CMPE 257 Wireless and Mobile Networking SET 3a Medium Access Control Protocols Spring 2005 UCSC CMPE257 1 MAC Protocol Topics Modeling and performance analysis of collision avoidance MAC protocols Spring 2005 UCSC CMPE257 2 MAC Protocols Contention based MAC protocols Collision avoidance CA with CSMA to combat the hidden terminal problem Include IEEE 802 11 FAMA RIMA etc Schedule based MAC protocols Collision free Require time slotted structure Spring 2005 UCSC CMPE257 3 Contention based MAC protocols Focus on sender initiated MAC IEEE 802 11 and its variants Most work is simulation based some analytical work is confined to singlehop networks Interaction between spatial reuse and CA needs closer investigation Spring 2005 UCSC CMPE257 4 Analytical Work Takagi and Kleinrock TK84 use a simple network model to derive the optimal transmission range of ALOHA and CSMA protocols for multi hop networks An interesting read Wu and Varshney WV99 use this model to derive the throughput of non persistent CSMA and some busy tone multiple access BTMA protocols We WG02 follow Takagi and Wu s line of modeling to analyze collision avoidance MAC protocols in multi hop ad hoc networks Spring 2005 UCSC CMPE257 5 Preliminaries for Markov Regenerative Processes Limiting probability of state j Def P j lim P X t j t Calc P j E time in j in one cycle E time of one cycle Steady state probability of state j R j Def The long run proportions of transition into state j D j Mean time spent in state j per transition Theorem to calculate P j R j D j P j i R i D i Throughput Th Psuccess Spring 2005 UCSC CMPE257 6 Analytical Modeling Network model Nodes are randomly placed according to 2dimensional Poisson distribution i S S p i S e i where i is the of nodes S is the size of an area and is the density Note S is the average of nodes Each node has equal transmission and reception range R The average number of competing stations within a 2 station s transmission and reception range R is N N R Spring 2005 UCSC CMPE257 7 Analytical Modeling Key assumptions Time slotted each slot lasts We use the time slotted system as an approximation Each node is ready to transmit independently in each time slot with probability p Each node transmits independently in each time slot with probability p Heavy traffic assumption All node always have packets to be sent Perfect collision avoidance a FAMA property later extended to imperfect collision avoidance Spring 2005 UCSC CMPE257 8 Channel Model Model the channel as a circular region where there are some nodes Nodes within the region can communicate with one another but have weak interaction with nodes outside the channel Channel status is only decided by the successful and failed transmissions of nodes in the region The radius of the circular region R is modeled by R where 2 and there are in effect M 2 N nodes in the region M R 2 R 2 2 R 2 2 N Spring 2005 UCSC CMPE257 9 Channel Model 4 state Markov chain long 1 PIL 1 idle short1 PIS1 1 PII Spring 2005 PIS2 Channel A region within which all the nodes share the same view of busy idle state and have weak interactions with nodes outside short2 UCSC CMPE257 10 Channel Model Calculate the duration of states and transition probabilities between states Calculate the long term probability that the channel is in idle state and get the relationship between the average ready probability p and the average transmission probability p p p Prob the channel is sensed idle p is more important here because it is the actual transmission probability after collision avoidance and resolution Spring 2005 UCSC CMPE257 11 Channel States Idle the channel is sensed idle Tidle Long the state when a successful four way handshake is done Tlong lrts lcts ldata lack 4 Short1 the state when more than one node around the channel transmit RTS packets at the same time slot T l short 1 rts Short2 the state when one node around the channel initiates failed to nodes Tshort 2a lrts lhandshake 2 cts outside the region Spring 2005 UCSC CMPE257 12 Transition Probabilities Idle to Idle Pii There are on average M nodes competing for the channel M R 2 R 2 2 R 2 2 N The prob of having i nodes competing for the channel M i e M i The average trans prob is that none of them transmits in the next slot i i M Pii 1 p e M i i 0 e p M Spring 2005 UCSC CMPE257 13 Transition Probabilities Idle to LongPil Let Ps denote the prob that a node starts a successful 4 way handshake at a time slot The transition happens if only one of i nodes initiates the above handshake while the other nodes do not transmit i M Pil ip s 1 p i 1 e M i i 1 ps Me p M Spring 2005 UCSC CMPE257 14 Transition Probabilities Idle to Short1Pis1 Given i competing nodes the prob of more than one nodes competing in a time slot equals 1 Prob no node transmits Prob only one node transmits i e 1 1 p i ip 1 p i 1 So the average transition prob equals i M Pis1 1 1 p i ip 1 p i 1 e M i i 2 1 1 Mp e p M Idle to Short2 Pis 2 1 Pii Pil Pis1 Spring 2005 UCSC CMPE257 15 Transition Probabilities Let i l s1 and s 2 denote the steady state probs of states Idle Long Short1 and Short2 respectively From the Channel Markov Chain we have ii Pii l s1 s 2 i i Pii 1 i i 1 i 2 e p M Spring 2005 UCSC CMPE257 16 Channel Idle State We can calculate the long term prob that the channel is found idle I iTidle lTlong Tidle Pil Tlong iTidle s1Tshort1 s 2Tshort 2 Tidle Pis1Tshort1 Pis 2Tshort 2 i Pil l i Pis1 s1 and i Pis 2 s 2 Then we obtain the relationship between p i p and pp p Spring 2005 Tidle Pil Tlong pTidle F p p s Pis1Tshort1 Pis 2Tshort 2 UCSC CMPE257 17 Node Model 3 state Markov chain succeed We derive the saturation throughput with regard to p assuming that each node always has a packet to send 1 PWS wait PWF Pww Spring 2005 1 fail UCSC CMPE257 18 Nodal States Wait the state when the node defers for other nodes or backs off Twait Succeed the state when the node can complete a successful 4 way handshake Tsucceed lrts lcts ldata lack 4 Fail the state when the node initiates an unsuccessful handshake T fail lrts lcts 2 Spring 2005 UCSC CMPE257 19 Transition Probabilities Wait to SucceedPws We first need to calculate Pws r the prob that node x initiates a successful 4 way handshake with node y at a time slot given that they are apart at a distance r Details omitted here The pdf of distance …