Leonard Kleinrock Leonard Kleinrock Professor, UCLA Computer - - PowerPoint PPT Presentation
Leonard Kleinrock Leonard Kleinrock Professor, UCLA Computer Science Dept Professor, UCLA Computer Science Dept Founder & Chairman, Nomadix Inc Founder & Chairman, Nomadix Inc SIGCOMM Tutorial SIGCOMM Tutorial August 31, 1999
Leonard Kleinrock 1999
Leonard Kleinrock Leonard Kleinrock
Professor, UCLA Computer Science Dept Professor, UCLA Computer Science Dept Founder & Chairman, Nomadix Inc Founder & Chairman, Nomadix Inc
SIGCOMM Tutorial SIGCOMM Tutorial August 31, 1999 August 31, 1999
Leonard Kleinrock 1999
My Early Years at MIT My Early Years at MIT
by by
Leonard Kleinrock Leonard Kleinrock
1959 Decided to pursue PhD, but decided NOT to work in Coding Theory, but rather set out to work in Coding Theory, but rather set out to uncover the principles of data networks uncover the principles of data networks
1961 Published PhD Proposal : 1st
st paper on modern data
paper on modern data networking networking
1962 Filed PhD Dissertation; MIT + McGraw-Hill decide to publish it as a book decide to publish it as a book
1963 Joined UCLA faculty
1960’s Telecom industry could care less!
1966 ARPA gets interested
1969+ The network locomotive starts its wild ride
Leonard Kleinrock 1999
Information Flow in Large Communication Nets Leonard Kleinrock July 24, 1961
Leonard Kleinrock 1999
Leonard Kleinrock 1999 Leonard Kleinrock 1999
Leonard Kleinrock 1999
“…The nets under consideration consist of nodes, connected to each other by links. The nodes receive, sort, store, and transmit messages that enter and leave via the links….” “The purpose of this thesis is to investigate the problems associated with information flow in large communication nets. ….” Time lapse between initiation and reception Channel capacity Transient behavior and recovery time Storage capacity size Routing doctrine
Leonard Kleinrock 1999
Leonard Kleinrock 1999 Leonard Kleinrock 1999
Leonard Kleinrock 1999
Under what conditions does the net jam up?
Leonard Kleinrock 1999
Leonard Kleinrock 1999
My Early Dissertation Work My Early Dissertation Work
Developed theory of stochastic flow of message traffic in connected networks of message traffic in connected networks of communication centers: communication centers:
Channel capacity limited
Mean response time as key metric
Optimal assignment of channel capacity
Choice of priority queueing discipline
Choice of routing procedure
Design of topological structure
Developed underlying principles of data networks networks
Leonard Kleinrock 1999
Systems of Flow Systems of Flow
Steady flow through a single channel
Trivial and deterministic
Unsteady flow through a single channel
Queueing theory; stochastics get you
Steady flow through a network of channels
Network flow theory; multicommodity gets you
Unsteady flow through a network of channels
A New domain; everything gets you!
Jackson’s networks of queues (1957)
Kleinrock’s Independence Assumption cracks the problem wide open wide open
Leonard Kleinrock 1999
Key Results in My PhD Key Results in My PhD Dissertation Dissertation
Set up the model:
Use of queueing theory; Erlang’s heritage
Independence assumption (critical!)
Evaluated network performance
Developed optimal design procedures
Capacity, topology, routing, message size
Introduced and evaluated distributed adaptive routing control routing control
Evaluated different queueing disciplines for handling traffic in the nodes, specifically, handling traffic in the nodes, specifically, chopping messages into smaller segments chopping messages into smaller segments
Leonard Kleinrock 1999
Key Equation for Networks Key Equation for Networks
Average network delay
T
= = Traffic on channel i (Msg/sec)
i
= Network throughput (Msg/sec)
T
= Average delay for channel i
i
i
T
T = T = λ λ λ λ i
i
Σ Σ Σ Σ
γ γ γ γ T Ti
i
i i
But how do you find this term?
This is EXACT!! This is EXACT!!
