store and forward: packets moveonehop at a time Nodereceives completepacket before forwarding Bandwidth division into “pieces” Dedicated allocation Resource reservation
Introduction 1-59 Packet Switching: Statistical Multiplexing Sequenceof A & B packets does not havefixed pattern, bandwidth shared on demand ➨ statistical multiplexing . TDM: each host gets same slot in revolving TDM frame. A B C 100 Mb/s Ethernet 1.5 Mb/s D E statistical multiplexing queueof packets waiting for output link
Introduction 1-60 Packet-switching: store-and-forward takes L/R seconds to transmit (push out) packet of L bits on to link at R bps storeand forward: entire packet must arrive at router before it can be transmitted on next link delay = 3L/R (assuming zero propagation delay) Example: L = 7.5 Mbits R = 1.5 Mbps transmission delay = 15 sec R R R L more on delay shortly …
Introduction 1-61 Packet switching versus circuit switching 1 Mb/s link each user: 100 kb/s when “active” active 10% of time circuit-switching: 10 users packet switching: with 35 users, probability > 10 active at sametimeis less than .0004 Packet switching allows moreusers to usenetwork! N users 1 Mbps link Q: how did weget value 0.0004? Use binomial distribution …
Introduction 1-62 Probability Background: variables, stats and distributions Discreterandomvariables: whereE[X] is theexpected (or mean) value 2 nd moment: ∑ 2200 = = k k X 1 ] Pr[ ∑ 2200 = = k k X k X E ] Pr[ ] [ ∑ 2200 = = k k X k X E ] Pr[ ] [ 2 2
Introduction 1-63 Continuous random variables: whereF[x] is thecumulativedistribution, f(y) is the probability density function, F[- ∞ ]=0, F[ ∞ ]=1 Variance: Var[X]=E[(X-E[X]) 2 ]=E[X 2 ]-(E[X]) 2 Standard deviation ∫ ∞ - = ≤ = x dy y f x X x F ) ( ] Pr[ ] [ ] [ X Var x = σ
Introduction 1-64 - Bernoulli experiment: - probability of success p, failure q=1-p - Geometric distribution: - X is the number of (independent identically distributed i.i.d.) Bernoulli experiments to get success - Pr[X=k]=q k-1 p (1 st k-1 failures then success) - E(X)= Σ kPr[X=k]=1/p - p=0.1, E(X)=1/p=10
Introduction 1-66 - Binomial distribution: • x is the number of successes in n Bernoulli experiments/trials • E[X]=np ( 29 ( 29 ! )! ( ! , ) ( k k n n k X P n k k k n n k p q - = = = -
Introduction 1-67 - Exponential distribution: F[x]=1-e - λ x , f(x)= λ e - λ x , Pr[X>x]=1-F[x]=e - λ x , E[X]=1/ λ
Introduction 1-68 Poisson Distribution: Pr[X=k]= ( λ k /k!) e - λ ,E[X]=Var[X]= λ Used in queuing theory: - Pr[k items arriving in T interval]= (( λ T) k /k!) e - λ T , - Expected number of items to arrive in T= λ T, where λ is the rate of arrival
Introduction 1-69 - Poisson processes areused in M/M/1 and M/D/1 queuing models - Inter-arrival times Ta - Pr[Ta<t]=1-e - λ t , E[Ta]=1/ λ , is exponentially distributed - good for modeling human generated actions - phone call arrivals - call duration - telnet/ftp session arrivals
Introduction 1-70 Packet switching versus circuit switching great for bursty data resource sharing (scalable!) simpler, no call setup, morerobust (re-routing) excessive congestion: packet delay and loss Without admission control: protocols needed for reliabledata
You've reached the end of your free preview.
Want to read all 97 pages?
- Spring '09
- Trigraph, State highways in Mississippi, ne twork, Ne tworks, ne de tworks