a.
Explanation of Solution
The expression used for calculating the transmission time of each packet in terms of size of packet (L) and rate of link (R) is
The queuing delay for transmitting the first packet is
The queuing delay for transmitting the second packet is
The queuing delay for transmitting the third packet is
Similarly, the queuing delay for transmitting the Nth packet is
The average queuing delay for transmitting the N number of packets is
b.
Explanation of Solution
The expression used for calculating the transmission time of each packet in terms of size of packet (L) and rate of link (R) is
Assume, the queuing delay for transmitting the first packet is
Then, the queuing delay for transmitting the second packet is
Similarly, the queuing delay for transmitting the Nth packet is
The average queuing delay for transmitting the N number of packets is
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EBK COMPUTER NETWORKING
- Consider a router buffer preceding an outbound link. In this problem, you will use Little’s formula, a famous formula from queuing theory. Let N denote the average number of packets in the buffer plus the packet being transmitted. Let a denote the rate of packets arriving at the link. Let d denote the average total delay (i.e., the queuing delay plus the transmission delay) experienced by a packet. Little’s formula is N=a⋅d . Suppose that on average, the buffer contains 10 packets, and the average packet queuing delay is 10 msec. The link’s transmission rate is 100 packets/sec. Using Little’s formula, what is the average packet arrival rate, assuming there is no packet loss?arrow_forwardEquation 1.1 gives a formula for the end-to-end delay of sending one packet of length L over N links of transmission rate R. Generalize this formula for sending P such packets back-to-back over the N links. Explainarrow_forwardProblem 2. Consider a packet of L bits that is sent over a path of Q links (i.e., a source and destination connected by a sequence of (Q-1) routers or switches). Each link transmits at R bps. This packet is the only traffic transmitted by the network (so there are no queuing delays) and the propagation delay and processing delay at routers are negligible. How long does it take to send this packet from source to destination if the network is: a) a packet-switched datagram network b) a circuit-switched network. Assume that bandwidth of R bps on each link is sliced into five individual circuits, so that cach circuit receives (R/5) bandwidth. Also assume that the circuit setup time is t,.. Give an expression for the number of links Q such that the packet delivery from the sender to the receiver will be faster over the packet-switched network, and the expression for the number of links Q such that the circuit-switched network will be faster.arrow_forward
- Computer Networks Consider a packet of length L that begins at end system A and travels over three links to a destination end system. These three links are connected by two packet switches. Let d, s, and R denotes the length, propagation speed, and the transmission rate of link i, for i=1,2,3 . The packet switch delays each packet by d . Assuming no queuing delays, in terms of d, s , R, (i=1,2,3), and L, what is the total end-to-end delay for the packet? Suppose now the packet is 1,500 bytes, the propagation speed on all three links is the transmission rates of all three links are 2 Mbps, the packet switch processing delay is 3 msec, the length of the first link is 5,000 km, the length of the second link is 4,000 km, and the length of the last link is 1,000 km. For these values, what is the end-to-end delay? In the above problem, suppose R1=R2=R3=R and dproc=0. Further, suppose the packet switch does not store-and-forward packets but instead immediately transmits each bit it…arrow_forwardComputer Networks Consider a packet of length L that begins at end system A and travels over three links to a destination end system. These three links are connected by two packet switches. Let d, s, and R denotes the length, propagation speed, and the transmission rate of link i, for i=1,2,3 . The packet switch delays each packet by d . Assuming no queuing delays, in terms of d, s , R, (i=1,2,3), and L, what is the total end-to-end delay for the packet? Suppose now the packet is 1,500 bytes, and the propagation speed on all three links are 3125km/sec, 10000 km/sec, and 3333km/sec respectively. The transmission rates of all three links are 2 Mbps, the packet switch processing delay is 3 msec, the length of the first link is 5,000 km, the length of the second link is 4,000 km, and the length of the last link is 1,000 km. For these values, what is the end-to-end delay? In the above problem, suppose R1=R2=R3=R and dproc=0. Further, suppose the packet switch does not store-and-forward…arrow_forwardConsider a network with a ring topology, link bandwidths of 100 Mbps, and propagation speed 2 × 108 m/s. What would the circumference of the loop be to exactly contain one 1500-byte packet, assuming nodes do not introduce delay? What would the circumference be if there was a node every 100 m, and each node introduced 10 bits of delay?arrow_forward
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- Consider a half-duplex point-to-point link using a stop-and-wait scheme, in which a series of messages is sent, with each message segmented into a number of frames. Ignore errors and frame overhead. A. What is the effect on line utilization of increasing the message size so that fewer messages will be required? Other factors remain constant. B. What is the effect on line utilization of increasing the number of frames for a constant message size? C. What is the effect on line utilization of increasing frame size?arrow_forwardAssume a wireless network consists of an access point (denoted as X) and two wireless nodes (denoted as A and B respectively). Assume that wireless nodes A and B cannot hear each other's transmissions, but they can hear X (i.e. X can hear A and B). Suppose ● ● At time 0 µs, X is sending a packet to some other node and it completes sending this packet at time 100 µs. At time 20 µs, a packet becomes available for transmission at A. A needs 150 μs to send this packet. At time 60 µs, a packet becomes available for transmission at B. B needs 100 µs to send its packet. Let the value of the backoff timer for A be 40 µs and the value of the backoff timer for B be 60 μs. 1) Sketch the above described topology to include wireless nodes X, A, B, and their coverage. You may use tools such as Word, Paint, Visio, etc. to complete this topology.arrow_forwardConsider two hosts, A and B that are connected by a transmissions link of2.1 Mbps. Assume that packets are of length 2.0 Kb (Kilobits) and the length of the link is 100Km. a. What is the propagation delay from A to B, that is the amount of time from when the first bit of the packet is transmitted at A, until it is received at B? b. What is the transmission time of the packet at A (the time from when the first bit of the packet is sent into the wire and the time at which the last bit is sent into the wire). c. Suppose now that that length of the link is doubled. What is the propagation delay from A to B now and what is the transmission time? d. Now suppose that node C is connected to node B also by a 2 Mbps, 100 Km link. How long does it take from when the first bit is transmitted by A to when the last bit is received at C, assuming B operates in a store-and -forward manner?arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole