word pro - ece246.part16.v1.~ts

8/8/2019 Word Pro - Ece246.Part16.v1.~Ts

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O If are independent PoissonA1(t),A2(t), ,Ak(t)

processes of rate , then 1, 2, ,

is a Poisson process of rateA1(t) + A2(t) +

+Ak(t)

1 + 2 + +

If each arrival of a Poisson process is independently

sent to system 1 with prob. pand system 2 with prob.

1-p, the arrivals to each system are Poisson and

independent.(see also Ex.3.11a)

1

p

1-p

random

independentselection

(see also Ex.3.10c)

p

(1-p)


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Routing in Data Nets

Datagarms: routing decision for every packet.

Virtual Circuits: one routing decision for all the

packets of the same session.

Issues

O selection of paths

O broadcasting of routing-related info.

Performance Measures

Throughput (quantity of service)

Average packet delay (quantity of service)

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As the routing algorithm succeeds in keeping delay

low, the flow control allows more traffic into the

network.

Good routing algorithms: higher throughput for the

same delay; smaller delay for a given throughput.

3

2 I I H U H G O R D G

) O R Z & R Q W U R O 5 R X W L Q J

' H O D \

W K U R X J K S X W

5 H M H F W H G O R D G

' H O D \

7 K U R X J K S X W

J R R G U R X W L Q J

S R R U U R X W L Q J


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Example:

O If everything routed through middle path the delay is

large.

O

Suppose input traffic at node 2 is increased to 15 units.

If a single path is used at least 5 units is rejected.

Therefore the delay and the maximum throughput

depend on routing.

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X Q L W V X Q L W V

R U L J L Q

R U L J L Q

G H V W L Q D W L R Q

$ O O O L Q N V K D Y H

F D S D F L W \ R I X Q L W V


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Routing may be:

1. Centralized or Distributed

O

Centralized: all routing choices are made at a centralnode.

O

Distributed: computation of routes is shared among

nodes who exchange information if necessary.

2. Static or Dynamic (adaptive)

O

Static: path used for an origin-destination pair is fixed.

O

Dynamic: path may changes in response to congestion.

Of course even with static algorithms paths will

change if nodes or links fail.

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Shortest Path problem

Directed graph G=(N,A) arcs have direction/

dij = length of (i,j)

The length of a directed path p={i,j,k,.....,l,m} isdefined asdij+ djk+ +dl

Given:G=(N,A) , dijswith no negative lengthcycles,

and a node 1

Problem: find the shortest path from every node itonode 1

Applications:a) dij=delay (i,j), then shortestpath corresponds to theminimum delay path

b) If pij = prob. (i,j) is operational.Let define dij = -lnpij . Then shortest path corresponds tomost reliable path

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Bellman-Ford algorithm

Let length of shortest path from ito 1 thatDih

uses > harc

D1

0 = 0

Di0 =

\ , i 1

*Dih+1 =

j. N(i)min [dij+ Dj

h]

After at most N-1 iterations * shortest path is

founded (provided that there are no negative length

cycles); shortest path distance .In factDi = DiN1

iteration terminates when after hiteration Dih= Di

N1

for all i

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Example: Bellman-Ford (infinite initial conditions)

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F R V W



V W 6 W H S

F X U U H Q W G L V W D Q F H W R Q R G H


Q G 6 W H S

U G 6 W H S


W K 6 W H S


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Example: Bellman-Ford zero initial conditions

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Routing in the ARPANET

Uses shortest paths from origin to destination.

1969 algorithm:Node icomputes an estimate of its distance to aDigiven node 0

Di =j. N(i)min (dij+ Dj), i

0,

:neighbors of iN(i) :obtained by neighbors every 0.62 secDj

D0 = 0

Originally(1969), lengths = number of packet indijbuffer (i,j)

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Instability problems (original ARPANET)

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$ V V X P H L V H T X D O W R I O R Z R Q L M

S D W K R I Q R G H Z L O O K D Y H

) H H G E D F N K H U H F D Q E H X Q V W D E O H

3 U R E O H P 6 K R U W H V W S D W K V U R X W H V I O R Z D U F O H Q J W K V

G L U H F W L R Q

1 R W H W K D W Q H [ W V K R U W H V W

D F R X Q W H U F O R F N Z L V H


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After updates, everybody will start sending packetsclockwise, and so on.....

Having a bias independent of flow in the arcdistances helps to prevent this problem(e.g. = constant + number of packets in the buffer)dij

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word pro - ece246.part16.v1.~ts

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