Thursday, November 24, 2005

A Scheme For Numbering Bus Routes



"When I use a word," Humpty Dumpty said, in a rather scornful tone,
"it means just what I choose it to mean - neither more nor less."
- Lewis Carroll, Through The Looking Glass

"But what about,” I asked him, “bus-route numbers?”.


The need for a more meaningful scheme for numbering bus-routes in cities is explained and a scheme suitable for this purpose is detailed in this paper. The proposed scheme entails the assignment of numbers to the station and the utilization of the multiplicative properties of the numbers to embed route-information in the route numbers in an efficient manner.


A numbering scheme for public buses is essential if a city has a lot of people of different origin, who speak different languages natively. The numbering of buses according to the routes that they service helps a great deal when you don't know how to read the favoured local language.

Democracy, the preferred ideology of this age, is about suiting the majority. If the majority of the local population can read the language, writing the names of the places enroute in that language will be very useful indeed. But the minority of the non-readers should not be neglected either; the route number should still be present, the number being their only cue. Democracy is also about the right of the minority to equality. The situation should be win-win-for-all, where possible.

1.1 Limitations of present schemes

The route numbers for buses, however, seem to be chosen arbitrarily or through an arcane and abstruse scheme. It is biased to suit the operators' convenience more than the passengers'. Ease of administration and maintenance seems to be the driving (excuse the pun) force behind the numbering of the routes.

For example, all that may be common to Buses 361, 362 and 363 may be that they start from the same location. This would not be very helpful for a person standing at that location, clueless as to how to choose from one of the buses at the station!

Very little conclusively useful information can be obtained from a route number. Numbers are used almost like names, meaningless. Such a scheme may be termed a number-as-name scheme.

1.2 Socio-economic impact

Any numbering scheme can be easily implemented by the bus-service operators or company. That being the case, the numbering scheme chosen must be as advantageous to the passenger as possible. A bus-service is, after all, intended as a service to the passengers.

Now, even if the chosen scheme is complex, the operators will eventually adapt to its complexity. A bus-service is, after all, a business too. And in a business, the customer is king. But this scenario will not arise: a scheme easily understood by the passengers will, necessarily, be easy for the operators as well.

A simple, intuitive numbering scheme would be helpful not only for the local-language-ignorant passengers but also for other linguistically challenged people like dyslexics and illiterates (they might be good with numbers). It would also encourage the use of the public transport mechanism; many a time, it is for want of a bus number that we take a cab. We can also eliminate the need for the names of the enroute stations to be written on the bus, as the scheme would be easily usable for the natives also.


2.1 Requirement:
A passenger, may not be familiar with the local language, has to be able to correctly decide whether a bus goes where he wants to go.

2.2 Assumption:
A passenger has basic knowledge of mathematics and numbers .

2.3 Base Scheme:
1. Assign each station a prime number. 2, 3 , 5, 7, 11, 13, 17, 19, 23, 29, 31, 37...
2. Enumerate the stations on the bus-route.
3. The product of the prime numbers denoting the stations enroute, is used as the route number.

2.4 Sufficiency:
Since each station is assigned a prime number, a route number will be unique. The passenger who knows the number of his destination can determine whether a given bus will go to his destination by checking whether the bus-number is divisible by the number of his destination.


3.1 Learning Curve

A question regarding the ease of learnability of the destination-numbers can be raised. The number can be displayed at all bus-stops, the passenger can make a note of it when he gets down if he thinks he will need to go there frequently.

A passenger will find it easier to remember the set of numbers representing his possible destinations than the numbers of all the buses going there. The number of numbers that a passenger will need to remember in this scheme is less by a multiplicative factor than in number-as-name schemes.

3.2 Length Of Route Numbers

The readily observable and noticed space on a bus is limited; the number of characters required for route-representation is an important criterion. The route numbers must be displayed prominently and they should also be easily analyzable.

Some of the route numbers if we use a purely prime-multiplicative scheme will be very long and too complex for an average individual to quickly analyze with his destination-key.

3.2.1 An alternative:
Let us consider a linear scheme in which we could assign numbers (needn't be prime) to the stations and we string together the numbers for the stations as the route number. On the face of it, this seem to be simpler than the prime-multiplicative scheme. But there could be problems interpreting a linear route number. For example, 123 could be interpreted as 1-2-3 , 12-3 or 1-23. But, if we include the dashes in the route number for clarity, the route number will be unnecessarily bloated; the dashes adding to the length. This would result in route numbers like 1-2-3-4-15-16-21. In the prime-multiplicative scheme such a number would probably be smaller, in terms of the number of characters required to represent it.

