# lec21 - UCI University of California Irvine EECS 161...

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EECS 161 - Introduction to Computer Networking Scott Jordan Performance UCI University of California, Irvine A Model of Packet Arrivals We want to model the times at which packets arrive at a router: Idea: split time into small intervals Suppose that a packet arrives in a small time interval with probability . To simulate this, flip a coin with -- Heads = packet arrival in this time interval, Tails = no packet arrival in this time interval. x x x T 1 T 2 T 3 t t h λ h P H ( ) λ h =

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EECS 161 - Introduction to Computer Networking Scott Jordan Performance UCI University of California, Irvine A Model of Packet Arrivals Flip a coin with -- Heads = packet arrival in this time interval, Tails = no packet arrival in this time interval. What is the distribution of time until the first packet arrives, i.e. what is ? Approach -- Consider the number of coin flips until you get Heads. This is a random variable with an Geometric distribution. The time until the first packet arrives is equal to the number of coin flips, times h .
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