 # Introduction to Packet-Switched Networks

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## 1.3 Packet Size and Optimizations

Packet size has a substantial impact on the performance of data transmission. Consider Figure 1.9, which compares the transmission of a 16-byte message from node A to node B through nodes D and C. Assume that for this transmission we would like to compare the transmission of the message with two different packet sizes but each requiring the same-size packet header of 3 bytes. In the first scheme shown in part (a) of the figure, the message is converted to a packet, P1, with 16-byte payload and 3-byte header. When the packet is received by node B, a total of 57-byte units have elapsed. If the message is fragmented into two packets, P1 and P2, of 8 bytes each as shown in part (b) of the figure, the total elapsed time becomes 44-byte units of delay. Figure 1.9 Comparison of two cases of transmitting data: (a) using three packets and (b) using six packets

The reason for the time reduction in the second case is the parallel transmission of two packets at nodes D and C. The parallel transmission of multiple packets can be understood better by referring again to Figure 1.7 or 1.8 in which the times of packets 2 and 1 are coinciding on the times of packets 3 and 2 in nodes D or C. The trend of delay reduction using smaller packets, however, is reversed at a certain point, owing to the dominance of packet overhead when a packet becomes very small.

To analyze packet size optimization, consider a link with a speed of s b/s or a rate of μ packets per second. Assume that packets of size d + h are sent over this link at the rate λ packets per second, where d and h are the sizes of the packet data and the packet header, respectively, in bits. Clearly,

We define link utilization to be ρ = λ/μ. Then the percentage of link utilization used by data, ρd, is obtained by

The average delay per packet, D, can be calculated by using μ – λ, where this term exhibits how close the offered load is to the link capacity:

Using Equations (1.3) and (1.4), we can rewrite the average delay per packet as

Apparently, the optimum size of a packet depends on several contributing factors. Here, we examine one of the factors by which the delay and the packet size become optimum. For optimality, consider d as one possible variable, where we want

This releases the two optimum values (we skip from the detail of derivation):

and

Note that here, dopt and Dopt are optimized values of d and D, respectively, given only the mentioned variables. The optimality of d and D can also be derived by using a number of other factors that will result in a more accurate approach.