Quantitative Comparison of Packet Switching and Circuit Switching Consider the t
ID: 3862331 • Letter: Q
Question
Quantitative Comparison of Packet Switching and Circuit Switching Consider the two scenarios below: A circuit-switching scenario in which N_cs users, each requiring a bandwidth of 10 Mbps, must share a link of capacity 150 Mbps. A packet-switching scenario with users sharing a 150 Mbps link, where each user again requires 10 Mbps when transmitting, but only needs to transmit 30 percent of the time Answer the following questions. a When circuit switching is used, what is the maximum number of circuit-switched users that can be supported? Explain your answer. b For the remainder of this problem, suppose packet switching is used You only need to provide formulas and no need to compute the results Suppose there are 29 packet-switching users (i.e. N_pa = 29) Can this many users be supported under circuit-switching? Explain c What is the probability that a given (specific) user is transmitting, and the remaining users are not transmitting?Explanation / Answer
a>When circuit switching is used, maximum 15 circuit switched user can be supported. Because for each of the user is allocated 10mbps bandwidth, and given link capacity is 150mbps.
b>No, for each user we allocate 10mbps, similarly for 29 user we will require 290 mbps link.
which is much more than 150 mbps.
c>
Probability that a given (specific) user is busy transmitting, which we'll denote p, is just the fraction of time it is transmitting,i.e., 0.100. The probability that one specific other user is not busy is (1-p), and so the probability that all of the other Nps-1 users are not transmitting is (1-p)Nps-1.Thus the probability that one pecific user is transmitting and the remaining users are not transmitting is p1(1-p) Nps-1, which has the numerical value of 0.00523347. This user will be transmitting at a rate of 10 Mbps over the 150 Mbps link, using a fraction 0.0667 of the link's capacity when busy.