Leonard Kleinrock 1999
Key Assumption Key Assumption
Each time that a message is received at a Each time that a message is received at a node within the net, a new length is node within the net, a new length is chosen for this message independently chosen for this message independently from an exponential distribution from an exponential distribution
The Independence Assumption The Independence Assumption
Leonard Kleinrock 1999
The Independence Assumption The Independence Assumption
Without the Independence Assumption, the problem is the problem is intractable.
intractable.
With the Independence Assumption, the problem is problem is totally manageable!!
totally manageable!!
We get:
C -
=
T i
i i
1
Capacity of channel i (Msg/sec) =
Ci
where
Leonard Kleinrock 1999
Response Time vs Throughput Response Time vs Throughput
Throughput Response Response Time Time
T
Leonard Kleinrock 1999
N = T N = T (Little’s Law)
(Little’s Law)
T = Nx + x T = Nx + x
How Do Queues Form? How Do Queues Form?
x x N N T = x / ( 1- x ) T = x / ( 1- x ) T = T x + x T = T x + x
0 Throughput
Response Response Time Time
T
T T
Leonard Kleinrock 1999
Simple 2-parameter Model Simple 2-parameter Model For Delay For Delay
Delay T
Throughput Throughput T T 0
* Leonard Kleinrock 1999
The General Optimization The General Optimization Problem Problem
Minimize
Channel Capacity Assignment Channel Capacity Assignment Routing Procedure Routing Procedure Message queueing discipline Message queueing discipline Topology Topology
Subject to:
D = D = d d i
i
Σ Σ Σ Σ
C Ci
i
i i
T = T = λ λ λ λ i
i
Σ Σ Σ Σ
γ γ γ γ T Ti
i
i i
Where Where C
Ci
i = Channel capacity of i
= Channel capacity of ith
th channel
channel d di
i = Cost to supply 1 unit of capacity to i
= Cost to supply 1 unit of capacity to ith
th channel
channel D D
= Total dollars available for design
= Total dollars available for design
Leonard Kleinrock 1999
Solution to the Problem Solution to the Problem
Exact solution for d
di
i = 1
= 1
Exact solution for arbitrary di
i
Implications for topology
Implications for routing procedure
Implications for message sizes
Leonard Kleinrock 1999
The Underlying Principles The Underlying Principles
Resource Sharing (demand access)
Only assign a resource to data that is present
Examples are:
Message switching
Packet switching
Polling
ATDM
Economy of Scale in Networks
Distributed control
It is efficient, stable, robust, fault-tolerant and WORKS! WORKS!
Leonard Kleinrock 1999
A Resource Resource is a device that can do is a device that can do work for you at a finite rate work for you at a finite rate
Examples:
A Communication Channel
A Computer
Resources Resources
Leonard Kleinrock 1999
Resources Resources
Leonard Kleinrock 1999
A Demand Demand requires work from requires work from resources resources
Examples:
Packets (require transmission)
Jobs (require processing)
Demands Demands
Leonard Kleinrock 1999
Demands Demands
Leonard Kleinrock 1999
Bursty Asynchronous Demands Bursty Asynchronous Demands
You cannot predict exactly when when they will demand access they will demand access
You cannot predict how much how much they they will demand will demand
Most of the time they do not need do not need access access
When they ask for it, they want immediate immediate access!! access!!
Leonard Kleinrock 1999
Resource Sharing Resource Sharing Type 0 Type 0 ? ? ! ! ! !
Ooops! Ooops! Chaos!
Leonard Kleinrock 1999
C C C
Resource Sharing Resource Sharing Type 1 Type 1 Dedicated Resources Dedicated Resources
Leonard Kleinrock 1999
C C C
Resource Sharing Resource Sharing
A Fancy Green Switch A Fancy Green Switch
Type 2 Type 2 Shared Resources Shared Resources
Leonard Kleinrock 1999
The Law of Large Numbers The Law of Large Numbers
(The First Resource Sharing Principle) (The First Resource Sharing Principle)
Although each member of a large population may behave in a random fashion, the population may behave in a random fashion, the population as a whole behaves in a predictable fashion. as a whole behaves in a predictable fashion.
