Queueing up

We all know how S'poreans like to queue up for everything. But there is really a theory behind queueing up and long lines. For customers, the marginal cost does not just include the amount of money paid, the monetary price of the good, it also includes the cost of waiting in line, for your turn to get the good. Of course nowadays, with more and more physical goods being transacted over the internet, waiting lines are growing shorter. But there are still many goods, in particular, services, that still involves the cost of waiting in line for your turn.

In particular, prices, quality of service, and the length of waiting lines, are related. Lower prices have a tendency to attract longer waiting lines. If a service is of low quality, waiting lines are likely to be non-existent. Waiting lines can also be reduced by increasing the supply of the service, but there is sometimes the tendency that increasing supply only attracts an increased demand for the service, causing waiting lines to be as long as before, or even longer than ever. Examples of waiting lines could be: MRT congestion, health care provision, your favourite curry chicken stall, etc.

Many people base their decisions on prices alone. Their MPC would be equal to the price of the good/service. Their MPB might be the amount of money saved by consuming this particular good/service over the choices of other alternatives. A completely rational human being would factor in all the intangible satisfaction derived from consumption of that particular good, and the time, space, and other non-monetary costs incurred. Because in a real world, we do not have perfect brains that can remember and compute everything, neither do we have the time to finish computing things. As a result we make a lot of decisions, on the spur of the moment. And prices are one of the most visible factor for us to make our decision instantly on the spot. When this occurs, the price mechanism may fail to properly allocate resources in the most optimal level.

Entrepreneurs providing a certain service, often can be counted upon to make decision that are rational. Because they are the one taking on the risks, of investing in capital, and organising labour and other resources, they can be counted upon to sit down and think through the costs and benefits of providing that service/good. However, consumers do now always do the same. If every time, we spend money we have to sit down and think through what we want and need, we will be wasting quite a lot of time. And sometimes end up not buying anything at all. This cautious attitude towards spending, was once more prevalent in the society, when wages were low, and always prevalent in an economy experiencing recession. In the more modern world today, the consumerist culture is the rise, thanks to higher real wages, and the power of advertisements.

Advertisements act to alter the incentives of consumers considering to buy a certain good/service. They play on the fact that many people make decisions on the spur of the moment, sometimes distorting the incentives abit, or significantly so as to change the intangible marginal benefit that we derive from consumption.

There are different objectives in different contexts about waiting lines. For example, we may want to reduce congestion on MRT trains. We could raise the prices of ticketing fees during peak hours, so as to lower the demand for MRT trains usage. Waiting lines, or crowds here at the MRT platform, reflect the marginal benefit to commuters of using the MRT trains. Because of the limited service, commuters incur the cost the having to wait for their turn, and space of using the MRT service. Higher prices forces commuters to take into account their cost of waiting in line. Not everybody have the same conversion factor of time to money. Some view their time as cheap in monetary terms. For others, their time is expensive. But those people with cheap time, create a spillover effect, because they are taking up the space and time of others. For some people, they are unwilling to pay in exchange for their time.

It is my observation, (not sure how true), that 'buying' time, is a luxury reserved for rich people. Similarly, health care, which is 'buying' life, or paying money in exchange for your life, is another luxury reserved for the rich. As much as we are unwilling to admit it, we need to make difficult choices everywhere, and sometimes, if we have to exchange money for things like time and life, we may have to do it.

Back to MRT trains, there is another type of congestion during peak hours at the certain interchange stations. Commuters there at the interchange stations do not just consist of people streaming into the station from the streets, they also bypass the station because they need to change to another line. At these stations, increasing the frequency of train arrivals at the station will not reduce this problem. This is because while increased freq. of trains arriving at the stations means that more people are transported away from the stations, it also means that more people are transported to that station. And because many people will alight at these interchange stations to switch lines, they contribute to the waiting crowds there.

For some services, they have become so ubiquitous to our daily lives, that we have forgotten that we still have the choice whether we want to consume the service or not. If I say the alternative is to cars and public transport is to use your own 2 legs and walk from your house to the school or your workplace, you would probably balk at me. Transport is an example of a service that has become indispensable. Solutions to this congestion problem, might be raising the prices of all public transport and COE prices, until people are willing to walk on the streets from house to work place. This solution is likely to be extremely unpopular, further exaggerating the inflation problem. Or we can lower prices until the waiting time for crowds in MRT stations is longer than the time taken to walk from place to place. But this solution is difficult for the service provider, because SMRT has its own costs to cover. Lowering prices to the required level is an option probably available only the government provided service. Quality of train transport will also fall correspondingly, destroying the point of traveling in relative comfort in the first place.

