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Unformatted text preview: CS4 Modelling and Simulation LN-15 15 The PC LAN as a SimJava Model 15.1 Introduction In this note we consider again the PC LAN first presented in lecture note 4 as a Markov process, and represented both as a GSPN and a PEPA model in subsequent lecture notes. Using simulation we are able to make the model somewhat more realistic in several respects: • inter-event times within the model are no longer restricted to be exponentially dis- tributed; • since the size of the state space does not concern us quite so much we can allow more realistic buffer sizes; • we can study the transient behaviour of the model (from “cold start” when the system is empty) just as easily as steady state measures; • moreover, in steady state we are not restricted to considering the means but can also find, for example, the maximum and minimum value of a random variable. Just as when we were deriving the Markovian model, we might not necessarily arrive at the correct characterisation of the system on our first attempt. However, it is often harder to establish confidence in a simulation model than a Markov process model, requiring the use of specific validation and verification techniques (see lecture note 14). 15.1.1 Description of the system Initially, as in lecture note 4, we aim to determine the mean waiting time for data packets at a PC connected to a local area network, operating as a token ring. We relax some of the assumptions that we made in the earlier model, but retain the restriction that a PC can transmit only when in possession of the token, and that the token circulates in round robin order. We now assume that whilst the inter-arrival time of packets is still exponentially distributed, packet transmission time is normally distributed and token circulation time is deterministic. In the model presented here we still assume that the PCs connected to the LAN all have the same characteristics. However, if you study the model you will see that it would be straightforward to parameterise the entity definitions in such a way as to differentiate between them. Without the state space restrictions imposed by numerical solution of the Markov process we no longer impose that at most one packet is waiting to be transmitted from each PC. As previously though, we assume that packets that arrive when the token is already at the node must wait for the next visit of the token. Various policies are used in practice. Our assumption represents what is termed gated service : this means that when the token arrives at the node a notional gate is closed. The token will remain at the node long enough to transmit all those packets in front of the gate (i.e. those packets that were waiting when the token arrived) but it will leave those behind the gate (i.e. those packets that arrived while the token was at the node) until the next visit....
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- Spring '10