Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when transmitting, but each user transmits only 10 percent of the time. (See the discussion of packet switching versus circuit switching in Section 1.3.) a. When circuit switching is used, how many users can be supported? b. For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting. c. Suppose there are 120 users. Find the probability that at any given time, exactly n users are transmitting simultaneously. (Hint: Use the binomial distribution.) d. Find the probability that there are 21 or more users transmitting simultaneously.

Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when transmitting, but each user transmits only 10 percent of the time. (See the discussion of packet switching versus circuit switching in Section 1.3.) a. When circuit switching is used, how many users can be supported? b. For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting. c. Suppose there are 120 users. Find the probability that at any given time, exactly n users are transmitting simultaneously. (Hint: Use the binomial distribution.) d. Find the probability that there are 21 or more users transmitting simultaneously.

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

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Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when transmitting, but each user transmits only 10 percent of the time. (See the discussion of packet switching versus circuit switching in Section 1.3.) a. When circuit switching is used, how many users can be supported? b. For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting. c. Suppose there are 120 users. Find the probability that at any given time, exactly n users are transmitting simultaneously. (Hint: Use the binomial distribution.) d. Find the probability that there are 21 or more users transmitting simultaneously.
Suppose users share a 2 Mbps link. Also suppose each user transmits continuously at 1 Mbps when transmitting, but each user transmits only 20 percent of the time. (See the discussion of statistical multiplexing in Section 1.3.) a. When circuit switching is used, how many users can be supported? b. For the remainder of this problem, suppose packet switching is used. Why will there be essentially no queuing delay before the link if two or fewer users transmit at the same time? Why will there be a queuing delay if three users transmit at the same time? c. Find the probability that a given user is transmitting. d. Suppose now there are three users. Find the probability that at any given time, all three users are transmitting simultaneously. Find the fraction of time during which the queue grows.
This problem will compare circuit switching and packet switching. Consider a single link with capacity 60 Mbps. Each user is active 20% of the time. When active, each user transmits at 1 Mbps half of the time and at 3 Mbps half of the time. (a) Suppose the network uses circuit switching. How many users can be supported if you want to guarantee that the blocking probability is zero? In parts (b)-(d), suppose the network uses packet switching and that there are 200 users. (b) Suppose that 20 users are simultaneously active. What is the traffic intensity (i.e., load)? (c) Write an expression for the probability that at least 30 users are simultaneously active. (d) If 30 users are simultaneously active, write an expression for the probability that the total instantaneous transmission rate of these 30 users exceeds the link capacity.
Suppose users share a 2 Mbps link. Also suppose each user transmits continuously at 1 Mbps when transmitting, but each user transmits only 20 percent of the time. a. When circuit switching is used, how many users can be supported? b. For the remainder of this problem, suppose packet switching is used. Why will there be essentially no queuing delay before the link if two or fewer users transmit at the same time? Why will there be a queuing delay if three users transmit at the same time? c. Find the probability that a given user is transmitting. d. Suppose now there are three users. Find the probability that at any given time, all three users are transmitting simultaneously. Find the fraction of time during which the queue grows.
Each question is a judgment question. Write down your answer with T for True, F for False, and give the explanation if the answer is False. Consider a system of bandwidth 10Mbps, with multiple users, each is active (i.e., have data to transmit at rate 1Mbps) with a low probability, e.g. 0.1. From the capacity perspective, packet switching is better than circuit switching because the former can support more users. Denial of Service (DoS) attack can be generated by a large number of (legitimate) TCP connection requests to the same targeted server at the same time. These TCP requests can be originated from different hosts in a botnet, which is controlled by the attacker. In VSAT systems the micro-stations do not have sufficient power to communicate directly with one another; hence, they use a ground station called a hub with a high gain antenna to relay traffic. In the current Internet, communication across the Atlantic Ocean between the USA and Europe is mostly done by wireless…
Suppose users in a network share a 4 Mbps communication link and each user requires 125 kbps when transmitting. However, each user transmits only 20 percent of the time. Suppose there are 30 users and packet switching is employed. Find the probability that at any given, there are 17 or more users transmitting simultaneously.
(2) Suppose a message of length 10 Mbytes needs to be transmitted from the router to your home PC and the message is broken up into one thousand (1000) equal-sized packets that are transmitted separately: (2.1) Please find the probability that a packet arrives at your home PC correctly. (2.2) Please find how many re-tries, on the average, it will take to get the packet arrived at your home PC correctly (2.3) Please find the probability that the entire message arrives at your home PC correctly.
Suppose, there are N = 4 nodes using the slotted ALOHA protocol. The nodes are contending for a 6 Mbps channel. Each node transmits only 50% of the time. What is the probability that at least one node succeeds in time slot 10.
Consider 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?
Consider two nodes (A, B) sharing the same broadcast channel of speed R =10Mbps. The propagation delay between the two nodes is 1ms. Consider a node C in the middle between both nodes. If A starts at time t=0 its transmission of a packet to node C, at what time can node B start transmitting its packet to a node D in the network in order for the two packets not to collide? Assume both nodes have each a packet of length L = 1000Bytes. О а. 1.3ms O b. 1ms О с. 0.5ms d. 1.8ms
Consider a client and a server connected through one router. Assume the router can start transmitting an incoming packet after receiving its first 0.6 Mbits instead of the whole packet. Suppose that the transmission rate of each link is 6 Mb/s and that the client transmits one packet with a size of 2 Mbits to the server. Assume the propagation, processing, and queuing delays are negligible. Answer the following questions (use up to 4 significant digits if needed; e.g., yy.xxxx): What is the end-to-end delay?3D seconds What is the end-to-end delay if there are 2 routers between the client and the server?= seconds
Each question is a judgment question. Write down your answer with T for True, F for False, and give theexplanation if the answer is False.a. Consider a system of bandwidth 10Mbps, with multiple users, each is active (i.e., have data to transmitat rate 1Mbps) with a low probability, e.g. 0.1. From the capacity perspective, packet switching isbetter than circuit switching because the former can support more users.b. Denial of Service (DoS) attack can be generated by a large number of (legitimate) TCP connectionrequests to the same targeted server at the same time. These TCP requests can be originated fromdifferent hosts in a botnet, which is controlled by the attacker.c. In VSAT systems the micro-stations do not have sufficient power to communicate directly with oneanother; hence, they use a ground station called a hub with a high gain antenna to relay traffic.d. In the current Internet, communication across the Atlantic Ocean between the USA and Europe ismostly done by wireless…