Circuit vs Packet Switching: Users & Overflow Probability, Assignments of Electrical and Electronics Engineering

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a) With circuit switching, we can support 1 Mbps/100Kbps= users b) Define: m number of active users, p(m=n) users are transmitting simultaneously with probability p=0.1 is: Solution to HW1: Question 1

!

P (m = n) =

n

"

$

%

&

' (0.1^ )

n

( 1 ( 0.1)

( 40 ( n ) c) Probability that m ≥11:

!

P (m " 11 ) = 1

m

$

%

&

'

(

) (0.1^ )

m

( 1 # 0.1)

( 40 # m ) m = 0 m = 10

* =^ 0.

P(m ≥11) small, thus more users can be supported w/ packet switching (but it requires that users are independent and traffic is bursty)!

Solution to HW1: Question 1 d) Now the probability that m=11 or more are transmitting at the same time is p(m≥11)=1. Eventually, any queue will overflow and random packet loss (= same loss for all users) will occur. Essentially, every user will only get 1 Mbps/40=25 Kbps (resp. a 75% loss rate from the required 100 Kbps). This is below the users’ requirements, and no one will get the demanded services. With circuit switching, at least 10 users could receive the demanded service, and the remaining 30 would not receive any service. Clearly, favoring circuit switching or packet switching depends on the application and the situation at hand and there is no absolute favorite.

Solution to HW1: Question 2, key points RFC 1958:

• general design principles for/in current internet architecture
• main goals:
  • connectivity,
  • relying on the Internet Protocol (IP) to provide for communication between hosts
• IP is application nonspecific (transparent) and hardware independent
• transparency allows for scalability and acceptable reliability according to the end-to-end argument
• Internet: packet switching, best effort service model

Solution to HW1: Question 2, key points End-to-end argument:

• addresses the question “where to implement what”
• only basic functionality in the network core, best effort funct.
• functions pertaining to applications in hosts cannot and should not be implemented in network
• it is the responsibility of the applications to ensure reliability and correctness of the functions needed (compare to UDP, later)
• scalability:
  • complexity/functionality in the hosts, not the network
  • no state information maintained inside the network
• IP independent of hardware medium, univ. naming scheme
• upgradeability is thereby ensured (new applications possible, only hosts need to be changed) The network is transparent to the application (=ignorant of)