Examples

Bike Sharing System

We consider a model for a bike sharing system. In the system bikes are made available in a number of stations that are placed in various areas of a city. Users that plan to use a bike for a short trip can pick up a bike at a suitable origin station and return it to any other station close to their planned destination.

One of the major issues in bike sharing systems is the availability and distribution of resources, both in terms of available bikes at the stations and in terms of available empty parking places in the stations.

In our scenario we assume that the city is partitioned in homogeneous zones and that all the stations in the same zone can be equivalently used by any user in that zone.

Bike Sharing System 2

We consider another model for a bike sharing system consisting of N=1000 stations of capacity K=30 and a fleet size of sN bikes, where s is the average number of bikes per station. The model abstracts from the actual distribution of bike stations in space (hence the attribute ``homogeneous’’) and assumes that stations are randomly chosen by users.

A generic station is modelled by the component HBSStation with two attributes: cp, recording the capacity (initialised to $K$ and constant in time); and npb, recording the number of bikes parked in the station. The behaviour of the station is straightforward; it consists of a single state Y since the relevant information is kept in attribute npb. The actions modelling getting and returning bikes have no synchronisation requirement (they play the role of ``internal’’ actions in the process algebra sense). The rate of a get transition of an individual station is constant. The rate of a ret transition is given by a constant multiplied by the number of bikes in circulation in the system divided by the total number of stations N. In the model, the number of bikes in circulation is kept in the global attribute incirculation.

SIER Model

We consider the classical SIER epidemic model. This model can be modelled in CARMA in different way:

• SIER1
• SIER2
• SIER3

BUS Model

We consider here a simple scenario composed by two routes, identified with the integers 1 and 2. These routes connect 8 stops numbered from 0 to 7. Route 1 is a slow line and connects all the stops in a sequential order. Differently, route 2 is a a fast line and only connects even stops. A special location numbered -1 is also used to identify the bus depot. Route 1 starts at location 0, while route 2 at location 4.