1. Univ. of TehranComputer Network1 Computer Networks Computer Networks (Graduate level) University of Tehran Dept. of EE and Computer Engineering By: Dr. Nasser Yazdani Lecture 10: Performance Evaluation

2. Univ. of TehranComputer Network2 Outline Strategy Performance factors Queuing Theory

3. Univ. of TehranComputer Network3 Strategies Circuit switching: carry bit streams Connection oriented. original telephone network Dedicated resource. Packet switching: store-and-forward messages Connectionless (IP) or connection oriented (ATM) Internet Shared resource. Packet switching is the focus of computer Networks.

4. Univ. of TehranComputer Network4 Packet Switching A R1 R2 R4 R3 B SourceDestination  It’s the method used by the Internet.  Each packet is individually routed packet-by-packet, using the router’s local routing table.  The routers maintain no per-flow state.  Different packets may take different paths.  Several packets may arrive for the same output link at the same time, therefore a packet switch has buffers.

5. Univ. of TehranComputer Network5 Packet Switching Simple router model R1 Link 1 Link 2 Link 3 Link 4 Link 1, ingressLink 1, egress Link 2, ingressLink 2, egress Link 3, ingressLink 3, egress Link 4, ingressLink 4, egress Choose Egress Choose Egress Choose Egress Choose Egress “4”

6. Univ. of TehranComputer Network6 Statistical Multiplexing On-demand time-division Schedule link on a per-packet basis Packets from different sources interleaved on link scheduling fairness, quality of service Buffer packets that are contending for the link Buffer (queue) overflow is called congestion …

7. Univ. of TehranComputer Network7 Statistical Multiplexing Basic idea time rate One flow Two flows Average rate Many flows  Network traffic is bursty. i.e. the rate changes frequently.  Peaks from independent flows generally occur at different times.  Conclusion: The more flows we have, the smoother the traffic. Average rates of: 1, 2, 10, 100, 1000 flows. rate

8. Univ. of TehranComputer Network8 Link rate, R X(t)X(t) B Dropped packets Queue Length X ( t ) Time Packet buffer Packets for one output Packet Switching Statistical Multiplexing DataHdr DataHdr DataHdr R R R  Because the buffer absorbs temporary bursts, the egress link need not operate at rate (N x R).  But the buffer has finite size, B, so losses will occur. 1 2 N

9. Univ. of TehranComputer Network9 Statistical Multiplexing B A time Rate C C A C B C

10. Univ. of TehranComputer Network10 Statistical Multiplexing Gain A B R 2C2C R < 2C A+B time Rate Statistical multiplexing gain = 2C/R Other definitions of SMG: The ratio of rates that give rise to a particular queue occupancy, or particular loss probability.

11. Univ. of TehranComputer Network11 Why does the Internet use packet switching? 1. Efficient use of expensive links: The links are assumed to be expensive and scarce. Packet switching allows many, bursty flows to share the same link efficiently. “Circuit switching is rarely used for data networks,... because of very inefficient use of the links” - Gallager 2. Resilience to failure of links & routers: ”For high reliability,... [the Internet] was to be a datagram subnet, so if some lines and [routers] were destroyed, messages could be... rerouted” - Tanenbaum

12. Univ. of TehranComputer Network12 Some Definitions Packet length, P, is the length of a packet in bits. Link length, L, is the length of a link in meters. Data rate, R, is the rate at which bits can be sent, in bits/second, or b/s. 1 Propagation delay, PROP, is the time for one bit to travel along a link of length, L. PROP = L/c. Transmission time, TRANSP, is the time to transmit a packet of length P. TRANSP = P/R. Latency is the time from when the first bit begins transmission, until the last bit has been received. On a link: Latency = PROP + TRANSP. 1. Note that a kilobit/second, kb/s, is 1000 bits/second, not 1024 bits/second.

13. Univ. of TehranComputer Network13 Packet Switching A R1 R2 R4 R3 B SourceDestination Host A Host B R1 R2 R3 TRANSP 1 TRANSP 2 TRANSP 3 TRANSP 4 PROP 1 PROP 2 PROP 3 PROP 4 “Store-and-Forward” at each Router

14. Univ. of TehranComputer Network14 Packet Switching vs. Message switching Breaking message into packets allows parallel transmission across all links, reducing end to end latency. It also prevents a link from being “hogged” for a long time by one message. Host A Host B R1 R2 R3 M/R Host A Host B R1 R2 R3 M/R

15. Univ. of TehranComputer Network15 Performance Metrics Bandwidth (throughput) data transmitted per time unit link versus end-to-end notation KB = 2 10 bytes Mbps = 10 6 bits per second Latency (delay) time to send message from point A to point B one-way versus round-trip time (RTT) components Latency = Propagation + Transmit + Queuing Queuing time can be a dominant factor

16. Univ. of TehranComputer Network16 Latency Latency ( Queuing Delay) Host A Host B R1 R2 R3 TRANSP 1 TRANSP 2 TRANSP 3 TRANSP 4 PROP 1 PROP 2 PROP 3 PROP 4 Q2Q2 The egress link might not be free, packets may be queued in a buffer. If the network is busy, packets might have to wait a long time. How can we determine the queuing delay?

17. Univ. of TehranComputer Network17 Queues and Queuing Delay Cross traffic causes congestion and variable queuing delay.

