Arrivals in any system in our lives are generally random in nature. Consider a simple queue at a movie theater for tickets. For simplicity assume that there is only one counter open selling tickets and people queue to purchase tickets. Using probability distribution we can mathematically model the arrival rate of people in the queue.

The most common probability distribution used to model arrivals in a queue is called a Poisson distribution. The number of people arriving in a given time interval would be discrete (integer) and hence Poisson distribution is an example of a discrete distribution. Its characterized by one parameter which is the mean number of arrivals in unit time.

In this example illustrating arrival times for a queue (Poisson arrivals). Lambda is the mean number of arrivals in 10 unit intervals. Mean duration between arrival = 10/lambda. Change lambda (< 10) to different values to see the output. This example plots arrival instants over a time window.

Sample value for Mean (lambda) = 1 is put here as default.

Lambda: