Taxi service simulation to minimize waiting time

Aditya Gupta (2011009)Sushant Mehta (2010088)Mayank Verma (2010048)

Group 7

Introduction

● Problem● Solutions● Simulation● Result

Problem

We run a taxi service in cities of varying density.

Pickup requests emerge dynamically (in time).

We must deploy limited taxis in realtime to minimize average pickup time.

Sound familiar?

● Dynamic Task Allocation Problem○ N cabs from {10, 20, 30}

■ Varying speed○ Dynamic Pickup+Drop Requests

■ Emerge anywhere■ Emerge anytime■ Can have any distance

○ Stochastic environment■ Eased density maps

Solutions

● Assign the every new request the nearest free taxi?

● Assign every free taxi the nearest possible request?

Solutions

● Assign the every new request the nearest free taxi? Greedy.

● Assign every free taxi the nearest possible request? Also Greedy. Pre-Emptive. Stable Matching. Futuristic (Queueing with cost). Costly? Try to achieve perfect queues?

More cool solutions

● What if I predict where the requests will come from?

● The optimal static (one-time) allocation.

More cool solutions

● What if I predict where the requests will come from? Simple centralized supervised learning.Back-to-base(s) (100). Tradeoff - (hot/far).

● The optimal static (one-time) allocation.The Hungarian method.

Simulation

● NetLogo 5.0○ ~ 300 lines

● Map generation● 4 solutions

○ Naive ○ Pre-emptive○ Back-to-base○ Hungarian

■ Java Extension

Some snaps and Demo

Hungarian Method● Combinatorial

optimization algorithm

● Running time O(n3)● Extendable to

skewed matrices as well.

What we measured

● Average waiting time● Fuel/Distance per tick

Safety checks● Avg distance● Completed orders

How we measured

S. No. Number of taxis Map Density Speed of taxis Varying factor

1 (Base Case) 20 Medium 2.5 -

2 10 Medium 2.5 Number of taxis

3 30 Medium 2.5 Number of taxis

4. 20 High 2.5 Map Density

5. 20 Low 2.5 Map Density

6. 20 Medium 1.5 Speed of taxis

7. 20 Medium 3.5 Speed of taxis

Results - Medium

Results - low density map

Naïve Pre-Emption Back to Base Hungarian

Average Waiting Time 5.15 5.19 5.25 5.29

Average Order Distance 49.38 51.11 51.3 50.39

No. of orders completed 8358 8622 8597 8675

Fuel used per Tick 6.75 6.93 7.78 7.09

Results - high density map

Naïve Pre-Emption Back to Base Hungarian

Average Waiting Time 10.55 6.86 9.16 8.35

Average Order Distance ~50 ~50 ~50 ~50

No. of orders completed 28901 28763 28794 28654

Fuel used per Tick 29.82 25.76 30.43 27.69

Results - Reduced taxis (10)

● Naive and back-to-base explode(?).● Hungarian and Pre-emption survive.● Together, they flourish.

Naïve Pre-emption Back to Base Hungarian All 3Average Waiting Time ~4000 21.08 Very High 21.32 16.81

Average Order Distance 49.85 49.2 ~50 49.62 49.32No. of orders completed ~15000 19529 ~16000 19594 19758

Fuel used per Tick 24.16 21.98 24.86 22.63 22.714

Results - Reduced speed

● Just like reduced taxi’s case.

● And we tried many permutations and combinations of these parameters and strategies.

Naïve Pre-Emption Back to Base Hungarian All 3264.21 13.19 151.97 18.76 12.81

~50 ~50 ~50 ~50 58.49

19459 19608 19406 19639 19420

29.3 18.51 28.79 21.35 19.6

What did we learn?

● Work best together. ○ 16.81 vs 21.08 points in reduced taxis case.○ 9 ~ 25% better times than Naive.

● Individually, pre-emption!○ Consistent performer across scenarios.

More results

● Efficiency gain apparent in critical application○ Reduced taxis/resources○ Reduced speed/efficiency○ High density maps

● Fuel and pickup time correlated (efficiency)○ Pre-emption not bad at all

● Back-to-base is a fuel efficiency disaster.

Conclusion

● Taxi allocation to minimize avg. pickup time○ Task allocation problem

● Multiple Strategies○ Predictive, futuristic, optimal, stable, greedy

● NetLogo simulation○ Java Extension

● Results and Findings

Possible extensions

● Discarding a few orders to further improve average waiting time

● Adding realistic constraints: roads, traffic etc.○ Assignment Problem○ Routing Problem

Thanks