Section 1.5. Exercises

1.5. Exercises

1.	We transmit data directly between two servers 6,000 km apart through a geostationary satellite situated 10,000 km from Earth exactly between the two servers. The data enters this network at 100 Mb/s. Find the propagation delay if data travels at the speed of light (2.3 x 10 8 m/s). Find the number of bits in transit during the propagation delay. Determine how long it takes to send 10 bytes of data and to receive 2.5 bytes of acknowledgment back.
2.	Repeat exercise 1, but this time, suppose that the two servers are 60 meters apart on the same campus.
3.	Stored on a CD-ROM is a 200 MB message to be transmitted by an e-mail from one mail server to another, passing three nodes of a connectionless network . This network forces packets to be of size 10 KB, including a packet header of 40 bytes. Nodes are 400 miles apart, and servers are 50 miles away from their corresponding nodes. All transmission links are of type 100 Mb/s. The processing time at each node is 0.2 seconds per packet. Find the propagation delays per packet between a server and a node and between nodes. Find the total time required to send this message.
4.	Equation 1.2 gives the total delay time for connection-oriented networks. Let t p be the packet-propagation delay between each two nodes, t f 1 be the data packet transfer time to the next node, and t r 1 be the data packet processing time. Also, let t f 2 be the control-packet transfer time to the next node, and t r 2 be the control-packet processing time. Give an expression for D in terms of all these variables .
5.	Suppose that a 200 MB message stored on a CD-ROM is to be uploaded on a destination through a virtual-circuit packet-switched network . This network forces packets to be of size 10 KB, including a packet header of 40 bytes. Nodes are 400 miles apart, and servers are 50 miles away from their corresponding nodes. All transmission links are of type 100 Mb/s. The processing time at each node is 0.2 seconds per packet. For this purpose, the signaling packet is 500 bit long. Find the total connection request/accept process time. Find the total connection release process time. Find the total time required to send this message.
6.	We want to deliver a 12 KB message by uploading it in the destination's Web site through a 10-node path of a virtual-circuit packet-switched network . For this purpose, the signaling packet is 500 bits long. The network forces packets to be of size 10 KB including a packet header of 40 bytes. Nodes are 500 miles apart. All transmission links are of type 1 Gb/s. The processing time at each node is 100 ms per packet and the propagation speed is 2.3 x 10 8 m/s. Find the total connection request/accept process time. Find the total connection release process time. Find the total time required to send this message.
7.	To analyze the transmission of a 10,000-bit-long packet, we want the percentage of link utilization used by the data portion of a packet to be 72 percent. We also want the ratio of the packet header, h , to packet data, d , to be 0.04. The transmission link speed is s = 100 Mb/s. Find the link utilization, . Find the link capacity rate, µ , in terms of packets per second. Find the average delay per packet. Find the optimum average delay per packet.
8.	Consider a digital link with a maximum capacity of s = 100 Mb/s facing a situation resulting in 80 percent utilization. Equal-size packets arrive at 8,000 packets per second. The link utilization dedicated to headers of packets is 0.8 percent. Find the total size of each packet. Find the header and data sizes for each packet. If the header size is not negotiable, what would the optimum size of packets be? Find the delay for each optimal- sized packet.
9.	Develop a signaling delay chart, similar to Figures 1.7 and 1.8, for circuit-switched networks. From required steps, get an idea that would result in the establishment of a telephone call over circuit-switched networks.
10.	In practice, the optimum size of a packet estimated in Equation (1.7) depends on several other contributing factors. Derive the optimization analysis, this time also including the header size, h . In this case, you have two variables: d and h . What other factors might also contribute to the optimization of the packet size?