Eight data terminals statistically share the capacity of an outgoing link. Traffic iscombined from the eight terminals and then served first-come first served. An(M/M/1) queue with infinite buffer is assumed. Find the expected number ofpackets in the system and the expected waiting time in the following cases:a) A terminal generates a packet every 10 seconds, the link speed is1024 bits/sec, and packet length = 512 bits.b) Repeat (a) using finite buffer k=10 and compare your results to the infinitebuffer caseA;=1/10=1024 bits/512 bits = 28 terminalsOut1=(1/10)*8 = 0.81

The Handwritten Solution is given below:

Answered: Eight data terminals statistically…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.4: The M/m/1/gd/∞/∞ Queuing System And The Queuing Formula L = Λw

Problem 7P

See similar textbooks

Similar questions

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, 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…
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…
This elementary problem begins to explore propagation delay and transmission delay, two central concepts in data networking. Consider two hosts, A and B, connected by a single link of rate R bps. Suppose that the two hosts are separated by m meters, and suppose the propagation speed along the link is s meters/sec. Host A is to send a packet of size L bits to Host B. a. Express the propagation delay, dprop, in terms of m and s.b. Determine the transmission time of the packet, dtrans, in terms of L and R.c. Ignoring processing and queuing delays, obtain an expression for the end-to-end delay.d. Suppose Host A begins to transmit the packet at time t = 0. At time t = dtrans, where is the last bit of the packet?e. Suppose dprop is greater than dtrans. At time t = dtrans, where is the first bit of the packet?f. Suppose dprop is less than dtrans. At time t = dtrans, where is the first bit of the packet?g. Suppose s = 2.5 * 108 meters/sec, L = 120 bits, and R = 0.112 Mbps. Find the distance m…
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?
A disadvantage of a broadcast subnet is the capacity wasted when multiple hosts attempt to access the channel at the same time. As a simplistic example, suppose that time is divided into discrete slots, with each of the n hosts attempting to use the channel with probability p during each slot. What fraction of the slots are wasted due to collisions?
A packet switch receives a packet and determines the outbound link to which the packet should be forwarded. When the packet arrives, one other packet is halfway done being transmitted on this outbound link and four other packets are waiting to be transmitted. Packets are transmitted in order of arrival. Suppose all packets are 1,200 bytes and the link rate is 2 Mbps. What is the queuing delay for the packet? More generally, what is the queuing delay when all packets have length L, the transmission rate is R, x bits of the currently-being-transmitted packet have been transmitted, and n packets are already in the queue?
This elementary problem begins to explore propagation delay and transmission delay, twocentral concepts in data networking. Consider two hosts, A and B, connected by a single link ofrate R bps. Suppose that the two hosts are separated by m meters, and suppose the propagationspeed along the link is s meters/sec. Host A is to send a packet of size L bits to Host B.a. Express the propagation delay, dprop, in terms of m and s.b. Determine the transmission time of the packet, dtrans, in terms of Land R.c. Ignoring processing and queuing delays, obtain an expression for the endto-end delay.d. Suppose Host A begins to transmit the packet at time t = 0. At time t = dtrans,where is the last bit of the packet?e. Suppose dprop is greater than dtrans. At time t = dtrans, where is the first bit ofthe packet?f. Suppose dprop is less than dtrans. At time t = dtrans, where is the first bit ofthe packet?g. Suppose s = 2.5 · 108, L = 120 bits, and R = 56 kbps. Find the distance mso that dprop equals…
Please dont copy your answer from other sourses i.e chegg A communication line capable of transmitting at a rate of 50 Kbits/secwill be used to accommodate 10 sessions each generating Poisson traffic at a rate 150 packets/min.Packet length are exponentially distributed with mean 1000 bits. For each session, find the averagenumber of packets in queue, the average number in the system, and the average delay per packetwhen the line is allocated to the sessions by using: i) 10 equal-capacity time-division multiplexed channels;ii) statistical multiplexing.
Consider the same pattern of red and green packet arrivals to a router’s output port queue, shown below. Suppose each packet takes one time slot to be transmitted, and can only begin transmission at the beginning of a time slot after its arrival. Indicate the sequence of departing packet numbers (at t = 1, 2, 3, 4, 5, 6, 7) under round robin scheduling. Assume a round-robin scheduling cycle beings with green packets. Give your answer as 7 ordered digits (each corresponding to the packet number of a departing packet), with a single space between each digit, and no spaces before the first or after the last digit, e.g., in a form like 7 6 5 4 3 2 1).
Copy from chegg == Report! A communication line capable of transmitting at a rate of 50 Kbits/secwill be used to accommodate 10 sessions each generating Poisson traffic at a rate 150 packets/min.Packet length are exponentially distributed with mean 1000 bits. For each session, find the averagenumber of packets in queue, the average number in the system, and the average delay per packetwhen the line is allocated to the sessions by using: i) 10 equal-capacity time-division multiplexed channels;ii) statistical multiplexing
Consider the following network with given line speeds and lengths: Assume the speed of light is 2×10^8 m/s, and that the processing and queuing delays are negligible. Node A sends a 1400-byte frame to node C through node B. Suppose Node A starts sending the first bit of the frame at t=0. Answer the following questions: a. At what time (t=?) node B receives the frame in full (i.e. the last bit)? b. After node B receives the frame in full, then it will start sending the frame to node C. Determine the time (t=?) when node C receives the frame in full. c. Suppose at this time node C sends a small acknowledgment back to node A. The transmission time for the acknowledgment is negligible. Calculate at what times (t=?) the acknowledgment arrives at nodes B and A. d. Assume after sending its frame, node A wait for the acknowledgment back from node C before sending the next frame. What is the average throughput (number of transmitted bits per second) of the data flow from node A to…
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…

SEE MORE QUESTIONS

Recommended textbooks for you

Operations Research : Applications and Algorithms

Computer Science

ISBN:

9780534380588

Author:

Wayne L. Winston

Publisher:

Brooks Cole

Principles of Information Security (MindTap Cours…

Computer Science

ISBN:

9781337102063

Author:

Michael E. Whitman, Herbert J. Mattord

Publisher:

Cengage Learning

Systems Architecture

Computer Science

ISBN:

9781305080195

Author:

Stephen D. Burd

Publisher:

Cengage Learning

Operations Research : Applications and Algorithms

Computer Science

ISBN:

9780534380588

Author:

Wayne L. Winston

Publisher:

Brooks Cole

Principles of Information Security (MindTap Cours…

Computer Science

ISBN:

9781337102063

Author:

Michael E. Whitman, Herbert J. Mattord

Publisher:

Cengage Learning

Systems Architecture

Computer Science

ISBN:

9781305080195

Author:

Stephen D. Burd

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS