockery, indifference and scorn; and on being the ones that moved the world.

“Throughout the centuries there were men who took first steps down new roads armed with nothing but their own vision. Their goals differed, but they all had this in common: that the step was first, the road new, the vision unborrowed, and the response they received — hatred. The great creators — the thinkers, the artists, the scientists, the inventors — stood alone against the men of their time. Every great new thought was opposed. Every great new invention was denounced. The first motor was considered foolish. The airplane was considered impossible. The power loom was considered vicious. Anesthesia was considered sinful. But the men of unborrowed vision went ahead. They fought, they suffered and they paid. But they won.”


On being charitable to the undeserving; on the urge of the society to attune itself to the unworthy.

“Is it advisable to spread out all the conveniences of culture before people to whom a few steps up a stair to a library is a sufficient deterrent from reading?”

This is a great piece of art that must be worshipped. You may or may not agree with the entirety of the philosophy of the book, but it sure spurs some deep introspection and appraisal of the social moorings of the society.

Highly recommended.

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