1 / 106

Chapter 4

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.

adeola
Download Presentation

Chapter 4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 4 Multiple users access the same communication channel

  2. Multi-access Communication • Multiple users access the same communication channel • Multiple access protocols can be classified according to the amount of coordination between users.

  3. Multi-access Communication Least coordination ALOHA S-ALOHA … CSMA CSMA/CD (Ethernet) Reservation-based protocols Overhead Most coordination

  4. Section 4.2 Slotted ALOHA

  5. 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

  6. 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.

  7. 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

  8. 4.2.2 Slotted ALOHA # of success Per second S 0.368  1/e G G : attempt rate : # transmit/slot S : # success transmit/slot

  9. 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

  10. 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 …… ……

  11. 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

  12. 4.2.2 Slotted ALOHA

  13. 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

  14. 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)

  15. 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

  16. Homework #2 • Due 11/15 • 3.9, 3.16, 3.37, 4.3 , 4.5 共5題

  17. 4.2.2 Slotted ALOHA • When qa and qr are small, PsuccG(n)e-G(n)

  18. 4.2.2 Slotted ALOHA

  19. 4.2.2 Slotted ALOHA G(n) mqr (qr>qa) mqa n m 0

  20. 4.2.2 Slotted ALOHA • Adjust qr such that attempt rate G=1 G(n) mqr adjust qr=> mqa n

  21. 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.

  22. 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

  23. 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

  24. 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

  25. 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↓

  26. 4.2.3 Stabilized Slotted Aloha • Properties of the Algorithm: • Assume : nk is Poisson distributed with mean nk1 • (1)

  27. 4.2.3 Stabilized Slotted Aloha

  28. 4.2.3 Stabilized Slotted Aloha Poisson

  29. 4.2.3 Stabilized Slotted Aloha

  30. 4.2.3 Stabilized Slotted Aloha • (2)

  31. 4.2.3 Stabilized Slotted Aloha • (3) • 以上(1)~(3) Assume Poisson is OK, and alg. to estimate nk+1 is reasonable.

  32. 4.2.3 Stabilized Slotted Aloha • (4) # of users with packets Probably of trans. What we want Maximum throughput.

  33. 4.2.3 Stabilized Slotted Aloha • (5)

  34. 4.2.3 Stabilized Slotted Aloha Mean nk+1 getting smaller e states

  35. 4.2.3 Stabilized Slotted Aloha P(Ik+Sk) P(Ck)

  36. 4.2.3 Stabilized Slotted Aloha

  37. 4.2.3 Stabilized Slotted Aloha

  38. 4.2.3 Stabilized Slotted Aloha

  39. 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?

  40. 4.2.3 Stabilized Slotted Aloha P(nk=0) P(nk=1)

  41. 4.2.3 Stabilized Slotted Aloha P(1 tx)

  42. 4.2.3 Stabilized Slotted Aloha

  43. 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

  44. 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

  45. 4.2.3 Stabilized Slotted Aloha

  46. 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

  47. 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

  48. 4.2.3 Stabilized Slotted Aloha • = fraction of packets successful transmitted from higher state # S S S S S

  49. 4.2.3 Stabilized Slotted Aloha

  50. 4.2.3 Stabilized Slotted Aloha

More Related