Minimizing End-to-End Delay on Real-Time Applications

Abstract

In real time communication system, packets of lower prioritized flows suffer a longer queuing delay than the packets having higher priority. As a result, they reach at the destination in a long end-to-end delay and become less useful. In this paper, we have proposed a real time packet scheduling technique to minimize overall end-to-end delay among multiple flows. Here, elapsed time plays a major role to calculate priority of a packet. The packets, already spent a long queuing delay are re-assigned to lower priority. Also, the model reduces the priority of the higher prioritized packets when they are very early and approaching to the destination node. This model gives more importance to middle aged packets (neither too early nor too late with respect to packet creation and deadline of packet receiving) so that they can reach the destination within time bound. The model is experimented using NS-2 and performance has been compared with other queuing policies. Performance evaluation of this model exhibits moderated end-to-end latency of the flows and works more efficiently than other techniques.

Appendix

Lemma 1

Elapsed time of a packet$\varGamma _s(i)$lies in [0−1]

Proof

According to Eq. 2, $\varGamma _s(i)$ is the ratio between $\lambda (i)$ and $\delta$. Where $\lambda$ is elapsed time, i.e., Always less than Round Trip Time (RTT) which is always less than expected end-to-end delay $\delta$ . Trivially, $\lambda$ is less than $\delta$. If, any intermediate node is not the source node of the packet, $\lambda$ can never become 0. Otherwise, it becomes 0, if the intermediate node is a source node. Hence, $\varGamma _s(i) \ge 0$. Collectively, we can claim that $\varGamma _s(i)$ lies in [0–1]. $\square$

Lemma 2

Weighted time of a packet lies in [0–0.5]

Proof

According to Eq. 3 weighted time of a packet ($\eta (i)$) depends on $\varGamma _s(i)$. In Lemma  1 it is proved that $\varGamma _s(i)$ lies in (0–1] and $\eta (i)$ is taken as the minimum value of $\varGamma _s(i)$ or $1 - \varGamma _s(i)$. Hence, it is trivial that $\eta (i)$ is always positive.

Case 1: If ($\varGamma _s(i) <$ 0.5), $1 - \varGamma _s(i) >$ 0.5. So, $\eta (i)$ is $\varGamma _s(i)$, i.e., $\eta (i) <$ 0.5.

Case 2: If ($\varGamma _s(i) >$ 0.5), ($1 - \varGamma _s(i))<$ 0.5. Hence, $\eta (i)$ is 1 - $\varGamma _s(i)$, i.e., $\eta (i) <$0.5.

Case 3: If ($\varGamma _s(i) =$ 0.5), $\varGamma _s(i)$ and $1 - \varGamma _s(i)$ is 0.5. Hence, $\eta (i)$ is 0.5.

Now, considering all the cases it is proved that $\eta (i)$ lies in [0–0.5]. $\square$

Lemma 3

The value of$\textit{Priority}_{\textit{max}}$lies between 1 and$\root 2 \of {\textit{max}(\alpha )+\textit{max}(\beta )}$.

Proof

As we have shown in Eq. 4 integrated priority of a packet is calculated in the form of $x^{\eta }$ where x is $\textit{max}(\alpha )+\textit{max}(\beta )$. In Lemma 2 it proves that value of $\eta$ ranges from 0 to 0.5. Hence, value of $\textit{Priority}_{\textit{max}}$ lies between 1 and $\root 2 \of {\textit{max}(\alpha )+\textit{max}(\beta )}$.