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by Abhijit S. Pandya; Ercan Sen CRC Press, CRC Press LLC
ISBN: 0849331390 Pub Date: 110198
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I. Queuing Model for the ATM Traffic Simulation
We describe next the queuing model used for the ATM traffic simulation. As mentioned earlier, the ATM switch under consideration is based on the input queuing model. As depicted in Figure 10-3, each
input port has its own dedicated queue. Since we use shared buffer space, the input queues are formed as logical queues. The queuing model can be described as a multiserver loss model since each input port is
a server and cell loss occurs due to limited finite buffer space. The model can be best represented as an GDmBK using the Kendall’s notation described in [Jain 1991], where we assume general arrival
distribution G, deterministic service time D, multiple servers m, limited buffer capacity B and limited finite customers K. More detailed coverage of the queuing models and their applications to
computer and communication systems can be found in [Cooper 1981] and [Tanner 1995]. We next elaborate on each aspect of the queuing model which we used to describe our ATM traffic model.
In an ATM network environment, cells arriving at an ATM node do not necessarily represent a Poisson behavior. As explained in the next section, our ATM traffic model abstracts incoming traffic at three
different levels: call level, message level and cell level. Although calls and messages can exhibit memoryless Poisson behavior, cells come in burst mode. This is due to fact that messages are broken
into fixed length ATM cells at the ATM network interface. The cells that constitute a user message enter into the ATM network in bursts. That is, there is no separation between the cells belonging to the same
burst. Thus, at the cell level there is a statistical correlation between the consecutive cells [Leduc 1994]. Because of this statistical correlation we can not assume Poisson arrival behavior at the cell level. An
extensive elaboration on the statistical correlation between the consecutive ATM cells and its influence on ATM traffic modeling can be found in [McDysan 1995] and [Leduc 1994].
It is also possible to consider cell bursts as a unit of arrival event and thus, assume that these cell bursts follow a Poisson arrival behavior. The decision to observe the incoming ATM traffic at the cell level or
at the burst level and model the ATM queue accordingly is determined by the characteristics of the server. If the server under consideration processes the incoming cell traffic one cell at a time, i.e., the
service time is equal to single cell transmission time one time-slot, then the observation of the arrival process should be at the cell level. On the other hand, if the server processes cell bursts as a single unit,
then the observation of the arrival process can be done at the burst level. In this case, the service time would be variable and can be modeled as an exponential service behavior. At the burst level, the ATM
queuing system can be modeled as an MMmBK queue. In our case, since we are concerned with an
Our queuing model is a multiserver m model since we consider each input port as a server with dedicated queues. As well known from the queuing theory, performance of a multiserver queue with a
single common queue is much better than the queuing model with a multiserver with dedicated queues for each server. In our case, servers are not generic servers, i.e., an incoming cell has to be handled by a
specific input port since the physical transmission path directly terminates to that input port. Of course, it is possible to channel all incoming cells to a single central server which then transmits them to the
corresponding output ports. However, in this case the central server has to run N times faster than the single port speed in order to be able to deliver N cells to N output ports in a single time slot for an N×N
switch. Given the high-speed operation of a single input port in the order of 100 Mbps, the central server has to run at a very high speed N×100 Mbps.
Figure 10-3 Queuing model for the ATM traffic simulation.
The limited buffer capacity B is a practical necessity. In our model, a fixed shared buffer space, which is determined at the design stage for an ATM switch under consideration, is dynamically allocated to
individual input queues as depicted in Figure 10-3. Unlimited buffer capacity, although feasible for a
Since virtual connections are set up in advance during call setup time, ATM cells typically come from a limited number of sources customers at the cell traffic level. Therefore, we assume a limited customer
population K for the queuing model. The size of the customer population can vary depending on where the observation is made. At the edge nodes where customers are connected to an ATM network, the
population size is fairly small for an input port whereas at the intermediate nodes population size tends to be larger. For the simulation, we consider the ATM traffic at the edge nodes where subscribers are
connected. Although the ATM traffic simulator is capable of generating simultaneous calls to different destinations, we are interested in a worst case scenario in which cells arriving at an input port exhibit a
high degree of statistical correlation. When cells arriving at the input port of an intermediate ATM node are observed, we expect a higher mixture of cells with different destination addresses. In other words,
there is less statistical correlation between the consecutive cells. In this case, it is possible to assume a Poisson arrival process at the intermediate ATM nodes which would certainly provide a better switching
performance. However, since we are interested in improving switching performance for the worst case scenario, we assume that each input port is associated with a single subscriber and the subscribers are
not allowed to initiate simultaneous calls to different destinations. In the next section we describe the traffic model for the ATM traffic simulator and explain this subscriber behavior in more detail.
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