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\title{EE 290Q Topics in Communication Networks\\
Lecture Notes: 6}
\author{Cliff Cordeiro}
\date{February 2, 1996}
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\begin{document}
\maketitle
\section*{Review of GPS}
\begin{itemize}
\item Advantages
\begin{itemize}
\item Isolation of users. Guaranteed bandwidth to a particular user regardless of other users' performance.
\item If each user is policed properly, end to end delay bounds are obtained.
\end{itemize}
\item Disadvantages
\begin{itemize}
\item How to choose $\phi_i^m$? It is not clear how to pick the
$\phi$ to satisfy delay bounds. There is no distributed
algorithm or dynamic algorithm to do this.
\item Traffic becomes more bursty as it passes nodes. The queue length becomes bigger than the initial leaky bucket, which requires bigger and bigger buffers as you go deeper into the network.
\item Implementation is not straightforward. There are too many individual connections to keep track of. A solution is to group connections into classes which require QoS guarantees as a class.
\end{itemize}
\end{itemize}
\section*{Main Ideas}
A new scheduling algorithm described in \cite{IBM} is to be discussed in the next few lectures. It has certain properties outlined below.
\begin{itemize}
\item Traffic shaping node-by-node in order to keep burstiness constant.
\item End to end delay bounds are decomposed into the sum of local delay bounds. The planning/allocation problem becomes a more distributed budgeting problem.
\item "Optimal" scheduling at each node.
\end{itemize}
Will the bounds given by this algorithm be good or bad in comparison with GPS? The additive method in the GPS case gives loose (bad) bounds. In this case, it is actually possible to outperform GPS.
\subsection*{Traffic Shaping}
Goal: reconstruct a delayed version of the (input) traffic pattern at a downstream node.
\begin{figure}
\centerline{\psfig{figure=shaper.eps}}
\caption {Diagram of the traffic shaper's location and function}
\label{f:shaper}
\end{figure}
\subsection*{Implementation}
The release time of packet i is the sum of the arrival time at node m and $D_i^m$.
\begin{itemize}
\item $P(i)$: virtual path of session $i$
\item $H_i$: number of nodes on $P(i)$
\item End-End Delay = $\sum_{m=1}^{H_i} D_i^{m*}$
\item Delay Jitter: Determines the size of buffer necessary. It's significantly smaller than GPS under this approach.
\item End-End Jitter: Delay jitter at the last node. (Due to the fact that there is no shaper after the last node).
\end{itemize}
\subsection*{Questions}
\begin{itemize}
\item How to design the schedulers at every node?
\item What is the end-end performance compared to GPS?
\end{itemize}
\subsection*{Scheduler}
Consider N sessions 1..N.
\begin{itemize}
\item Each session i has burstiness curve ${\stackrel{\land}{A}}_i(t)$.
\item Let $\pi$ be a scheduling policy.
\item $R^\pi$ = set of all delay bounds ($D_1^*$, $D_2^*$, ... , $D_N^*$) that can be guaranteed.
\item Def: $\pi^*$ is said to be "optimal" if
$\forall \pi R^{\pi*} \ge R^\pi$
\item $R^{\pi*}$ is the schedulable region which depends on
${\stackrel{\land}{A}}_i(t)$ \end{itemize}
\subsection*{Earliest Deadline/Due Date First}
{\bf Theorem:} optimal policy is earliest due date first.
\begin{itemize}
\item Requirements: ($D_1$, ... , $D_N$)
\item Packet from i arrives at time $t$.
\item Stamp due date $t+D_i$, sort and serve packets with earliest due date.
\item Minimizes maximum latency of any packet.
\item $r$ = rate of server
\item $R^{\pi*}=\{(D_1, D_2, ... , D_N): \sum_{i=1}^{m}
{\stackrel{\land}{A}}_i(t-D_i) \le rt, \forall t\}$
\begin{figure}
\centerline{\psfig{figure=graph.eps}}
\caption {Illustration of $R^{\pi*}$}
\label{f:graph}
\end{figure}
\item ${\stackrel{\land}{A}}_i(t) = \{0, t<0; \sigma_i+\rho_{i}t, t>0\}$
\item ${\stackrel{\land}{A}}_i(t)$ is piecewise linear, which means it is sufficient to verify at the breakpoints $D_1$, $D_2$, ... , $D_N$. This leads to a simpler formula:
\item $R^{\pi*}=\{(D_1, D_2, ... , D_N): \sum_{i=1}^{m}
{\stackrel{\land}{A}}_i(D_j-D_i) \le rD_j, j=1,2,...,N \}$ \end{itemize}
\subsection*{Performance Comparison with GPS}
\begin{figure}
\centerline{\psfig{figure=network.eps}}
\caption {A network of EDF nodes}
\label{f:network}
\end{figure}
Given a virtual path of length $H_i$ $(\sigma_i, \rho_i)$ characterized
traffic, delay grows linearly with $H_i$. A network of EDD nodes is shown
in figure ~\ref{f:network}.
\begin{figure}
\centerline{\psfig{figure=gps.eps}}
\caption {Unmodified GPS}
\label{f:gps}
\end{figure}
In figure ~\ref{f:gps},
$\phi_{i}r=\rho_i$
$\sigma_i/\rho_i =$ end-end delay bound for GPS (independent of the
number of nodes!) The additive method would give $H_i \sigma_i/\rho_i$.
\begin{figure}
\centerline{\psfig{figure=smoothgps.eps}}
\caption {GPS with smoothing at the edge}
\label{f:smoothgps}
\end{figure}
In figure ~\ref{f:smoothgps}, adding a smoother consolidates the GPS delay
into the
smoother, with 0 delay in the nodes. We will use this approach next time
in order to better compare the two scheduling policies.
\begin{thebibliography}{1}
\bibitem{IBM}
L. Georgiadis, R. Guerin, V. Peris, K.N. Sivarajan (1995).
Efficient Network QoS Provisioning Based on per Node Traffic Shaping. {\em IBM Research Report}, (05/17/95), RC 20064, pp. 1-34.
\end{thebibliography}
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