Dataword Codeword 0000 0000000 0001 0001011 0010 0010110 0011 0011101 0100 0100111 0101 0101100 0110 0110001 Belman-Ford Equation 0111 0111010 Dataword 1000 1001 1010 1011 1100 1101 1110 1111 COE371 – Computer Networks – Formula Sheet ARQ Protocols Nodal delay • COMPUTER NETWORKS AND THE INTERNET Utilization of Stop-and-Wait ARQ: U sw = t n = t pc + t q + t t r + t pr A B Propagation ! 668 PART IV NETWORK LAYER Total packets, linksat each node along the path. The most packetdelay suffers for fromM several types ofNdelays important of these delays areTthe nodal queuing delay, transmisD 1 +processing d 2 + · · · + ddelay, tot = N sion delay, and propagation delay; together, these delays accumulate to give a total Transfer all the packets through 1st link: nodal delay. The performance of many Internet applications—such as search, Web D 1 = tinstant t t r [2] + . . .and + t tvoice-over-IP—are browsing, email, maps, greatly affected t r [1] +messaging, r [M ] + t pr [M ] by network In order to acquire a deep remaining understanding packet switching and Transfer the delays. M -th and last packet through (N of − 1) links. computer For i = 2, 3,networks, . . . , N : we must understand the nature and importance of these delays. d i = t pc [M ] + t q [M ] + t t r [M ] + t pr [M ] Types of Delay Sender Dataword Avg. response time without web caching: Ttot = TLAN + Tacc + TInt Avg. response time with web caching where 0 ≤ η ≤ 1: ¡ ¢¡ ¢ Ttot = ηTLAN + 1 − η TLAN + Tacc + TInt a3 a2 a1 a0 RTTa [k] = (1 − α) RTTa [k − 1] + αRTTi [k] ¯ ¯ ∆i [k] = ¯RTTa [k] − RTTi [k]¯ ¡ ¢ ∆a [k] = 1 − β × ∆a [k − 1] + β × ∆i [k] CIDR a3 a2 a1 a0 r2 r1 r0 Block assignment Fraction m bits q bits site The reasonDefines that classful addressing has become obsolete is address depletion. Since the Defines subnet Defines interface addresses were not distributed properly, the Internet was faced with the problem of the addresses being rapidly used up, resulting in no more addresses available for organizations and individuals that needed to be connected to the Internet. Ton:understand the prob48 bits Decision logic Checker Shared Unreliable transmission b 3 b 2 b 1 b 0 q 2 q 1 q0 Codeword Codeword Multiple Access In the encoder, the dataword has k bits (4 here); the codeword has n bits (7 here). ALOHA The size Throughput: of the dataword is augmented by adding n − k (3 here) 0s to the right-hand side of the word. The n-bit result is(fed into the generator. The generator uses a divisor of size Ge −2G for pure ALOHA n − k + 1 (4 here), predefined S ≈ and agreed upon. The generator divides the augmented dataword by the divisor (modulo-2 division). The quotient of the division is discarded; Ge −G for slotted ALOHA the remainder (r2r1r0) is appended to the dataword to create the codeword. The decoder receives the codeword (possibly corrupted in transition). A copy of all CSMA/CD efficiency: n bits is fed to the checker, which is a replica of the generator. The remainder produced 1 ηe ≈ 1 + 5t pr /t t r ATM AAL5: Number of bytes in data, padding, and trailer must be divisible by 48: D + X + 8 = 0 mod [48] Multimedia Networks Sampling frequency: f s ≥ 2 f max Network Security SKC property: K e = K d = K s → K s [K s (m)] = m Class D is not divided into prefix and suffix. It is used for multicast addresses. All 128 bits PKC property: addresses that start with 1111 in binary belong to class E. As in Class D, Class E is not dividedGlobal into prefix and suffixSubnet and isidentifier used as reserve. Interface identifier routing prefix n bits Divisor d3 d2 d1 d0 Generator TO[k] = RTTaspace 4 ×IPv6 ∆a [k] [k] +of Like the address space of IPv4, the address is divided into several blocks of varying size and each block is allocated for a special purpose. Most of the blocks are TCP Throughput still unassigned and have been set aside for future use. Table 22.1 shows only the assigned blocks. In this table, the+last column shows the fraction each block occupies in Wmin Wmax without loss the whole address space. 2RTT Ra ≈ 1.22 MSS assigned Table 22.1 Prefixes for with probability of loss ℓ pIPv6 addresses RTT ℓ 18 INTRODUCTION TO NETWORK LAYER CHAPTER 531 Address Depletion Accept Syndrome s2 s1 s0 TimeoutAddress value: Space Allocation 22.1.3 Block prefix Dataword Decoder 000 Let’s explore these delays in the context of Figure 1.16. As part of its end-to-end 0000 Internet Protocol 0000 0000::/8 Special addresses 1/256 For arrival rate λ, transmission time t t ra i.e. transmission ratethe µ: upstream node route between source and destination, packet is sent from 001 2000::/3 Global unicast 1/8 IP Routers 18.18 Occupation of the address space in classful addressing = λ/µ λtto = λL/R b the nodal delay at router A.Figure through router A to router B.ρOur goal=is t r characterize 1111 110 FC00::/7 Unique local unicast 1/128 Required buffering for N TCP flows going through router port: Note that router A has an outbound link leading to router B. This link is preceded by 1111 1110 10 FE80::/10 Link local addresses 1/1024 Packet Error Rate, P ( e a queue (also known as a buffer). When the packet arrives at router A from the 1111 1111 FF00::/8 Multicast 1/256 RTTspace: · R b 4,294,967,296 whenaddresses N small Address addresses For bit error raterouter p b and packet size L bits:header to determine the appropriate upstream node, A examines the of packet’s B≈ p ¡ the ¢packet RTT · R b / N when N large L outbound link for the packet and then directs to this link. In this example, Global Unicast Addresses Pe = 1 − 1 − pb the outbound link for the packet is the one that leads to router B. A packet can be A B C D E IP Addressing space that is used for unicast (one-to-one) communication transmitted Delay on a linkModel only if there is no other packet currently being transmitted on The block in the address HTTP1.0 50% 25% 12.5% 6.25%6.25% between two hosts in the Internet is called the global unicast address block. CIDR for IPv4 classful addresses: the link and if there are no other packets preceding it in the queue; if the link is HTTP1.0 response time: which three leftmost bits are the same for all bits 8 bits means 8 bitsthat the 8 bits currently busy or if there are other packets already queued for the link, the newly the block is 82000::/3, bits, which isFirst more than addresses in this block (001). The size of this block Class is 2125Prefixes = N (2RT T + t t r ) byte totqueue. arriving packet will then join Tthe enough expansion for many years to come. n =address 8 bits in this Class Afor0 Internet A An 0 toblock 127 is Prefix Suffix HTTP1.1 Delay Models divided parts: global routing prefix (n bits), Bsubnet (m128 bits), and n = identifier 16 bits Class Binto 10 threePrefix to 191 Suffix Processing Delay without pipelining: interface (q bits), also the to recomn = 24 bitsshows 192 Class C identifier 110 C figure 223 Prefixas shown in Figure Suffix22.1. The mended length for each part. Ttot the = RT T + N header t t rdetermine (RT T + ) D Not applicable 224 to 239 Multicast addresses The time required to examine packet’s and where to direct the Class D 1110 E Not applicable 240 to 255 Reserved for future use packet is part of the processing delay. The processing delay can also include other Class E 1111 with pipelining: factors, such as the time needed to check for bit-level errors in the packet that occurred Figure 22.1 Global unicast address 2RT T + N tnode tot ≈the tr in transmitting the packet’s bitsTfrom upstream to router A. Processing delays IPv6 global unicast addresses with typical n = 48, m = 16, q = 64: Web Caching Receiver Encoder a3 a2 a1 a0 EWMA algorithm with α = 1/8 and β = 1/4: Total delay for 1 packet, N links Traffic Intensity, ρ Figure 10.5 CRC encoder and decoder CRC Technique Timers The nodal delay at router A ¡ ¢ ¡ ¢ Ttot = N t t r + t pr + (N − 1) t pc + t q Link Layer Transmission Control Protocol Nodal Queueing Transmission processing (waiting for transmission) Figure 1.16 d x (y) = min[c (x, a) + d a (y); c (x, b) + d b (y); c(x, c) + d c (y)] Figure 10.5 shows one possible design for the encoder and decoder. tt r t t r + RT T Utilization of pipelined ARQ with window size w: w · tt r U pl = t t r + RT T Utilization in terms of bandwidth-delay product a p = RT T /t t r : w U pl = 1 + ap Sum of processing, queuing, transmission, and link propagation Codeword 1000101 1001110 1010011 1011000 1100010 1101001 1110100 1111111 Discard Network Delay Remainder PTER 1 Table 10.3 A CRC code with C(7, 4) £ ¤ £ ¤ K A+ K A− (m) = K A− K A+ (m) = m RSA algorithm: C = P e mod n ↔ P = C d mod n