---
# System prepended metadata

title: MSSI - Problem Formalisation
tags: [MSSI]

---

# MSSI - Problem Formalisation
###### tags: `MSSI`

## Project Title
Accessible and sustainable ITS API for pricing schemes.

## Problem (definition + goals)
The purpose of the work is to analyze pricing schemes for different approaches of mobility sharing vehicles. Also, we will observe the effects of the number of seats in the pricing schemes and the traffic itself. 
	The simulation will be structured with 2 roads: a fee-less road and a taxed highway. The pricing scheme of this highway, as well as the total number of vehicles circulating, will be controlled by us and the changes it causes on the number of occupied seats in each vehicle and on the number of vehicles on the road will be analysed. We assume that in each scenario, all the vehicles have the same starting point.
The objective is to maximize the profit whilst keeping traffic to a minimum.


## Assumptions and premisses:
- Different types of vehicles have different taxes prices
- All the vehicles have the same starting point and the same ending point
- all vehicles drive at the same velocity
- fuel will be "infinite" for simulation purposes

## Constraints and Limits
- There will be 2 types of roads: and taxed highway with a higher max velocity and a fee-less road with a lower max velocity
- There will be using the golden gate map and, we use the same roads on every scenario;

## Input Model
- number of vehicles (>10);
- vehicles type (cars, trucks, bus, motorcycles, bicycles and pedestrians);
- pricing schedule;
- number of occupied seats in each vehicle (1-50);

Our pricing scheduele will be based on Golden Gate bride fee.
For 2 axles cars:
- $7.00: Monday through Friday, 5:00 a.m.to 10:00 a.m. and 3:00 p.m. to 7:00 p.m.;
- $6.00: weekends;
- $6.00: all other times.

For the others:
- 3 axles - $16.00
- 4 axles - $21.00
- 5 axles - $26.00
- 6 axles - $31.00
- 7 axles - $36.00


## Performance metrics/Output
We expect to analyze some metrics such as:
- number of vehicles on the road;
- total amassed money;


## Cost/utility functions

#### Duration of a trip:
    t(d) = v * d
    
- t(d): durations in minutes of a trip with d distance
- v: velocity of the vehicle
- d: distance from starting point to ending point

#### Money spent in taxes 
    m(n) = tx / n
- m(n): money spent in taxes divided by the number of passengers
- tx: taxes bitch
- n: number of passengers in the vehicle

#### Money spent in fuel
    g(d) = d * c * r
- g(d): money spent in fuel on a trip with d distance
- d: distance from starting point to ending point
- c: price of fuel
- r: ratio of consumption of the vehicle

#### Optimisation function
    min(m, g) = (m + g) * t
- min(m, g): cost of the trip with fuel cost g and taxes cost m
- Different cars may have different "min" functions to assess how different personal preferences (time vs cost) affects decisions and traffic

## Scenarios
We will start with a simplified version of the problem, simulating only cars with one or two seats. Then we will attach an alternative road to the main road with different pricing. Finally, we will add more different types of cars and more road alternatives.
In each scenario will be tested traffic congestion and the car route.


## Methodology

#### System model




## Authors
Duarte Faria - up201607176@fe.up.pt 
João Ribeiro - up201704851@fe.up.pt 
Maria Carolina Soares - up201605010@fe.up.pt 


