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Chapter 4. Multiple users access the same communication channel. Multi-access Communication. Multiple users access the same communication channel Multiple access protocols can be classified according to the amount of coordination between users. Multi-access Communication. Least coordination.
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Chapter 4 Multiple users access the same communication channel
Multi-access Communication • Multiple users access the same communication channel • Multiple access protocols can be classified according to the amount of coordination between users.
Multi-access Communication Least coordination ALOHA S-ALOHA … CSMA CSMA/CD (Ethernet) Reservation-based protocols Overhead Most coordination
Section 4.2 Slotted ALOHA
4.2 Slotted ALOHA • Slotted System : fixed length packets packet transmission time = 1 slot, all transmit are synchronized. • Poisson arrivals : arrival to each of the m stations is an independent Poisson process with rate /m. (because close to real world situation, and easy to analysis) infinite # users, each user generates a small fraction of total traffic, the aggregate traffic → Poisson In fact, Slot time 較 transmit time大
4.2 Slotted ALOHA • Collision or perfect reception : If 2 or more nodes send a packets in a slot, then collision. If exacting one node transmits, then it is received correctly. • 0, 1, e: immediate feedback more than one • Retransmissions : Collided packets will be retransmitted.
4.2.2 Slotted ALOHA • Simple throughput analysis Let G = expected # of transmit in a slot = + rate of retransmits Assume(incorrect) : the # of transmit in a slot, K, is Poisson. • Poisson Rate of re-tx So never Poisson for G
4.2.2 Slotted ALOHA # of success Per second S 0.368 1/e G G : attempt rate : # transmit/slot S : # success transmit/slot
4.2.2 Slotted ALOHA • Delay Analysis : Markov model(6a:assume no-buffering p.276) • Backlogged node is node with packet to be retransmitted. • Unbacklogged node is node that may generate new traffic. • After a collision, a backlogged node waits L slots before re-transmit, where P(L=i)=(1-qr)i-1qr, i=1,2,… • An unbacklogged node, will transmit a new packet with probability qa=P(at least one new packet in a slot) • is total arrived rate # users=m
4.2.2 Slotted ALOHA State of Markov process is the # of backlogged nodes. Let Nt=# of backlogged nodes at the beginning of slot t. 0 1 2 n m 不可能 …… ……
4.2.2 Slotted ALOHA Let Qa(i, n)=probably of i unbacklogged nodes transmit in a given slot, given N=n Let Qr(i, n)=probably of i backlogged nodes transmit in a given slot, given N=n
4.2.2 Slotted ALOHA • {Nt, t=0,1,2,…} is an irreducible a periodic Markov Chain. Thus, limit probability {n, n=0,1,…,m} exist Can find delay?(using Little’s theorem) N=T 直覺上，leave qr大? But for large m? heavy backlog very long
4.2.2 Slotted ALOHA • Let Dn = drift = expected change in backlog over one slot time given state n. = (m-n)qa-[Qa(1,n)Qr(0,n) +Qa(0,n)Qr(1,n)] increase in backlog decrease in backlog =Psucc. (4.5)
4.2.2 Slotted ALOHA • Let G(n)=expected # of attempted tx (new+backlogged) in a slot, given state n = (m-n)qa+nqr • Let A(n)=expected # of new tx in a slot, given state n = (m-n)qa
Homework #2 • Due 11/15 • 3.9, 3.16, 3.37, 4.3 , 4.5 共5題
4.2.2 Slotted ALOHA • When qa and qr are small, PsuccG(n)e-G(n)
4.2.2 Slotted ALOHA G(n) mqr (qr>qa) mqa n m 0
4.2.2 Slotted ALOHA • Adjust qr such that attempt rate G=1 G(n) mqr adjust qr=> mqa n
4.2.2 Slotted ALOHA • Psucc : at most e-1 for large m. • qr ↑ , delay in re-tx ↓, but G(n)↑with n 同樣的n，qr ↑相對G(n)較大 Psucc 圖形會被壓縮。 上圖U點向左移較少n即到達U • 反之qr↓, retx delay↑, but only one state point.
4.2.3 Stabilized Slotted Aloha • Change qr dynamically to maintain G(n)=1, n = estimate n. • [Pseudo-Bayesian Algorithm] (Rivest) • Assumptions: • Slotted, Poisson Arrivals, collision or perfect reception, immediately feedbacks. • Infinite # of nodes – each newly arriving packets arrives at a new nodes. • All nodes with a packet(new or old) transmits in a slot with probably qr
4.2.3 Stabilized Slotted Aloha • Let nk = # of backlogged nodes at the beginning of slot k (全部看成backlogged, if 有packet(new or old)) • Ik = the event slot k is idle • Sk = the event slot k is success • Ck = the event slot k is collision • Ak = # of new arrivals in slot k
4.2.3 Stabilized Slotted Aloha • nk+Ak if Ik • nk+1= nk+Ak-1 if Sk • nk+Ak if Ck • Let nk be the estimate of nk computed by each node. • Each node assumes nk is Poisson dist. nk nk+1 Slot k
4.2.3 Stabilized Slotted Aloha • Algorithm: • Each backlogged node transmits in slot k with probably. • Each node updates its estimate by Try to get G=1 If Ik or Sk減少 qr↑ If Ck增加 qr↓
4.2.3 Stabilized Slotted Aloha • Properties of the Algorithm: • Assume : nk is Poisson distributed with mean nk1 • (1)
4.2.3 Stabilized Slotted Aloha Poisson
4.2.3 Stabilized Slotted Aloha • (3) • 以上(1)~(3) Assume Poisson is OK, and alg. to estimate nk+1 is reasonable.
4.2.3 Stabilized Slotted Aloha • (4) # of users with packets Probably of trans. What we want Maximum throughput.
4.2.3 Stabilized Slotted Aloha Mean nk+1 getting smaller e states
4.2.3 Stabilized Slotted Aloha P(Ik+Sk) P(Ck)
4.2.3 Stabilized Slotted Aloha • [Approximate delay for Pseudo-Bayesian] • (之前prove, estimate is accurate G(n)→1, max throughput stable) How about delay?
4.2.3 Stabilized Slotted Aloha P(nk=0) P(nk=1)
4.2.3 Stabilized Slotted Aloha P(1 tx)
4.2.3 Stabilized Slotted Aloha Wi = delay from the i-th arrival until the beginning of the slot of the i-th departure Qi = # of backlogged pkts(excluding possible successful trans) at the instant before the i-th arrival. 假設FCFS, 因為average is the same. Qi t1 t2 tQi yi i-th departure ri L S Wi i-th arrival
4.2.3 Stabilized Slotted Aloha Let yi = # of slots from the Qi-th successful tx (end of slot) until the beginning of the i-th successful tx Where tj = # of slots needed for the j-th successful tx after the i-th arrival
4.2.3 Stabilized Slotted Aloha • Let L be the slot #, immediately following Qi-th success tx. • Suppose nL=1, then E(y| nL)=0 • Suppose nL>1, then E(y| nL>1)=e-1 yi+S S success
4.2.3 Stabilized Slotted Aloha • P1 = fraction of slots in which n=1 and pkt is successfully tx. • = fraction of slots in which there is a successful tx • = fraction of packets successfully trans. From state 1
4.2.3 Stabilized Slotted Aloha • = fraction of packets successful transmitted from higher state # S S S S S
