Lecture8

# Lecture8 - ECE-547 Introduction to Computer Communication...

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Purdue University ECE ECE - - 547 547 Introduction to Computer Introduction to Computer Communication Networks Communication Networks Instructor: Instructor: Xiaojun Xiaojun Lin Lin Lecture 8 Lecture 8

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Purdue University Poisson Process Poisson Process Definitions: I. The arrival process {N(t), t 0} is said to be a Poisson Process with rate λ >0 , if 1. N(0) = 0 2. P{N(t) = 1 } = λ t + o(t) 3. P{N(t) 2} = o(t) 4. For any t 0, s 0, N(t +s) – N(t) is independent of {N(u): u t}. ¾ This is known as the Independent Increments property. 5. For any t , s 0, the distribution of N(t+s) – N(t) is independent of t. ¾ This is known as the Stationary Increments property.
Purdue University Poisson Process Poisson Process ¾ Remember : A function f is said to be o(h) if ¾ In this case, does the earlier definition make sense or do we need to modify it, i.e., provide limits? 0 ) ( lim 0 = h h f h

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Purdue University Poisson Process Poisson Process II.
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Lecture8 - ECE-547 Introduction to Computer Communication...

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