## Abstract

As shown in Section 2.1, a stochastic process can be described by the laws of probability at each point of time t ≥ 0. As shown in Fig. 2.1.1, we are very much interested in the random variable *N*(*t*), which denotes the number of arriving customers up to time *t*,where *N*(*t*) = 0, 1, 2,…. A *counting process* {*N*(*t*), *t*≥ 0} is one of the stochastic processes, and Fig. 2.1.1 shows a “sample function” or “sample path” of the counting process {*N*(*t*), *t* ≥ 0}. We can consider several examples of counting processes, where the “customer” is replaced by other relevant words such as the “call” in congestion theory, the “failure” of machines, and the arriving “job” or arriving “transaction” of computer systems.

## Keywords

Poisson Process Interarrival Time Counting Process Probability Mass Function Stationary Increment## Preview

Unable to display preview. Download preview PDF.