I am reading a few interesting scriptures on Algorithms. As I come across many algorithms which solve spcific tasks related to various problems, I started wondering if there is any 'Best' way of solving my 'Bus traveling' problem.
This is the problem I face everyday and I follow a certain way to tackle this problem. It is actually somewhat interesting if you are a frequent traveller using public transports in India.
My mode of communication from my home to office is public transport buses (BMTC - Bangalore Metropolitan Transport Corporation). The frequency and timing of the buses are erratic which I will define as the 'Degree of erraticity'. I generally have to change buses at three different points. I begin from my house and the bus stop near my house is the first place. I have to go to Bangalore Central Bus Stand which is my second. From there I got to another place called Marathalli which is just 1.5 kms from my office and I board a bus from Marathalli and reach my destination. I stay nearly 22 kms from my office. The distance from my house to Central Bus Stand is nearly 4 kms. Distance from the central Bus Stand to Marathalli is 16.5 Kms.
Now regarding the frequency of the buses. The frequency of buses from the bus stop near my house to Central Bus Stand is atleast one every 5 mins. This is really erratic. Sometimes, more than one buses to the same Central Bus Stand come one behind another and there is a small war between the buses as to who reaches the destination first. Sometimes, I would have to wait for nearly 15 minutes at my bus stop to get a bus to Central Bus Stand. It takes 15-20 minutes to reach the central bus stand from the stop depending on the bus. I have observed that there is atleast one bus between 6:10am and 6:15 am for certain. Sometimes, there are two and one of these two is really fast and I can reach Central Bus Stand in 15 minutes.
Once, I reach the Central Bus Stand, I have two option. There is a bonus bus which takes me directly to the office from the central bus stand and the frequency is very low. The driver of this bus is drives at normal speed and I can reach office in 40 minutes. One every 40 minutes is the frequency. There is one of such buses which leaves Central Bus Stand between 6:25am and 6:30 am. Once every 3 days he is really late and leaves the Central Bus Stand at 6:40. The route number of the buses plying between the Central Bus Stand and My office is '333W'. While, there is another option, which is the more general. I will have to get into that bus ,get down at Marathalli and board another bus from Marathalli to reach my destination. The frequency of this bus is pretty high. 2 buses every 5 minutes. But, there is a catch. I have observed that a few bus drivers drive the bus fast and I can reach Marathalli quite quickly compared to other bus drivers who drive at the normal speed. The extra overhead time if I travel in the buses which are driven by slow drivers is around 5-15 minutes. If the bus is fast I can reach Marathalli in 30 minutes. The route number of the buses plying between Central Bus Stand and Marthalli is '335E'.
From Marathalli to my office, distance is around 1.5kms. I will have to board another bus from Marathalli. But, the frequency is really low. One bus every 10 mins. But, I have an option here where I can get into a private cabs and reach the office, but, this comes at an extra cost. The extra cost is negligible, provided I do not take this option everyday. It takes 5 minutes to reach my office from Marathalli. If I leave my home after 6:30am the time each stage takes gets increased by 10 minutes.
Provided these conditions only, what is the most efficient way of travelling to Office ?
This is the problem I face everyday and I follow the following method to reach the office:
I reach the bus stop no matter what, between 6:10 and 6:15. I reach Central Bus Stand. I start searching for 333W, the direct bus to my destination. If I do not find the bus, I get into 335E. I reach Marathalli. Once, every 2-3 days I wait for 10 minutes to get a bus to reach my destination. Once in a while, if I am lucky, I get the same 333W which would have left late. Once in a while I take the private cabs. Is this the best solution or do better ones exist ? Can it be proved mathematically ???
This problem becomes more interesting once we start thinking more about that. Answers anyone ?? :-)
This is the problem I face everyday and I follow a certain way to tackle this problem. It is actually somewhat interesting if you are a frequent traveller using public transports in India.
My mode of communication from my home to office is public transport buses (BMTC - Bangalore Metropolitan Transport Corporation). The frequency and timing of the buses are erratic which I will define as the 'Degree of erraticity'. I generally have to change buses at three different points. I begin from my house and the bus stop near my house is the first place. I have to go to Bangalore Central Bus Stand which is my second. From there I got to another place called Marathalli which is just 1.5 kms from my office and I board a bus from Marathalli and reach my destination. I stay nearly 22 kms from my office. The distance from my house to Central Bus Stand is nearly 4 kms. Distance from the central Bus Stand to Marathalli is 16.5 Kms.
Now regarding the frequency of the buses. The frequency of buses from the bus stop near my house to Central Bus Stand is atleast one every 5 mins. This is really erratic. Sometimes, more than one buses to the same Central Bus Stand come one behind another and there is a small war between the buses as to who reaches the destination first. Sometimes, I would have to wait for nearly 15 minutes at my bus stop to get a bus to Central Bus Stand. It takes 15-20 minutes to reach the central bus stand from the stop depending on the bus. I have observed that there is atleast one bus between 6:10am and 6:15 am for certain. Sometimes, there are two and one of these two is really fast and I can reach Central Bus Stand in 15 minutes.
Once, I reach the Central Bus Stand, I have two option. There is a bonus bus which takes me directly to the office from the central bus stand and the frequency is very low. The driver of this bus is drives at normal speed and I can reach office in 40 minutes. One every 40 minutes is the frequency. There is one of such buses which leaves Central Bus Stand between 6:25am and 6:30 am. Once every 3 days he is really late and leaves the Central Bus Stand at 6:40. The route number of the buses plying between the Central Bus Stand and My office is '333W'. While, there is another option, which is the more general. I will have to get into that bus ,get down at Marathalli and board another bus from Marathalli to reach my destination. The frequency of this bus is pretty high. 2 buses every 5 minutes. But, there is a catch. I have observed that a few bus drivers drive the bus fast and I can reach Marathalli quite quickly compared to other bus drivers who drive at the normal speed. The extra overhead time if I travel in the buses which are driven by slow drivers is around 5-15 minutes. If the bus is fast I can reach Marathalli in 30 minutes. The route number of the buses plying between Central Bus Stand and Marthalli is '335E'.
From Marathalli to my office, distance is around 1.5kms. I will have to board another bus from Marathalli. But, the frequency is really low. One bus every 10 mins. But, I have an option here where I can get into a private cabs and reach the office, but, this comes at an extra cost. The extra cost is negligible, provided I do not take this option everyday. It takes 5 minutes to reach my office from Marathalli. If I leave my home after 6:30am the time each stage takes gets increased by 10 minutes.
Provided these conditions only, what is the most efficient way of travelling to Office ?
This is the problem I face everyday and I follow the following method to reach the office:
I reach the bus stop no matter what, between 6:10 and 6:15. I reach Central Bus Stand. I start searching for 333W, the direct bus to my destination. If I do not find the bus, I get into 335E. I reach Marathalli. Once, every 2-3 days I wait for 10 minutes to get a bus to reach my destination. Once in a while, if I am lucky, I get the same 333W which would have left late. Once in a while I take the private cabs. Is this the best solution or do better ones exist ? Can it be proved mathematically ???
This problem becomes more interesting once we start thinking more about that. Answers anyone ?? :-)
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