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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 Spring '08
 Healey
 Networking, Computer network, Coin flipping, Scott Jordan

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