Translating the relative delay

The relative delay gives us a sense of the change in queueing, but it tells us nothing about the actual number of packets represented by this number. We translate the sum of relative delays into the equivalent number of queued packets by first calculating the average packet service time (sec/pkt) achieved by a session over an interval. This rate over the forward path is of course limited by the bottleneck link. Our model of the bottleneck link, depicted in Figure 5, consists of two delay parameters: queueing delay, $\tau _{Q}$; and output service time, pktS, the amount of time to service a packet. The queuing delay is variable and is controlled by the congestion control algorithm by changing the sender's congestion window. We get a sense of this value with the relative delay measurements. The output rate of a FIFO queue will vary according to the number of sessions and the burstiness of the arrivals from various sessions. The packet service rate is calculated as $pktS = \frac{R}{\mathrm{\char93 \; pkts \; received}}$, where R is the difference in arrival time of the two packets as calculated from the timestamps returned by the receiver. Because this rate changes throughout an interval, we calculate the average packet service time, $\overline{pktS}$ over the interval. Finally, we translate the accumulated relative delays over the interval into the equivalent number of packets by dividing the amount of time a packet is delayed with respect to another (relative delay) by the average time to service a packet to obtain the number of packets represented by the delay:

$$M_{W_{i-1}} = \displaystyle{\frac{\sum D^{F}_{k}}{\overline{pktS}}}$$

where k are packet-pairs within window W_i-1. The total queueing at the end of the interval is determined by Equations 2 and 3.

  

Figure: Bottleneck Link: Delay consists of two parts: $\tau _{Q}$, the delay due to queuing and pktS, the packet service time over the link.