3.2.2 Adapting the prime-multiplicative scheme:
Through judicious and intelligent choices, the length of the route number can be minimized. Some approaches are mentioned below -

a) Use of smaller numbers for stations that are on busier routes. In fact, if all of the buses pass a station, that needn't have a number at all!

b) In the case that all buses passing through a station A come from another station B, the square of B's code can be used for A and so on. This would mean just multiplication with B's code instead of with another prime number which would have been larger.

c) A hybrid combination of the linear and multiplicative schemes may be essential for very large cities. In case the resulting route number is too big, and only then, it can be decomposed into two smaller, more manageable numbers. The passenger can decide whether the bus goes to a destination if either is divisible by the destination-key.

In the opinion of this author, upto a pair of four digit numbers would be quickly analyzable. In most cases, it should be possible to manage with smaller pairs.

d) Colour-coding of the buses and division of cities into sub-areas are also possibilities. But this should be done only if absolutely necessary, as it destroys the uniformity and simplicity of the scheme and creates confusion.


A bus-route numbering scheme based on prime-multiplicative encoding can be used, after suitable modifications and adaptation to location-specific peculiarities, for embedding route-information into bus-route numbers in an efficient manner.

A limitation of this scheme is that some of the route-numbers could be unmanageably long - some of the possible workarounds have been explained - but there should be no problem implementing the scheme for at least the most important locations of a city.

The implementation of this or a similar route-information-encoding scheme for bus-numbering would be beneficial.

-Thomas Jay Cubb


  1. Thomas,

    I had given a thought to the same and has found the think can become complex and you have made it a complex lot.When it comes to large prime number say 31 and 37 the division will be complex .It works well in the lower version of the prime numbers .

  2. As an academic thought, the idea is good. Actually it is another brilliant usage of prime numbers.

    Unfortunately, factoring is a hard problem.

  3. Actually ... one has a verrry simple method without getting into the numbers and it doesnt need any mathematics or some scientific papers to explain. Just "Ask". Nobody gets into any bus without knowing their destination's name atleast right? Simply asking the driver or the conductor or the passenger simplifies life...

  4. @kousik
    It's not factoring, but multiplication here. Wouldn't that be somewhat simpler? In any case, the problem cannot be trivially solved.

    The thing is you don't know the local language- how would you ask?...u r right, there was no need for a scientific paper... which is why this was NOT one! :-)

  5. Exactly .. i dont know the "local-language" but i do know the place name. Say, if i need to go to Velacheri from Koyambedu...a questioning glance with the word "Velacheri" is a question enough for any local to point the bus

  6. thomacha...
    its an nice structured writeup..
    although i wud prefer askin the conductor or the passengers where the bus goes to ;)

  7. @cold
    u can always do that of course...ask! but there are a huge lot of problems with asking...isn't there? the reply might be in the local language, he might not know, he might launch into a barrage of numbers (leaving you shell-shocked)...

    Would a little bit of independence hurt?

  8. good idea... only a couple of problems..

    1) resistance to change... i know i will take 314 bus.. u name it 648.. wil i be able to remember it.

    2) first and formost.. its more important that the route is bi-lingual so that non kanada can also read the destination and figure out the bus route.

  9. Hi,
    I really like the thought, but am not too convinced about the solution proposed.

    I think you have identified a good problem to solve but it may take more digging before you find a more scalable and feasible solution.

    I dont have numbers to back me up here but I would assume that many users of the bus transport system are illiterate and therefore wouldn't be too good with calculations. Even for the literate, dealing with prime numbers and calculations can be a challenge.

    If you look at other transport systems like the London underground and other international train systems, most have tried to use a visual system rather than numerical system (it also solves the illiteracy problem). And these work really well. Maybe that could be a possible solution for the bus system here as well.

    On another note, depending on what you come up with finally and after doing some "user testing" to see if people would be comfortable with this system, I feel you should try and get this implemented in reality. I know that's not gonna be easy. But you could try and take help from this organisation, Janagraha ( Ramesh Ramanathan, who runs it, is well known in Bangalore as an advocate for such "people friendly governance". I feel he would be really interested in this. (BTW, I don't know him personally...only heard of him, but know of a friend who has worked with him).

    Do email me if you need further inputs/info. All the best.


  10. @param

    thanks for the inputs. will mail you later.

    i do not say that prime numbers MUST be used...only that some kind of mechanism must be in place to embed route information.

    it's really exasperating, having to ask people who might not know or learning all the bus numbers to all the places there are...

  11. Use any numbering system keeping a 3-digit system. Then at each bus stop put up a signboard that shows the route taken by each bus. This could be either as a map or a list or both. The three-language formula would work best - Local language, Hindi and English.