Computer Networks (Graduate level)

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

2. Outline • Strategy • Performance factors • Queuing Theory Computer Network

3. 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. Computer Network

4. A B Packet Switching R2 Source Destination R1 R3 R4 • 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. Computer Network

5. “4” “4” Packet SwitchingSimple router model Link 1, ingress Link 1, egress Choose Egress Link 2 Link 2, ingress Choose Egress Link 2, egress R1 Link 1 Link 3 Link 3, ingress Choose Egress Link 3, egress Link 4 Link 4, ingress Choose Egress Link 4, egress Computer Network

6. 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 … Computer Network

7. Statistical MultiplexingBasic idea One flow Two flows rate rate Average rate time Many flows rate time Average rates of: 1, 2, 10, 100, 1000 flows. • Network traffic is bursty.i.e. the rate changes frequently. • Peaks from independent flowsgenerally occur at different times. • Conclusion: The more flows we have, the smoother the traffic. time Computer Network

8. Packet SwitchingStatistical Multiplexing Packets for one output Queue Length X(t) Dropped packets 1 Data Hdr R X(t) B R 2 Data Hdr Link rate, R R Packet buffer N Data Hdr Time • Because the buffer absorbs temporary bursts, the egress link need not operate at rate (NxR). • But the buffer has finite size, B, so losses will occur. Computer Network

9. Statistical Multiplexing A Rate C C A time B Rate C C B time Computer Network

10. Statistical Multiplexing Gain A+B Rate 2C R < 2C A R B time 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. Computer Network

11. Why does the Internet usepacket switching? • 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 • 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 Computer Network

12. 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. Computer Network

13. A B Host A TRANSP1 “Store-and-Forward” at each Router TRANSP2 R1 PROP1 TRANSP3 R2 PROP2 TRANSP4 R3 PROP3 Host B PROP4 Packet Switching R2 Source Destination R1 R3 R4 Computer Network

14. M/R M/R Host A Host A R1 R1 R2 R2 R3 R3 Host B Host B 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. Computer Network

15. Performance Metrics • Bandwidth (throughput) • data transmitted per time unit • link versus end-to-end • notation • KB = 210 bytes • Mbps = 106 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 Computer Network

16. Latency (Queuing Delay) 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. TRANSP1 Host A Q2 TRANSP2 How can we determine the queuing delay? R1 PROP1 TRANSP3 R2 PROP2 TRANSP4 R3 PROP3 Host B PROP4 Computer Network

17. Queues and Queuing Delay Cross traffic causes congestion and variable queuing delay. Computer Network

18. A router queue Model of router queue Buffer Server A(t), l D(t) m Q(t) Computer Network

19. Model of router queue Buffer Server A(t), l D(t) m Q(t) A router queue (cont) • Usually buffer size is finite • State of the system depends on : • Packet arrival process, (Poisson, deterministic, etc) • Packet length distribution • The service discipline (FCFS, LCFS, priority, etc) • # of Server, service process Computer Network

20. Model of FIFO router queue A(t), l D(t) m Q(t) 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) Computer Network

21. A simple deterministic modelbytes or “fluid” Cumulative number of bits that arrived up until time t. A(t) A(t) Cumulative number of bits D(t) Q(t) m Service process m time D(t) • Properties of A(t), D(t): • A(t), D(t) are non-decreasing • A(t) >=D(t) Cumulative number of departed bits up until time t. Computer Network

22. Simple deterministic model Cumulative number of bits d(t) A(t) Q(t) D(t) time • 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) Computer Network

23. Example Cumulative number of bits Q(t) 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? d(t) A(t) 100 D(t) time 0.1s 0.2s 1.0s Computer Network

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

25. Properties of queues • Time evolution of queues. • Examples • Burstiness increases delay • Determinism minimizes delay • Little’s Result. • The M/M/1 queue. Computer Network

26. Time evolution of a queuePackets Model of FIFO router queue A(t), l D(t) m Q(t) Packet Arrivals: time Departures: Q(t) Computer Network

27. 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: • Npackets 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). Computer Network

28. 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. Computer Network

29. Little’s Result Computer Network

30. 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) Computer Network

31. The Poisson process (cont) • Poisson process is a probability distribution function. Σp(k) = 1 for all k=0, 1, … • How many arrivals in t second? It is the expected value: Σkp(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 Computer Network

32. 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. Computer Network

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

34. An M/M/1 queue (cont) • Prob. that the system move from state n-1 to n is l , with no departure, and probability that it moves from state n to n-1 is m. In order the system to be in stationary state the probability of departure and moving state should be equal. (l + m)Pn = lPn-1 + mPn+1 l l l l l l …. n+1 n n-1 2 1 0 m m m m m m m Computer Network

35. An M/M/1 queue (cont) • Considering the rate of interring and leaving the surface gives us . Pn = mPn+1 => Pn+1= rPn => Pn = rnP0 What is the value of P0? ΣnPn =1 => P0Σnrn=1 => P0 =1 –r Pn =(1 –r) rn l l l l l …. n+1 n n-1 2 1 0 m m m m m m Computer Network

36. An M/M/1 queue • If A(t) is a Poisson process with rate l, and the time to serve each packet is exponentially distributed with rate m, then: Model of FIFO router queue A(t), l D(t) m Computer Network

37. 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!) Computer Network