SIMULATION AND OPTIMISATION OF DATA MULTIPLEX SYSTEM

SIMULATION AND OPTIMISATION OF DATA MULTIPLEX

SYSTEM

Roman Trobec, Viktor Avbelj, Bo󰂚tjan SlivnikJo󰂞ef Stefan Institute, Jamova 3961000 Ljubljana, SLOVENIAe-mail: roman.trobec@ijs.si

1. Problem description

To efficiently use hardware recourses and better utilise a transmission channel, data

multiplexing is used often in digital telecommunications and computer networks [1]. Severalinput data streams of the rate Ri have to be multiplexed into an aggregate output data stream of

the higher data rate Ro. The number of input channels may be as low as one, or there may be an

arbitrary number of n channels. The data rates of different input channels may be equal, in some

relation or totally independent. Similar problems arise also in other research areas such as in the

queue theory, transport problems or in many physical systems.

To properly interpret the transmitted data on the demultiplex side, an unique transmissionframe has to be constructed. It consists of a predefined number of information bits Ni and an

adequate number of control bits Nc. Control bits are for example frame-start identification

word, stuffing indication bits in plesyochronous (PDH) transmission systems, or section and

path overhead in synchronous (SDH) systems. Consequently, the data rate of the aggregate

channel is higher than the sum of data rates of all n input channels.

Additional consequence of the above concept is the need for a kind of circular buffers on

each input channel. They serve as a temporary store for the time of insertion of control

information, at the same time they compensate input data rate irregularities (jitter). Data rates

are never enough accurate. This inaccuracy could produce temporary loss of information,

because of the limited length of circular buffers. Therefore, a mechanism for compensation of

such inaccuracies has to be embedded in each multiplex unit. To implement this request a

specific part of the transmission frame is reserved for the information that is transferred

occasionally. A fundamental problem of digital multiplexing is accommodating signals that are

not identical in data rate. This process is called synchronisation, and there are several

synchronisation techniques known. Bit justification and pointer processing are mainly usedtoday. Each synchronisation technique produces jitter and there are many jitter reduction

methods known [2], [3], [4]. We limit our discussion to positive justification scheme, which is

normally used in asynchronous multiplexing [5]. The insertion of justified information is

triggered by a distance comparator between the write and the read pointer in each circular

buffer. The activity of the read pointer on the multiplex side is equal to the channel multiplexingdata rate Rc. Similar but the reverse process is performed on the demultiplex side. The control

bits are removed and for each channel an appropriate PLL (phase locked loop) regenerates the

original data rate frequency and removes the induced jitter. The jitter with a very low frequency

spectrum (waiting-time jitter) still remains in the signal, hence its generation has to be minimised

[5]. Waiting-time jitter is generated primarily as a function of the justification ratio ri, which is

one of the main parameter in a multiplexer design [6]. According to the above discussion, a

general multiplex system with input and output channels and appropriate circular buffers isshown in Figure 1.

control bits

control bitsInput channel

Input channelOutput channelCircularbuffer 1

Circularbuffer ndistance

distance4i1

4in4c1

4cn4oMUX1

n

Figure 1. The functional block of a general multiplex system.

2. Mathematical equations for simulation and optimisation

In this chapter mathematical equations will be given that are implemented in the simulation

and optimisation software. It will be shown that there exists no simple explicit solution for the

optimisation problem.3. Software package description

The Multiplex Simulation and Optimisation (MSO) program is a menu driven package,

written for PC-compatible systems. All options have a graphic output. Discrete solutions are

represented with points. All diagrams start with a list of input values and the momentary

selected solution. This solution is denoted with the cursor in the graphic diagram. With some

special keys, input parameters can be changed. As a consequence, the cursor is automatically

moved on the appropriate solution in the plotted diagram, and all values of multiplexing

parameters are appropriately updated. More details will be given in the final version of the

paper.

4. Example

An example for multiplexing of two independent input channels into a common output