# Homework Help: Bus simulation in excel, exponential distribution departure

1. Nov 1, 2009

### AGS

1. The problem statement, all variables and given/known data

The bus service operates between points A and B. The buses depart from the terminal station A with headways that follow the negative exponentioal distributiona with parameter 10 trips per hour.
Assume that the characteristics of the system remain the same over time (not time dependent). Run simulation for 5 hours and find the average headway in each of the 5 hours.

So what Im having trouble with is the exponential distributed departure for each bus.

2. Relevant equations
no eq. given

3. The attempt at a solution
I think that the formula to work with is
f(x)=lamda*exp(-lamda*x)
Im little confused if lamda is 10 or 10/60=1/6 but it 1/6 makes more sence to me since I think the mean (mui=expected value) headway is 6 minutes and lamda=1/mui.
Im using excel and used the randbetween(0,35) to give me random x and than I plotted it and got a plot that looked ok. I also tried with lamda=10 but than I used rand() that gives random number between (0,1).
My problem is that I don´t know how to use this information to get random exponential distrebuted headways for each bus!
Should I maby use the inverse? T=-lnU/lamda (use rand() to get U)

Last edited: Nov 1, 2009
2. Nov 1, 2009

### Cygni

Hey,

Given that you have time constraint, parameter $$\lambda$$ and that that the bus journeys are discrete I think u will have to use Poisson distribution to generate the probabilities, however, You must not forget to multiply the parameter by 5 as your simulation is going to take 5 hours. Once this is completed one can generate probabilities for 5 hour bus journeys and create a rule for simulation.