For congestion at the interchange stations, perhaps the only way to alleviate this problem is to create a more extensive network. Such a network would have to be compact so that the commuters easily switch from one line to another, without having to climb several escalators, walk out on to the road across the street to switch from train to bus. At the present moment, there are only a few key interchange MRT stations to change lines, meaning that interchange would have to handle a heavy traffic of circulating commuters in the transport system. Buses and taxis are supposed to the capillarial, serving to move commuters to places where trains cannot reach. However, relative prices between buses and taxis and trains do not properly take into account differences in quality of service between these transport service is such that commuters are not efficiently diverted to their destinations. Besides, I myself do not like when I have to take a train ride then have to cross out onto the streets to wait for the bus. COE prices and petrol prices also affect the travelling patterns of the commuters, and therefore are also factors to consider when trying to solve the congestion problem in the transport network.

Woo, long post indeed, next one will probably extend to the the example of the 'favourite curry chicken stall', the healthcare system, and potential profits to be made from queueing up.

Diffraction

Some things never change; now I'm here to crap about the diffraction..

I just realised that we do now have a clear picture of why diffraction occurs. We are told that diffraction always occurs for waves passing through slits with slit length of comparable order of magnitude as the wavelength of the waves, but we are not told why it occurs, or the mechanism by which it occurs.

Perhaps we can try and find this process, while keeping in mind the the wave is a collection of particles. In a 1-dimensional wave, each particle pulls the next particle into motion. In a 2 dimensional wave, each particle pulled by all neighbouring particles, whereby each particle contributes a little pull, and they all exert a net force on a certain particle, and this particular particle into SHM. Since each particle have the roughly the same number of particles on each side of it, the net force would be as such as to keep the wave moving in the same direction as it were. Each particle can be treated as a point source in other words and we just have to calculate where the forces cancel out.

At the location of the slit however, we have a bit of a situation. Some particles no longer have the same number of particles on each side of it. Especially the particles at the sides of the slit. This situation is not so unlike one of a packed lift, where people inside the lift are trying desperately to jostle out of the narrow door, and spreads in all directions at the doorway, particularly, to the 2 sides of the door.

Keeping this in mind, is it thus very strange to find that electrons undergo diffraction too? If electrons are emitted fast and rapidly, we can imagine them jostling around at the slit, and thus, would spread outwards from the slit too. Perhaps it is more strange that the same diffraction pattern can be observed for electrons that are shot singly at the slits, one at a time. Quantum mechanics say that the probability wave of the electrons interfere with itself as it passes the double slits. But I really hope that there is a more 'real' explanation. For example, maybe as one electron happen to pass closer to one end of the slit, it is deflected by electrons and protons of the material constituting the slit.

But I really do not like it when they say diffraction is a phenomena particular to the waves. Its as if, particles do no exhibit such behaviour. I am sure that if enough particles participate, diffraction patterns can similarly be observed. The problem is to resolve the problem when electrons are moving forward in straight lines, and hence, could just 'jostling' be present?

Leader A

Quite a long gap since my last post. This is because I was away for 2+ weeks for field camp, outfield for situational test.

The commanders keep asking us if we want to go to command school, OCS or SISpec. Clearly, a leader is not something that I say I want it, then I just get it like that. Even ask the sergeants what it means to be a good leader, they only say that you must be able to lead, you must be able to inspire, blah blah. But how exactly do you lead? What guides your decision? How do you utilise your men?

Being a leader in some sense, is not like a trivial thing to talk about. Therefore, I see so many wayang people out there, with loud voices and action, and they think they are leading. But anybody can shout at people and order them about. If your men do not respect you, no matter how much you shout at them, do you really think they will follow you with their heart? You can punish them all you want, and still silently in their hearts, they will never follow you.

A leader knows each of his men personally, he earns his respect by leading from the front, from the side, and from the back. I dunno, I am not a great leader myself, but have taken a few appointments myself, and observed others. And I have come some conclusions. A leader always makes decisions that are difficult. Because his decision will not make everyone happy, but if his followers are true to him, they will respect his decision. Subsequently, in this respect, that is where are flaws come in, for more often than not, we are selfish and greedy, myself included.

Being a leader is not easy, it is a wonder why so many want that post so badly. Is the allure of power so great? I have seen too many who go up and falter in the end, find out that its so stressful after all. Ah, but I'm blabbering..

Happy Chinese New Year Peeps.. Enjoy your bookout hols guys..