B.Krishna Chaitanya 
		     			 Mtech '03, KreSIT
		       			   IIT BOMBAY	
		              	      chaitanya@it.iitb.ac.in
		   	       
	     	
	  		

				
				
     	    Network protocols are studied for various parameters like fairness, throughput, etc. These protocols are 
usually simulated using standard network simulators like   NS-2 (USC/ISI/LBNL/Xerox PARC) ,Gosip (QoS IP simulation) 
NetViz ,NIST Net (NIST) ,REAL  etc. But these simulations can be used to study how a protocol performs for particular 
instances. However mathematical analysis and analytical evaluation of a protocol will prove  the veracity of  protocol 
under all possible instances that the protocol works on.The paper shows this by evaluating IEEE 802.11 protocol
analytically and compares the results with simulation instances.

1.Introduction

        	Importance of analytical modelling is specified here. Difference between analytical modelling and 
		simulation explained. 


2.Marcov Chains

	Basic definition of marcov chains. Computation of n-step transition probabilities, State classification and
	limiting distributions explained.

	Reference:
	
	"Probability and statistics with reliability and queing and computer science applications"
		by Kishor S. Trivedi

3.IEEE 802.11

	A introduction to protocol. A very brief introduction to PCF & DCF. Diffent access mechanisms in
	DCF i.e basic access mechanisms and RTS/CTS are explained.
	
	Reference:
	
	"Wireless local area network and 802.11"
				by Plamen Nedeltchev

	"IEEE 802.11 Wireless LAN: Capacity Analysis & Protocol Enhancement" F.Cali,M.Conti and Enrico Gregori
 consiglio Narionale delie Ricerche,Italy. 
				

4.Modelling backoff scheme using Marcov chains.
	
	How Marcov chains are used to model the backoff window size in 802.11 DCF is explained pictorially.
	Expressions for probability that a station transmits in a randomly choosen time slot is derived using
	Marcov chains.

	Reference:
	
	Performance Analysis of the IEEE 802.11 Distributed Coordination Function
		by Giuseppe Bianchi

5.Throughput

	Expressions for saturation throughput for both basic access mechanisms and RTS/CTS mechanisms are 
	derivated using above results.

	Reference:
	
	Performance Analysis of the IEEE 802.11 Distributed Coordination Function
                by Giuseppe Bianchi


6.Expression for Maximum saturation throughput.	

	Various factors that determine the throughput are studied analytically using the above throughput formulae.
	Above throughput formulae is diffentiated to get the maximum saturation throughput.
	
	
	Reference:
	
	Performance Analysis of the IEEE 802.11 Distributed Coordination Function
                by Giuseppe Bianchi

	

7.Simulation of IEEE 802.11 protocol

	A set of parameters that are assumed for simulation are specified for diffent underlying physical media.
	
	Reference:
	
	Performance Analysis of the IEEE 802.11 Distributed Coordination Function
                by Giuseppe Bianchi


8.Comparison of simulated results and analytical results

	The following relations are compared:

	1.Throughput v/s number of stations
	2.Throughput v/s transmission probability for basic and RTS/CTS
	3.Throughput v/s initial size of  backoff window for basic and RTS/CTS
	4.Throughput v/s maximum backoff  stage.
	5.Throughput v/s packtet size.

	The above relations are studied using simulation model and analytical model and results are compared.

	
	Reference:
	
	Performance Analysis of the IEEE 802.11 Distributed Coordination Function
                by Giuseppe Bianchi

9.Conclusions.
	A brief summary of above work.

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