This predictable fashion presents a total demand equal to the sum of the average demand equal to the sum of the average demands of each member. demands of each member.
This is the “smoothing effect” of large populations. populations.
Leonard Kleinrock 1999
Resource Sharing: Resource Sharing:
Telephone Trunks Telephone Trunks
Buildings @ 2/3 Erlangs Buildings @ 2/3 Erlangs Trunks Blocking Trunks Blocking
17% 17% 1 1 3 3 2 2 4 4
4(2/3) Erlangs 4(2/3) Erlangs
2 2 1 1 3 3 4 4
4 Trunks 4 Trunks
40% 40% 1 1 1 1
2/3 Erlangs 2/3 Erlangs 1 Trunk 1 Trunk
Leonard Kleinrock 1999
Resource Sharing: Resource Sharing:
Telephone Trunks Telephone Trunks 0.05% 0.05% 1 1 2 2 64 64
64(2/3) Erlangs 64(2/3) Erlangs
2 2 1 1 64 64
64 Trunks 64 Trunks
3% 3%
16(2/3) Erlangs 16(2/3) Erlangs
1 1 2 2 16 16 2 2 1 1 16 16
16 Trunks 16 Trunks
Blocking
Leonard Kleinrock 1999
C C C
Resource Sharing Resource Sharing
A Fancy Green Switch A Fancy Green Switch
Type 2 Type 2 Shared Resources Shared Resources
Leonard Kleinrock 1999
C C C A Fancy Green Switch A Fancy Green Switch
Resource Sharing Resource Sharing Type 3 Type 3 LARGE Shared Resources LARGE Shared Resources
Leonard Kleinrock 1999
Conflict Resolution Conflict Resolution
Queueing:
One gets served
All others wait
Splitting:
Each gets a piece of the resource
Blocking:
One gets served
All others are refused
Smashing:
Nobody gets served !
Leonard Kleinrock 1999
If you scale up throughput and capacity by some factor F, then you reduce by some factor F, then you reduce response time by that same factor. response time by that same factor.
If you scale capacity more slowly than throughput while holding response time throughput while holding response time constant, then efficiency will increase constant, then efficiency will increase (and can approach 100%). (and can approach 100%).
The Economy of Scale The Economy of Scale
(The Second Resource Sharing Principle) (The Second Resource Sharing Principle)
Leonard Kleinrock 1999
Resource Sharing: Resource Sharing:
Data Communications Data Communications T(B,C) T(B,C) 1 1
B Blocks/sec B Blocks/sec
1 1
C Bits/sec C Bits/sec
T(NB,NC) T(NB,NC)
NB Blocks/sec NB Blocks/sec NC Bits/sec NC Bits/sec
1 1 1 1 T(NB,NC) = T(B,C) / N
Leonard Kleinrock 1999
Key Tradeoff: Key Tradeoff:
Response Time, Throughput, Efficiency Response Time, Throughput, Efficiency
Efficiency Throughput 100 80 60 40 20 Constant Response Time Throughput Increasing Efficiency Improving
1 = Response Time, T 10 10 2 3 4
Response Time Improving Response Time Improving Throughput Increasing Throughput Increasing Efficiency Improving Efficiency Improving Response Time Improving, Response Time Improving, Throughput Increasing Throughput Increasing Constant Efficiency Constant Efficiency
Leonard Kleinrock 1999
Resource Sharing Resource Sharing
Type 0 Type 0
? ? ! ! !
C C CType 1 Type 1
C C CType 2 Type 2
A Fancy Green Switch A Fancy Green Switch C C CType 3 Type 3
A Fancy Green Switch A Fancy Green Switch Leonard Kleinrock 1999
Economy of Scale in Networks Economy of Scale in Networks
Throughput Throughput Cost Cost
Locus of Locus of Network Designs Network Designs
$/ $/Kbps
Kbps Throughput Throughput
Slope = Kbps/$
Small Net Large Net Large Net Small Net
Slope = Kbps/$
Leonard Kleinrock 1999
www.lk.cs.ucla.edu