Lectures15-16

Lectures15-16 - 1 ECE & CSE ECE-CSE 861: Introduction...

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Unformatted text preview: 1 ECE & CSE ECE-CSE 861: Introduction to Computer Communication Networks Ness B. Shroff ECE & CSE Lectures 15-16 ECE & CSE Derivation of P-K formula Can we use continuous time Markov chain analysis? No, because service time distribution is not exponential Focus on the departure instances in queue ¡ Service time of jth packet 1 − j N j N 1 + j N 1 + j t j t 1 − j t ν j arrive N j : # of packets that remain in queue just after the departure of packet j v j : # of packets that arrive in the service time of packet j t j : departure time of packet j ECE & CSE 1 j-1 1 1 1, if N 1 ,otherwise ( ) 1, if x 1 ( ) 0, otherwise j j j j j j j j N N N N U N U x ν ν ν − − − + − ≥ = = − + ≥ = First, the statistics of ! j can be expressed as functions of the statistics of the service time. (1) ECE & CSE For example, to calculate σ v 2 , we first calculate: ( ) 2 2 2 ( ) { } ( ) , where is the r.v. denoting the service time k k E...
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This note was uploaded on 03/05/2011 for the course ECE 861 taught by Professor Shroff during the Winter '11 term at Ohio State.

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Lectures15-16 - 1 ECE & CSE ECE-CSE 861: Introduction...

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