Alert dont submit AI generated answer. Solve the following problem:Consider the following network configuration.RouterRouterQ3.10 Mbps10 MbpsDestinationSourceSource wants to transmit 4 packets to the destination. Each packet is 1 Mb long. How long will the 4 packetstake to reach at the destination? Capacity of each communication link is 10 Mbps (as shown in the figure).(Neglect propagation delay, processing delay, and queuing delay.)Q4.Solve the following problem:10 MbpsConsider the following figure.Nusers2-10 MbpsRouter1 Gbps link-ERouter10 MbpsAssume that we can support 35 users in the above communication system. Each user can stay active 20% oftime. When each user is active, they transmit in 200 Mbps rate. The total capacity of communication link thatcan support users is 1Gbps. Calculate the probability of more than 5 users (i.e., 6 or more users) to stayactive at the same time?(If you are overwhelmed with the calculation, please write a program in your favorite programming language, justlike to way I wrote the program in my lecture slide.)

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Solve the following problem: Consider the following network configuration. Router Router Q3. 10 Mbps 10 Mbps 10 Mbps Router -E 10 Mbps Destination Source Source wants to transmit 4 packets to the destination. Each packet is 1 Mb long. How long will the 4 packets take to reach at the destination? Capacity of each communication link is 10 Mbps (as shown in the figure). (Neglect propagation delay, processing delay, and queuing delay.) Router 10 Mbps

Solve the following problem: Consider the following network configuration. Router Router Q3. 10 Mbps 10 Mbps 10 Mbps Router -E 10 Mbps Destination Source Source wants to transmit 4 packets to the destination. Each packet is 1 Mb long. How long will the 4 packets take to reach at the destination? Capacity of each communication link is 10 Mbps (as shown in the figure). (Neglect propagation delay, processing delay, and queuing delay.) Router 10 Mbps

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.10: Exponential Queues In Series And Open Queuing Networks

Problem 8P

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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?
Total latency is equal to a summation of network delay contributors such as frame transmission time, queuing time, and propagation time. Use the assumptions listed below to answer the questions below. Assumptions: • Host A and Host B are connected to a network. Packets sent from Host A to Host B transit through two Routers, R1 and R2 (Host A ? Router 1? Router 2 -? Host B) • The links that connect the hosts and routers are Ethernet 1000B and are short distance and can be ignored in any further delay calculations • The link between the two routers is 8km long and are connected by a T-1 WAN link (line rate = 1.544Mbps) • a single packet (size = 1500bytes) is routed from Host A to Host B through the network. The two routers, R1 and R2, introduce queuing delay of 3 msec and 5 msec, respectively. • Assume the signal propagation velocity in the T-1 channel = Vp = 2 x 108 m/sec a. Calculate the latency (in msec) required to send the 1500byte packet from Host A to Host B
Suppose that KJ sends 3596 back-to-back packets, with each packet composed of 14,000 bits, to TA over 5 links (shown below). Suppose that the transmission rate of each link is 70,000 bits/sec (bps). Consider the routers to be store-and-forward routers. In such a scenario, find the endto- end delay of sending all the packets to TA (i.e., the time needed for the last bit of the last packet to arrive at TA since KJ starts transmitting the first bit of the first packet). Note, consider only the transmission delay that occurs in sending packets in your analysis. Show the steps used for derivation in detail. 70,000 bps 70,000 bps 70,000 bps 70,000 bps 70,000 bps KJ Router 1 Router 2 Router 3 Router 4 ТА
Performance: Maximum Throughput (2). Now consider the network shown below, with two senders on the left sending packets to a common receiver on the right. The links have transmission rates of R₁ =75 Mbps, R₂ = 100 Mbps, and R3 = 60 Mbps. R₁ R₁ 235 Mbps 30 Mbps What is the maximum end-to-end throughput achieved by each session, assuming both sessions are sending at the maximum rate possible? 310 Mbps 60 Mbps 100 Mbps R₂- 75 Mbps R3 wwww
In this problem, we consider sending real-time voice from Host A to Host B over a packet switched network (VoIP). Host A converts analog voice to a digital 64 kbps bit stream on the fly. Host A then groups the bits into 56-byte packets. There is one link between Hosts A and B; its transmission rate is 2 Mbps and its propagation delay is 10 msec. As soon as Host A gathers a packet, it sends it to Host B. As soon as Host B receives an entire packet, it converts the packet's bits to an analog signal. How much time elapses from the time a bit is created (from the original analog signal at Host A) until the bit is decoded (as part of the analog signal at Host B)?
3. The figure below shows a network of four clients: A, B, C, and D, connected through a router, X. The transmission rate of each device and length of each link are shown on the figure. In addition, the processing delay of the router is 200ms. At t = 0, clients A, B, and C each send a packet of size 2 Mbits to Client D (through the router X). Assume that the propagation speed over all links is 2 x 108 m/s and the router's queue (buffer) is empty. Calculate the total delay for each packet until they are received at D. R₁ = 1 Mbits/s C B Rc=3 Mbits/s 4000 Km 4000 Km 4000 Km Processing delay = 200 ms R = 10 Mbits/s 6000 Km RB = 2 Mbits/s X D
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 packets but…
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 receives before waiting…
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 di, si, and Ri denote the length, propagation speed, and the transmission rate of link i, for i=1,2,3. The packet switch delays each packet by dproc. Assuming no queuing delays, in terms of di, si, Ri, (i=1,2,3), and L, what is the total end-to-end delay for the packet? Suppose now the packet is 1,200 bytes, the propagation speed on all three links is 2.5x10^8 m/s, 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 4,000 km, the length of the second link is 3,000 km, and the length of the last link is 1,500 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 receives…
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 di, si, and Ri denote the length, propagation speed, and the transmission rate of link i, for i=1,2,3. The packet switch delays each packet by dproc. Assuming no queuing delays, in terms of di, si, Ri (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 2.5*108 m/s, 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?
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 denote 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, , 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 2.5⋅108m/s 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?
2. Packet transmission. a. Consider a packet of length L that begins at end system A and travels over 2 links to a destination end system B. These two links are connected by one packet switch. Let d₁, S₁, and R₁ denote the length, propagation speed and transmission rate of link I, for i in {1, 2}. The packet switch delays each packet by dproc b. There is a queuing delay of 100 msec at the switch (but no queuing delay at A). The packet is 1500 bits in length, the propagation speed on all links is 2.5 x 108 m/sec, the transmission rate on both links is 1 Mbps, and the packet switch processing delay is 3 msec. The length of the first link is 4000 km and the second link is 1000 km. What is the end-to-end delay from A to B? c. The switch fails and is replaced. This changes the following information for the switch only. The packet switch processing delay is reduced from 3 msec to 2 msec, the queuing delay is reduced from 100 msec to 40 msec but the second transmission link increases to 8,500…