Chapter 5

Suppose four active nodes - nodes A, B, C and D-are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to transmit in each slot with probability \(p\). The first slot is numbered slot 1 , the second slot is numbered slot 2 , and so on. a. What is the probability that node A succeeds for the first time in slot \(5 ?\) b. What is the probability that some node (either A, B, C or D) succeeds in slot 4? c. What is the probability that the first success occurs in slot 3 ? d. What is the efficiency of this four-node system?

Consider a broadcast channel with \(N\) nodes and a transmission rate of \(R\) bps. Suppose the broadcast channel uses polling (with an additional polling node) for multiple access. Suppose the amount of time from when a node completes transmission until the subsequent node is permitted to transmit (that is, the polling delay) is \(d_{\text {poll }}\). Suppose that within a polling round, a given node is allowed to transmit at most \(Q\) bits. What is the maximum throughput of the broadcast channel?

Recall that with the CSMA/CD protocol, the adapter waits \(K \cdot 512\) bit times after a collision, where \(K\) is drawn randomly. For \(K=100\), how long does the adapter wait until returning to Step 2 for a 10 Mbps broadcast channel? For a \(100 \mathrm{Mbps}\) broadcast channel?

Suppose nodes \(\mathrm{A}\) and \(\mathrm{B}\) are on the same \(10 \mathrm{Mbps}\) broadcast channel, and the propagation delay between the two nodes is 325 bit times. Suppose CSMA/CD and Ethernet packets are used for this broadcast channel. Suppose node A begins transmitting a frame and, before it finishes, node B begins transmitting a frame. Can A finish transmitting before it detects that B has transmitted? Why or why not? If the answer is yes, then A incorrectly believes that its frame was successfully transmitted without a collision. Hint: Suppose at time \(t=0\) bits, A begins transmitting a frame. In the worst case, A transmits a minimum-sized frame of \(512+64\) bit times. So A would finish transmitting the frame at \(t=512+64\) bit times. Thus, the answer is no, if B's signal reaches A before bit time \(t=512+64\) bits. In the worst case, when does B's signal reach A?

Suppose nodes A and B are on the same \(10 \mathrm{Mbps}\) broadcast channel, and the propagation delay between the two nodes is 245 bit times. Suppose A and \(B\) send Ethernet frames at the same time, the frames collide, and then \(\mathrm{A}\) and \(\mathrm{B}\) choose different values of \(K\) in the CSMA/CD algorithm. Assuming no other nodes are active, can the retransmissions from \(\mathrm{A}\) and \(\mathrm{B}\) collide? For our purposes, it suffices to work out the following example. Suppose A and B begin transmission at \(t=0\) bit times. They both detect collisions at \(t=245\) bit times. Suppose \(K_{A}=0\) and \(K_{B}=1\). At what time does B schedule its retransmission? At what time does A begin transmission? (Note: The nodes must wait for an idle channel after returning to Step 2 -see protocol.) At what time does A's signal reach B? Does B refrain from transmitting at its scheduled time?

In this problem, you will derive the efficiency of a CSMA/CD-like multiple access protocol. In this protocol, time is slotted and all adapters are synchronized to the slots. Unlike slotted ALOHA, however, the length of a slot (in seconds) is much less than a frame time (the time to transmit a frame). Let \(S\) be the length of a slot. Suppose all frames are of constant length \(L=k R S\), where \(R\) is the transmission rate of the channel and \(k\) is a large integer. Suppose there are \(N\) nodes, each with an infinite number of frames to send. We also assume that \(d_{\text {prop }}

Let's consider the operation of a learning switch in the context of a network in which 6 nodes labeled A through F are star connected into an Ethernet switch. Suppose that (i) B sends a frame to E, (ii) E replies with a frame to \(\mathrm{B}\), (iii) A sends a frame to B, (iv) B replies with a frame to A. The switch table is initially empty. Show the state of the switch table before and after each of these events. For each of these events, identify the link(s) on which the transmitted frame will be forwarded, and briefly justify your answers.

In this problem, we explore the use of small packets for Voice-over-IP applications. One of the drawbacks of a small packet size is that a large fraction of link bandwidth is consumed by overhead bytes. To this end, suppose that the packet consists of \(P\) bytes and 5 bytes of header. a. Consider sending a digitally encoded voice source directly. Suppose the source is encoded at a constant rate of \(128 \mathrm{kbps}\). Assume each packet is entirely filled before the source sends the packet into the network. The time required to fill a packet is the packetization delay. In terms of \(L\), determine the packetization delay in milliseconds. b. Packetization delays greater than 20 msec can cause a noticeable and unpleasant echo. Determine the packetization delay for \(L=1,500\) bytes (roughly corresponding to a maximum-sized Ethernet packet) and for \(L=50\) (corresponding to an ATM packet). c. Calculate the store-and-forward delay at a single switch for a link rate of \(R=622 \mathrm{Mbps}\) for \(L=1,500\) bytes, and for \(L=50\) bytes. d. Comment on the advantages of using a small packet size.

In this problem, you will put together much of what you have learned about Internet protocols. Suppose you walk into a room, connect to Ethernet, and want to download a Web page. What are all the protocol steps that take place, starting from powering on your \(\mathrm{PC}\) to getting the Web page? Assume there is nothing in our DNS or browser caches when you power on your PC. (Hint: the steps include the use of Ethernet, DHCP, ARP, DNS, TCP, and HTTP protocols.) Explicitly indicate in your steps how you obtain the IP and MAC addresses of a gateway router.