1. IIT Bombay Data Structures and Algorithms Prof. Ajit A. Diwan Prof. Ganesh Ramakrishnan Prof. Deepak B. Phatak Department of Computer Science and Engineering IIT Bombay Session: Bus Queue 1Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

2. IIT Bombay Bus Queue: Overview Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay2 People Arrive and stand in a queue at the bus stop Wait for the bus to arrive Buses Arrive at around scheduled time Limited available seats (varies for each bus) Waiting time of a person = Time of boarding the bus – Arrival time of person at bus stop

3. IIT Bombay Let us demonstrate the entire process Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay3

4. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay4 A bus stop

5. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay5 Waiting for bus to arrive PersonArrival Time 100114:15

6. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay6 Waiting for bus to arrive PersonArrival Time 100114:15 100214:19

7. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay7 Waiting for bus to arrive PersonArrival Time 100114:15 100214:19 100314:21

8. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay8 Waiting for bus to arrive PersonArrival Time 100114:15 100214:19 100314:21 100414:22

9. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay9 Waiting for bus to arrive PersonArrival Time 100114:15 100214:19 100314:21 100414:22 100514:27

10. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay10 Bus arrived: 14:30 Available Seats: 2 PersonArrival Time 100114:15 100214:19 100314:21 100414:22 100514:27

11. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay11 Bus arrived: 14:30 Available Seats: 2 Person 1 waited for 15 min Person 2 waited for 11 min PersonArrival Time 100114:15 100214:19 100314:21 100414:22 100514:27

12. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay12 Waiting for next bus to arrive PersonArrival Time 100114:15 100214:19 100314:21 100414:22 100514:27

13. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay13 Bus arrived: 14:40 Available Seats: 7 PersonArrival Time 100114:15 100214:19 100314:21 100414:22 100514:27

14. IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay14 PersonArrival Time 100114:15 100214:19 100314:21 100414:22 100514:27 Bus arrived: 14:40 Available Seats: 7 Person 3 waited for 19 min Person 4 waited for 18 min Person 5 waited for 13 min

15. IIT Bombay Average wait time Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay15 In our example, with assumed ‘hypothetical’ timings, we have: Person 1 waited for 15 min Person 2 waited for 11 min Person 3 waited for 19 min Person 4 waited for 18 min Person 5 waited for 13 min 5 persons waited for 76 minutes The ‘average’ wait time, is thus 15.06 minutes In actual practice, passengers will arrive randomly. Buses will also have random arrivals around their scheduled time. Even the number of available seats will have to be generated randomly

16. IIT Bombay References Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay16 All images are taken from https://openclipart.org These are released in public domain

17. IIT Bombay Thank you Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay17