How much data (in number of characters) must be exchanged between A and B in order for the connection-oriented communication to yield a shorter session than the connectionless communication? Explain.

In this exercise we will use a simplified mathematical model to analyze the tradeoff between connection-oriented communication and connectionless communication. Explain your answer.
On a certain network both forms of communication are provided:
• Using connection-oriented communication, it takes 50 second to establish a connection, after which a packet of up to 10 characters can be sent in 1.0 seconds over the connection, in either direction.
• Using connectionless communication, a packet of up to 10 characters can be sent in 1.2 second. (The sending of each packet takes slightly longer than in the connection-oriented case, since each packet must find its way to the receiver.)
Suppose A and B exchanges messages on this network. A initiates the communication and sends to B a message of 100 characters, which are partitioned into 10 packets. In reply, B sends a message of 50 characters, which are partitioned into 5 packets.
Assuming that there is no delay other than the time it takes for establishing a connection (in the connection-oriented case) and for packet transmission:

Suppose the breakeven point occurs when N packets are exchanged between A and B, then:
50 + N * 1.0 < N * 1.2
Solving for N yields N > 250, and hence the smallest number of packets for the connection-oriented communication to yield a shorter time is N =251 packets.
In terms of number of characters, let a and b be the number of characters sent by A and B respective. Then
ceiling of (a/10) + ceiling of (b/10) = 251
For the equation to hold, any of the following combination will work:

a = (1,9), b = (2491,2499)
that is, A sends 1 to 9 characters in 1 packet; B sends 2491 to 2499 characters in 250 packets
a = (11,19), b = (2481,2489)
a = (21,29), b = (2471,2579)
and so forth.

Choosing the smallest number of characters on each side, one comes up with 2492 characters as the smallest for 251 packets to be exchanges. Hence 2492 characters or more must be exchanged between A and B in order for the connection-oriented communication to yield a shorter session than the connectionless communication.