| POISSON (Random) EVENTS | 1 | ||||||||||||
| How many events will likely take place during a time interval of a specified length? | |||||||||||||
| How many vehicles will arrive in the next 20 seconds? | |||||||||||||
| How many vehicles will a toll booth serve in the next half minute? | |||||||||||||
| The Poisson equation can be used to answer these questions if: | |||||||||||||
| 1.) | The events are indeed random (independent) | ||||||||||||
| 2.) | The events are infrequent | ||||||||||||
| 3.) | The underlying arrival (or service) rate does not change during the analysis period | ||||||||||||
| The Poisson distribution is a discrete distribution, not a continuous distribution | |||||||||||||
| I. | P(n)=e-ut(ut)n/n! | ||||||||||||
| u = lambda | |||||||||||||
| P(n) = | probability of n events occurring during interval t | ||||||||||||
| where u = mean rate at which the events occur | |||||||||||||
| "events" are usually arrivals in transportation applications | |||||||||||||
| Example: | |||||||||||||
| What is the probability of exactly 3 vehicles arriving in 1 minute if the arrival rate is 120 vph? | |||||||||||||
| P(3)=e-(120veh/hour)(1min*1 hr./60 min)[(120veh/hr)(1min*1hr./60min)]3/3! = 0.180 | |||||||||||||