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 • • 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 st paper on modern data 1961 Published PhD Proposal : 1 st paper on modern data • 1961 Published PhD Proposal : 1 • networking networking 1962 Filed PhD Dissertation; MIT + McGraw-Hill • 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 • • 1963 Joined UCLA faculty • 1960’s Telecom industry could care less! 1960’s Telecom industry could care less! • • 1966 ARPA gets interested 1966 ARPA gets interested • • 1969+ The network locomotive starts its wild ride 1969+ The network locomotive starts its wild ride • Leonard Kleinrock 1999
July 24, 1961 Information Flow in Large Communication Nets Leonard Kleinrock Leonard Kleinrock 1999 Leonard Kleinrock 1999
Leonard Kleinrock 1999 Leonard Kleinrock 1999
“The purpose of this thesis is to investigate the problems associated with information flow in large communication nets. ….” “…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….” Time lapse between initiation and reception Storage capacity size Channel capacity Transient behavior and recovery time 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 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 Channel capacity limited • • Mean response time as key metric Mean response time as key metric • • Optimal assignment of channel capacity Optimal assignment of channel capacity • • Choice of priority queueing discipline Choice of priority queueing discipline • • Choice of routing procedure Choice of routing procedure • • Design of topological structure Design of topological structure • • Developed underlying principles of data Developed underlying principles of data • networks networks Leonard Kleinrock 1999
Systems of Flow Systems of Flow Steady flow through a single channel • Steady flow through a single channel • • Trivial and deterministic Trivial and deterministic • • Unsteady flow through a single channel Unsteady flow through a single channel • • Queueing theory; stochastics get you Queueing theory; stochastics get you • • Steady flow through a network of channels Steady flow through a network of channels • • Network flow theory; multicommodity gets you Network flow theory; multicommodity gets you • • Unsteady flow through a network of channels Unsteady flow through a network of channels • • A New domain; everything gets you! A New domain; everything gets you! • • Jackson’s networks of queues (1957) Jackson’s networks of queues (1957) • • Kleinrock’s Independence Assumption cracks the problem 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: Set up the model: • • Use of queueing theory; Erlang’s heritage Use of queueing theory; Erlang’s heritage • • Independence assumption (critical!) Independence assumption (critical!) • • Evaluated network performance Evaluated network performance • • Developed optimal design procedures Developed optimal design procedures • • Capacity, topology, routing, message size Capacity, topology, routing, message size • • Introduced and evaluated distributed adaptive Introduced and evaluated distributed adaptive • routing control routing control • Evaluated different queueing disciplines for 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 T Σ Σ Σ Σ λ λ i λ λ i T i T T = T = γ γ γ γ i i i i This is EXACT!! This is EXACT!! T Average network delay = = Traffic on channel i (Msg/sec) i Network throughput (Msg/sec) = T = Average delay for channel i i But how do you find this term ? Leonard Kleinrock 1999
Key Assumption Key Assumption The Independence Assumption The Independence 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 Leonard Kleinrock 1999
The Independence Assumption The Independence Assumption • Without the Independence Assumption, Without the Independence Assumption, • intractable. the problem is intractable. the problem is • With the Independence Assumption, the With the Independence Assumption, the • totally manageable!! problem is totally manageable!! problem is • We get: We get: • 1 T i = C - i i C i = Capacity of channel i (Msg/sec) where Leonard Kleinrock 1999
Response Time vs Throughput Response Time vs Throughput T Response Response Time Time 0 Throughput Leonard Kleinrock 1999
How Do Queues Form? How Do Queues Form? N x N x T T T T = Nx + x T = Nx + x Response Response N = T (Little’s Law) N = T (Little’s Law) Time Time T = T x + x T = T x + x 0 Throughput T = x / ( 1- x ) T = x / ( 1- x ) Leonard Kleinrock 1999
Simple 2-parameter Model Simple 2-parameter Model For Delay For Delay Delay T T 0 T 0 0 * Throughput Throughput Leonard Kleinrock 1999
The General Optimization The General Optimization Problem Problem Σ Σ λ i λ Σ Σ λ λ i • Minimize Minimize T i T • T = T = γ γ γ γ i i i Channel Capacity Assignment Channel Capacity Assignment Routing Procedure Routing Procedure Message queueing discipline Message queueing discipline Topology Topology Σ Σ Σ Σ i d • Subject to: Subject to: • D = D = C i d C i i i i Where C Where th channel = Channel capacity of i th C i i = Channel capacity of i channel th channel d i = Cost to supply 1 unit of capacity to i th channel d i = Cost to supply 1 unit of capacity to i D = Total dollars available for design D = Total dollars available for design Leonard Kleinrock 1999
Solution to the Problem Solution to the Problem • Exact solution for Exact solution for d • d i i = 1 = 1 • Exact solution for arbitrary d Exact solution for arbitrary d i • i • Implications for topology Implications for topology • • Implications for routing procedure Implications for routing procedure • • Implications for message sizes Implications for message sizes • Leonard Kleinrock 1999
The Underlying Principles The Underlying Principles • Resource Sharing (demand access) Resource Sharing (demand access) • • Only assign a resource to data that is present Only assign a resource to data that is present • • Examples are: Examples are: • • Message switching Message switching • • Packet switching Packet switching • • Polling Polling • • ATDM ATDM • • Economy of Scale in Networks Economy of Scale in Networks • • Distributed control Distributed control • • It is efficient, stable, robust, fault-tolerant and It is efficient, stable, robust, fault-tolerant and • WORKS! WORKS! Leonard Kleinrock 1999
Resources Resources • A 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: Examples: • • A Communication Channel A Communication Channel • • A Computer A Computer • Leonard Kleinrock 1999
Resources Resources Leonard Kleinrock 1999
Demands Demands • A A Demand Demand requires work from requires work from • resources resources • Examples: Examples: • • Packets (require transmission) Packets (require transmission) • • Jobs (require processing) Jobs (require processing) • Leonard Kleinrock 1999
Demands Demands Leonard Kleinrock 1999
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