Network layer ppt in computer networks

network layer performance model and network layer design issues ppt and Network layer performance model

Dr.ShivJindal,India,Teacher

Published Date:19-07-2017

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Computer Communication Networks (CCN) Network Layer Performance Modeling & Analysis 1Overview • Network Layer Performance Modeling & Analysis – Part I: Essentials of Probability – Part II: Inside a Router – Part III: Network Analysis Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 2Network Layer Performance Modeling & Analysis: Part II Inside a Router • Basic Single Queue Model • Poisson Arrival Model • The M/M/1 Queue • Read any of the queuing theory references, e.g. Schwartz (Sections 2.1-3), Molloy, Kleinrock. Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 3Queuing in the Network Layer at a Router Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 4Basic Single Queue Model • Classical queuing theory can be applied to an output link in a router. Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 5Basic Single Queue Model • For example, a 56 kbps transmission line can “serve” 1000-bit packets at a rate of 56,000 bits/sec  56 packets/sec 1000 bits/packet Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 6Applications of Queuing Analysis Outside of Networking • Checkout line in a supermarket • Waiting for a teller in a bank • Batch jobs waiting to be processed by the CPU Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 7Applications of Queuing Analysis Outside of Networking • “That’s the way the whole thing started, Silly but it’s true, Thinking of a sweet romance Beginning in a queue.” -G. Gouldman, “Bus Stop” The Hollies Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 8The Poisson Arrival Model • A Poisson process is a sequence of events “randomly spaced in time” Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 9The Poisson Arrival Model • Examples – Customers arriving to a bank – Packets arriving to a buffer • The rate λ of a Poisson process is the average number of events per unit time (over a long time). Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 10Properties of a Poisson Process • For a length of time t the probability of n arrivals in t units  4 of time is n ()t t P() t e n n Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 11Properties of a Poisson Process • For 2 disjoint (non-overlapping) intervals, (s , s ) and (s , s ), (i.e. 1 2 3 4 s s s s ), the number of  1 2 3 4 arrivals in (s , s ) is independent 1 2 of the number of arrivals in (s , 3 s ) 4 Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 12Interarrival Times of a Poisson Process • Pick an arbitrary starting point in time (call it 0).  • Let = the time until the next 1 arrival t P( t) P (t) e 10 Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 13Interarrival Times of a Poisson Process • So  tt F (t) P( t)1e and f (t) e  1 11  ,the time until the first arrival, 1 Has an exponential distribution Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 14Interarrival Times of a Poisson Process  • Let = the length of time 2 between the first and second arrival. • We can show that t P( t  s) P( t) e for any s,t 0 2 1 2  i.e. is exponential and 2  independent of 1 Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 15Interarrival Times of a Poisson Process 3  • Similarly define as the time between the second and third  arrival; as the time between 4 the third and fourth arrival;… 3    • The random variables , , , 2 1 … are called the interarrival times of the Poisson process Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 16Interarrival Times of a Poisson Process • The interarrival time random   variables, , , … 1 2 3 – Are (pair-wise) independent. – Each has an exponential distribution with mean 1/λ. Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 17The M/M/1 Queue • An M/M/1 queue has – Poisson arrivals (with rate λ) – Exponential service times (with mean 1/μ, so μ is the “service rate”). – One (1) server – An infinite length buffer • The M/M/1 queue is the most basic and important queuing model. Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 18Queuing Notation “M/M/1” is a special case of more general (Kendall) notation: X/Y/m/k, where • X is a symbol representing the interarrival process – M = Poisson (exponential interarrival times, )   – D = Deterministic (constant ). Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 19Queuing Notation • Y is a symbol representing the service distribution M = exponential, D = deterministic  G = General (or arbitrary). • m = number of servers • k = number of buffer slots (omitted when k = )  Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar 20

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