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## The Final Present

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**The Final Present**Lee Jeng-Shiou Computer Network of E.E**Outline**• Throughput Analysis Review for Single-hop Networks • Throughout Analysis for Multi-hop Networks • Mathematical Analysis of the String Topology • Analytical and Simulation Results • An Alternative Mathematical Analysis of the String Topology • Conclusion**Throughput Analysis Review for Single-hop Networks**• (s(t), b(t)) • s(t): the backoff stage • b(t): the backoff time counter • p: the conditional collision probability • τ: the probability that a station transmits in a generic slot time**Throughput Review for Single-hop Networks (cont~)**• The transmission probability τ in a randomly chosen ”generic” slot is • The collision probability is expressed by • Throughput S is obtained by**Throughout Analysis for Multi-hop Networks**• We concentrate on the impact of the hidden node problem. • We analyze the throughput based on a single station’s point of view. • The analysis method is similar to the single-hop case. • Obtaining the stationary probability τ using a Markov model. • Expressing the throughput as function of τ by studying the events that can occur within a generic slot time.**Throughout Analysis for Multi-hop Networks**• Assumption: • All packets are destined for neighbor nodes. • There is no capture effect. • Each station always has packets to transmit.**A1**R=r A B A Simplified Condition • The carrier sense range is equal to the transmission range.**A Simplified Condition (cont~)**• The simulations have been done by the network simulator - ns2. • Simulation area 1500x1500 m2. • We consider five topology scenarios and each scenario includes four traffic patterns. • Each node generates packets based on CBR model with packet sizes 256, 512, 1024 and 2048 bytes. • They correspond to packet arrival interval of 0.0013, 0.0026, 0.0052 and 0.01 sec.**A1**R r A B A Realistic Carrier Sense Range • The carrier sense range is 550 meters and the transmission range is 250 meters.**Conclusions**• The throughput performance of the IEEE 802.11 DCF scheme in multi-hop ad hoc networks is analyzed. • It also shows the proposed model is accurate when degenerated into single-hop networks. • The throughput of a single station is decreased as the number of stations increases. • The total throughout almost stays at a constant value.**Conclusions (cont~)**• The total network throughput is decreased as much as by 55% when the carrier sense range is equal to 550 meters. • The larger packet size results in the higher network throughput. • For spatial reuse factor, the results shows that there no clear relationship with the number of stations and packet size.**Mathematical Analysis of the String Topology (cont.)**• Six possible situations observed by station 0 at the beginning of a slot.**Node 0 “idle” (1-τ) (cont.)**• One of n1 and n2 Tx (P2) (assume n1 Tx)**success: n2 idle during**• collision: n2 Tx during Tv**Analytical and Simulation Results (cont.)**• The simulation throughput (13 stations) and the analytical throughput.**An Alternative Mathematical Analysis of the String Topology**• One directional traffic between two stations • No collisions ->**An Alternative Mathematical Analysis of the String Topology**(cont.) • The normalized throughput of the basic access scheme when there is one traffic.**An Alternative Mathematical Analysis of the String Topology**(cont.) • The normalized throughput of the RTS/CTS access scheme when there is one traffic.**An Alternative Mathematical Analysis of the String Topology**(cont.) • Bi-directional traffic between two stations • Collisions may occur. • Evaluating the average backoff time • All newly generated backoff values, such as X ,Y ,and M ,are identically distributed from uniform distribution. where A represents the CWmin**An Alternative Mathematical Analysis of the String Topology**(cont.) • Let Z=|X-Y|. We have • A newly generated backoff value is M with the probability distribution as X, and Y. Let W=|M-Z|. We have • -> Z and W are identical distribution. • The expected backoff interval is**An Alternative Mathematical Analysis of the String Topology**(cont.) • Evaluating the collision probability**An Alternative Mathematical Analysis of the String Topology**(cont.) • The normalized throughput of the basic access scheme considering the collisions when there is two traffic.**An Alternative Mathematical Analysis of the String Topology**(cont.) • The normalized throughput of the RTS/CTS access scheme considering the collisions when there is two traffic.**Conclusions**• We first analyze the transmission behavior of stations in a string topology in the multi-hop environment. • In the presence of the hidden and exposed terminal problems, the mathematical analysis is more complicated compared to the single-hop wireless network. • From the analytical and simulation results, we find that a larger packet size can increase the normalized throughput.**Conclusions (cont.)**• For future research, we will proceed with the alternative mathematical analysis. • We may discuss the behavior under the assumption that the carrier sensing range is much larger than the transmission range, and the capture effect may be included. • Besides, we may extend our one-dimension topology to different types of topology.**Conclusion**• What we have done • We propose a new method to improve IEEE 802.11 performance and establish a model for analysis. • Simulation and comparison • What we are going to do • A general equation (even solution) for our model • More simulation