Simulation and Modelling - Old Questions

6. Define arrival pattern. Explain non-stationary Poisson process.

Arrival defines the way customers enter the system. Mostly the arrivals are random with random intervals between two adjacent arrivals. Typically the arrival is described by a random distribution of intervals also called Arrival Pattern. Arrivals may occur at scheduled times or at random times. When at random times, the inter arrival times are usually characterized by a probability distribution and most important model for random arrival is the poisson process. In schedule arrival interarrival time of customers are constant.

The non-stationary Poisson process is a Poisson process for which the arrival rate varies with time. More specifically, it can be defined as follows:

The counting process N(t) is a non-stationary Poisson process if:

a) The process has independent increments.

b) 

    Where, λ(t) = the arrival rate at time t

                dt = differential sized interval