# Erlang Models

These models and simulations have been tagged “Erlang”.

​S-Curve + Delay for Bell Curve Showing Erlang Distribution

Generation of Bell Curve from Initial Market through Delay in Pickup of Customers

This provides the beginning of an Erlang distribution model

The Erlang distribution is a two parameter family of continuous probability distributions with support . The two parameters are:

• a positive integer 'shape'
• a positive real 'rate' ; sometimes the scale , the inverse of the rate is used.

This model is a classic instance of an Erlang Queuing Process.

We have the entities:
- A population of cars which start off in a "crusing" state;
- At each cycle, according to a Poisson distribution defined by "Arrival Rate" (which can be a constant, a function of time, or a Converter to simulate peak hours), some cars transition to a "looking" for an empty space state.
- If a empty space is available (Parking Capacity  > Count(FindState([cars population],[parked]))) then the State transitions to "Parked."
-The Cars stay "parked" according to a Normal distribution with Mean = Duration and SD = Duration / 4
- If the Car is in the state "Looking" for a period longer than "Willingness to Wait" then the state timeouts and transitions to impatient and immediately transitions to "Crusing" again.

The model is set to run for 24 hours and all times are given in hours (or fraction thereof)

WIP:
- Calculate the average waiting time;
- Calculate the servicing level, i.e., 1- (# of cars impatient)/(#cars looking)

A big THANK YOU to Scott Fortmann-Roe for helping setup the model's framework.
The VANET handles situation of parking in crowded areas. It takes into account the parking capacity, arrival rate of cars, already parked cars , while making decisions.
The description of states are :

1. Cruising : State of cars which are moving out of parking area, but are still inside the parking lot.

2.Parked : State of cars which are already parked.

3. Just entered : State of cars which have just entered the parking lot and are searching for parking position.

If an accident occurs at a place, the master car informs the OBUs of neighbouring cars in group about the accident and they change direction . Some of the cars depending upon their position become master car in other groups and the process of warning is propagated to car population in radius of the accident.
If an accident occurs at a place, the master car informs the OBUs of neighbouring cars in group about the accident and they change direction . Some of the cars depending upon their position become master car in other groups and the process of warning is propagated to car population in radius of the accident.
If an accident occurs at a place, the master car informs the OBUs of neighbouring cars in group about the accident and they change direction . Some of the cars depending upon their position become master car in other groups and the process of warning is propagated to car population in radius of the accident.
​S-Curve + Delay for Bell Curve Showing Erlang Distribution

Generation of Bell Curve from Initial Market through Delay in Pickup of Customers

This provides the beginning of an Erlang distribution model

The Erlang distribution is a two parameter family of continuous probability distributions with support . The two parameters are:

• a positive integer 'shape'
• a positive real 'rate' ; sometimes the scale , the inverse of the rate is used.

This model is a classic instance of an Erlang Queuing Process.

We have the entities:
- A population of cars which start off in a "crusing" state;
- At each cycle, according to a Poisson distribution defined by "Arrival Rate" (which can be a constant, a function of time, or a Converter to simulate peak hours), some cars transition to a "looking" for an empty space state.
- If a empty space is available (Parking Capacity  > Count(FindState([cars population],[parked]))) then the State transitions to "Parked."
-The Cars stay "parked" according to a Normal distribution with Mean = Duration and SD = Duration / 4
- If the Car is in the state "Looking" for a period longer than "Willingness to Wait" then the state timeouts and transitions to impatient and immediately transitions to "Crusing" again.

The model is set to run for 24 hours and all times are given in hours (or fraction thereof)

WIP:
- Calculate the average waiting time;
- Calculate the servicing level, i.e., 1- (# of cars impatient)/(#cars looking)

A big THANK YOU to Scott Fortmann-Roe for helping setup the model's framework.
This model is a classic instance of an Erlang Queuing Process.

We have the entities:
- A population of cars which start off in a "crusing" state;
- At each cycle, according to a Poisson distribution defined by "Arrival Rate" (which can be a constant, a function of time, or a Converter to simulate peak hours), some cars transition to a "looking" for an empty space state.
- If a empty space is available (Parking Capacity  > Count(FindState([cars population],[parked]))) then the State transitions to "Parked."
-The Cars stay "parked" according to a Normal distribution with Mean = Duration and SD = Duration / 4
- If the Car is in the state "Looking" for a period longer than "Willingness to Wait" then the state timeouts and transitions to impatient and immediately transitions to "Crusing" again.

The model is set to run for 24 hours and all times are given in hours (or fraction thereof)

WIP:
- Calculate the average waiting time;
- Calculate the servicing level, i.e., 1- (# of cars impatient)/(#cars looking)

A big THANK YOU to Scott Fortmann-Roe for helping setup the model's framework.
This model is a classic instance of an Erlang Queuing Process.

We have the entities:
- A population of cars which start off in a "crusing" state;
- At each cycle, according to a Poisson distribution defined by "Arrival Rate" (which can be a constant, a function of time, or a Converter to simulate peak hours), some cars transition to a "looking" for an empty space state.
- If a empty space is available (Parking Capacity  > Count(FindState([cars population],[parked]))) then the State transitions to "Parked."
-The Cars stay "parked" according to a Normal distribution with Mean = Duration and SD = Duration / 4
- If the Car is in the state "Looking" for a period longer than "Willingness to Wait" then the state timeouts and transitions to impatient and immediately transitions to "Crusing" again.

The model is set to run for 24 hours and all times are given in hours (or fraction thereof)

WIP:
- Calculate the average waiting time;
- Calculate the servicing level, i.e., 1- (# of cars impatient)/(#cars looking)

A big THANK YOU to Scott Fortmann-Roe for helping setup the model's framework.
This model is a classic instance of an Erlang Queuing Process.

We have the entities:
- A population of cars which start off in a "crusing" state;
- At each cycle, according to a Poisson distribution defined by "Arrival Rate" (which can be a constant, a function of time, or a Converter to simulate peak hours), some cars transition to a "looking" for an empty space state.
- If a empty space is available (Parking Capacity  > Count(FindState([cars population],[parked]))) then the State transitions to "Parked."
-The Cars stay "parked" according to a Normal distribution with Mean = Duration and SD = Duration / 4
- If the Car is in the state "Looking" for a period longer than "Willingness to Wait" then the state timeouts and transitions to impatient and immediately transitions to "Crusing" again.

The model is set to run for 24 hours and all times are given in hours (or fraction thereof)

WIP:
- Calculate the average waiting time;
- Calculate the servicing level, i.e., 1- (# of cars impatient)/(#cars looking)

A big THANK YOU to Scott Fortmann-Roe for helping setup the model's framework.
The VANET handles situation of parking in crowded areas. It takes into account the parking capacity, arrival rate of cars, already parked cars , while making decisions.
The description of states are :

1. Cruising : State of cars which are moving out of parking area, but are still inside the parking lot.

2.Parked : State of cars which are already parked.

3. Just entered : State of cars which have just entered the parking lot and are searching for parking position.

This model is a classic instance of an Erlang Queuing Process.

We have the entities:
- A population of cars which start off in a "crusing" state;
- At each cycle, according to a Poisson distribution defined by "Arrival Rate" (which can be a constant, a function of time, or a Converter to simulate peak hours), some cars transition to a "looking" for an empty space state.
- If a empty space is available (Parking Capacity  > Count(FindState([cars population],[parked]))) then the State transitions to "Parked."
-The Cars stay "parked" according to a Normal distribution with Mean = Duration and SD = Duration / 4
- If the Car is in the state "Looking" for a period longer than "Willingness to Wait" then the state timeouts and transitions to impatient and immediately transitions to "Crusing" again.

The model is set to run for 24 hours and all times are given in hours (or fraction thereof)

WIP:
- Calculate the average waiting time;
- Calculate the servicing level, i.e., 1- (# of cars impatient)/(#cars looking)

A big THANK YOU to Scott Fortmann-Roe for helping setup the model's framework.
​S-Curve + Delay for Bell Curve Showing Erlang Distribution

Generation of Bell Curve from Initial Market through Delay in Pickup of Customers

This provides the beginning of an Erlang distribution model

The Erlang distribution is a two parameter family of continuous probability distributions with support . The two parameters are:

• a positive integer 'shape'
• a positive real 'rate' ; sometimes the scale , the inverse of the rate is used.

9 months ago
This model is a classic instance of an Erlang Queuing Process.

We have the entities:
- A population of cars which start off in a "crusing" state;
- At each cycle, according to a Poisson distribution defined by "Arrival Rate" (which can be a constant, a function of time, or a Converter to simulate peak hours), some cars transition to a "looking" for an empty space state.
- If a empty space is available (Parking Capacity  > Count(FindState([cars population],[parked]))) then the State transitions to "Parked."
-The Cars stay "parked" according to a Normal distribution with Mean = Duration and SD = Duration / 4
- If the Car is in the state "Looking" for a period longer than "Willingness to Wait" then the state timeouts and transitions to impatient and immediately transitions to "Crusing" again.

The model is set to run for 24 hours and all times are given in hours (or fraction thereof)

WIP:
- Calculate the average waiting time;
- Calculate the servicing level, i.e., 1- (# of cars impatient)/(#cars looking)

A big THANK YOU to Scott Fortmann-Roe for helping setup the model's framework.
​S-Curve + Delay for Bell Curve Showing Erlang Distribution

Generation of Bell Curve from Initial Market through Delay in Pickup of Customers

This provides the beginning of an Erlang distribution model

The Erlang distribution is a two parameter family of continuous probability distributions with support . The two parameters are:

• a positive integer 'shape'
• a positive real 'rate' ; sometimes the scale , the inverse of the rate is used.

​S-Curve + Delay for Bell Curve Showing Erlang Distribution

Generation of Bell Curve from Initial Market through Delay in Pickup of Customers

This provides the beginning of an Erlang distribution model

The Erlang distribution is a two parameter family of continuous probability distributions with support . The two parameters are:

• a positive integer 'shape'
• a positive real 'rate' ; sometimes the scale , the inverse of the rate is used.

9 months ago