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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Copyr ight © CRC Pr ess LLC
by Abhijit S. Pandya; Ercan Sen CRC Press, CRC Press LLC
ISBN: 0849331390 Pub Date: 110198
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II. ATM Traffic Model
The traffic model presented here describes the cell generation behavior of the ATM traffic simulator. It reflects the behavior of a typical ATM subscriber. An ATM subscriber starts a call and during the active
call state it generates many messages which are broken into fixed length ATM cells. These messages appear as a burst of cells to the ATM switch. Following a quiet period message interarrival time, the
next message is transmitted as another burst of cells. This behavior repeats itself until the call is completed. Then, the subscriber goes through a silent period. At the end of the silent period, the
subscriber initiates another call. Due to the memoryless property of interarrival times between
consecutive bursts, i.e., the interarrival time between the k
th
and the k+1
th
arrrivals is independent of the previous interarrival time between the k-1
th
and the k
th
arrivals, the behavior of an active call can be represented as a two-state ONOFF Markov Process. Figure 10-4 illustrates the corresponding ON
OFF Markov process transition diagram for an active call period in which the subscriber goes through ON-OFF state transitions with certain probabilities. When it is in the OFF state, it remains in this state
with the probability 1-
α D or switches to ON state with the probability
α D. Similarly, when it is in the
ON state, it remains in this state with the probability 1- β
D and generates cells for the current message. The subscriber switches to the OFF state with the probability
β D. This traffic model falls into the
category of Markov Modulated Bernoulli Process with two states, MMBP2. The model provides a good approximation for voice and computer data traffic and a rough approximation for video traffic
[Leduc 1994].
According to the model described above, a subscriber initiates a burst with the probability α
D which has an exponential distribution and ends a burst with the probability of
β D which has a geometric
distribution in a particular cell time. The D represents the cell duration in seconds. The average burst duration d in cells can be calculated using the standard geometric series as described in [McDysan
1995]:
The traffic model also defines the behavior of the subscriber at the call level. At the call level, calls are
Figure 10-4 Traffic model for the ATM traffic simulator.
III. Validation of Simulation Results
When performance of a system is analyzed via a simulation technique, it is necessary to validate simulation results against some reference data. In simulations of complex queuing systems such as
Multiserver Loss Models, one common approach for validation is to approximate the queuing system under study into one of the basic queuing models such as MM1, MG1 or MD1 for which analytical
models are well defined. The MM1 model describes a queue with Poisson arrival, exponential service time, single server, infinite buffer capacity, infinite customer population, and First-Come, First-Served
FCFS service discipline. The MG1 and MD1 models differ from the MM1 model with respect to the service time. The MG1 assumes that the service time follows a General distribution where as the M
D1 model assumes a Deterministic constant service time. The detailed description and mathematical analysis of these basic queuing models can be found in [Cooper 1981, Jain 1991, Tanner 1995]. The
operational behavior of the system under consideration is approximated as one of the basic queuing models. Then, the simulation is run for the approximated queuing model. The result of the simulation is
compared against the data obtained from the analytical reference model. If the simulation data is consistent with the analytical data, it can be assumed that the simulation environment is reliable.
The ATM queuing model which is used for the simulation can be best approximated as the MD1
For the validation, the following performance characteristics were used: Mean Queue Length L
Q
, Mean Time-in-System T
Q
T
S
in service time units cell units. The Queue Length corresponds to an average number of cells in the queuing system and is given by the well-known Pollacek-Khinchine
formula for MD1 model [Cooper 1981, Tanner 1995]:
The Mean Time-in-System T
Q
T
S
for the MD1 model in service time units is given by
where T
Q
is the Mean Time-in-System, T
S
is the Mean Service Time, and ρ
is the server utilization. The server utilization
ρ represents the degree of server utilization and it can be calculated as described in
[Tanner 1995]:
where λ
is the mean arrival rate. For the MD1 queue model, the server utilization is the same as the offered load a.
The comparison of the simulation and the analytical MD1 model was done using the performance measures which we just described above. Figure 10-5 illustrates the comparison for the Mean Queue
Length while the comparison for the Mean Time-in-System is shown in Figure 10-6. These two comparisons clearly demonstrate that our simulation environment is able to approximate the analytical
data very closely and that the ATM traffic simulator is functioning properly.