18. Univ. of TehranComputer Network18 A router queue  A(t), D(t)D(t) Model of router queue Q(t)Q(t) Buffer Server

19. Univ. of TehranComputer Network19 A router queue (cont)  A(t), D(t)D(t) Model of router queue Q(t)Q(t) Buffer Server Usually buffer size is finite State of the system depends on : 1.Packet arrival process, (Poisson, deterministic, etc) 2.Packet length distribution 3.The service discipline (FCFS, LCFS, priority, etc) 4.# of Server, service process

20. Univ. of TehranComputer Network20 A simple deterministic model Service discipline is FIFO Buffer can be finite of infinite Properties of A(t), D(t):  A(t), D(t) are non-decreasing  A(t) >= D(t)  A(t), D(t)D(t) Model of FIFO router queue Q(t)Q(t)

21. Univ. of TehranComputer Network21 A simple deterministic model bytes or “fluid” A(t)A(t) D(t)D(t) Cumulative number of departed bits up until time t. time Service process Cumulative number of bits Cumulative number of bits that arrived up until time t.  A(t)A(t) D(t)D(t) Q(t)Q(t) Properties of A(t), D(t) :  A(t), D(t) are non-decreasing  A(t) >= D(t) 

22. Univ. of TehranComputer Network22 D(t) A(t) time Q(t) d(t) Queue occupancy: Q(t) = A(t) - D(t). Queuing delay, d(t), is the time spent in the queue by a bit that arrived at time t, and if the queue is served first-come-first-served (FCFS or FIFO) Simple deterministic model Cumulative number of bits

23. Univ. of TehranComputer Network23 D(t) A(t) time Q(t) d(t) Example Cumulative number of bits Example: Every second, a train of 100 bits arrive at rate 1000b/s. The maximum departure rate is 500b/s. What is the average queue occupancy? 0.1s0.2s1.0s 100

24. Univ. of TehranComputer Network24 Queues with Random Arrival Processes 1. Usually, arrival processes are complicated, so we often model them as random processes. 2. The study of queues with random arrival processes is called Queueing Theory. 3. Queues with random arrival processes have some interesting properties. We’ll consider some here.

25. Univ. of TehranComputer Network25 Properties of queues Time evolution of queues. Examples Burstiness increases delay Determinism minimizes delay Little’s Result. The M/M/1 queue.

26. Univ. of TehranComputer Network26 Time evolution of a queue Packets  A(t), D(t)D(t) Model of FIFO router queue Q(t)Q(t) time Packet Arrivals: Departures: Q(t)Q(t)

27. Univ. of TehranComputer Network27 Burstiness increases delay Example 1: Periodic arrivals 1 packet arrives every 1 second 1 packet can depart every 1 second Depending on when we sample the queue, it will contain 0 or 1 packets. Example 2: N packets arrive together every N seconds (same rate) 1 packet departs every second Queue might contain 0,1, …, N packets. Both the average queue occupancy and the variance have increased. In general, burstiness increases queue occupancy (which increases queuing delay).

28. Univ. of TehranComputer Network28 Determinism minimizes delay Example 3: Random arrivals Packets arrive randomly; on average, 1 packet arrives per second. Exactly 1 packet can depart every 1 second. Depending on when we sample the queue, it will contain 0, 1, 2, … packets depending on the distribution of the arrivals. In general, determinism minimizes delay. i.e. random arrival processes lead to larger delay than simple periodic arrival processes.

29. Univ. of TehranComputer Network29 Little’s Result

30. Univ. of TehranComputer Network30 The Poisson process Arrival process is Poisson Queuing system is M/M/1, Poisson arrival, Exponential service, with 1 server. Arrival process is momeryless or arrival of packets are independent of each others Prob. of one arrival in Δt is λ Δt + o(Δt)

31. Univ. of TehranComputer Network31 The Poisson process (cont) Poisson process is a probability distribution function. Σ p(k) = 1 for all k=0, 1, … How many arrivals in t second? It is the expected value: Σ kp(k) = λt What is interarrival time, r, between two arrival f(r) = λe -λr This is the same the service time. f(r) = μe - μr

32. Univ. of TehranComputer Network32 The Poisson process Why use the Poisson process? It is the continuous time equivalent of a series of coin tosses. It is known to model well systems in which a large number of independent events are aggregated together. e.g. Arrival of new phone calls to a telephone switch Decay of nuclear particles “Shot noise” in an electrical circuit It makes the math easy. Be warned Network traffic is very bursty! Packet arrivals are not Poisson. But it models quite well the arrival of new flows.

33. Univ. of TehranComputer Network33 An M/M/1 queue A(t) is a Poisson process with rate, and the time to serve each packet is exponentially distributed with rate , then: We assume the system is in steady state, or stationary, with none time varying values. P n is the probability that there are n customer in the queue including the one in the service. ρ=  ration of load on capacity, is utilization or traffic intensity.  A(t), D(t)D(t) Model of FIFO router queue

34. Univ. of TehranComputer Network34 An M/M/1 queue (cont) Prob. that the system move from state n-1 to n is  with no departure, and probability that it moves from state n to n-1 is  In order the system to be in stationary state the probability of departure and moving state should be equal.  P n  P n-1  P n+1 0 2 1 n-1 n n+1        ….

35. Univ. of TehranComputer Network35 An M/M/1 queue (cont) Considering the rate of interring and leaving the surface gives us. P n  P n+1 => P n+1 =  P n => P n =  n P 0 What is the value of P 0 ? Σ n P n  => P 0 Σ n  n  =  => P 0 =  –  P n =(  –  n 0 2 1 n-1 n n+1       ….

36. Univ. of TehranComputer Network36 An M/M/1 queue If A(t) is a Poisson process with rate, and the time to serve each packet is exponentially distributed with rate , then:  A(t), D(t)D(t) Model of FIFO router queue

37. Univ. of TehranComputer Network37 Next Lecture: MAC How to share the wire How to extend to multiple segments Assigned reading [MB76] ETHERNET: Distributed Packet Switching for Local Area Networks [B+88] Measured Capacity of an Ethernet: Myths and Reality Chap. 2 of book (Recommended!)