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In single token operation, there are a couple cases to consider – when the time to transmit a frame is greater than or equal to the ring latency and when the time to transmit a frame is less than the ring latency.
Frame Transmission Time, X/R >=
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Ring Latency, τ'
In this case, the busy token arrives at the transmitter before the transmission has completed. When this occurs, the idle token or next busy token is generated immediately after the data frame leaves the source host. The same behavior occurs in multiple token operation.
Frame Transmission Time, X/R
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< Ring Latency, τ'
In this case, the link is unavailable while the transmitter waits for the busy token to return. A gap in time occurs between the end of the data frame and the start of the subsequent idle token or busy token. During this time, the transmitter waits.
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The average transfer delay is expressed differently for different frame distributions. Let's consider fixed length frames and exponentially distributed frame lengths.
Average Transfer Delay for Fixed Length Frames
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If a' <= 1, T is given by the expression for multiple token operation with fixed length frames. If a' > 1, E = τ' for each frame, which implies for fixed length frames:
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Note that for a' > 1, stability is achieved only if Sa' > 1, i.e. if S < 1/a'. Also note that for a' > 1, W does not depend on E[X]; however, T does depend on E[X].
Average Transfer Delay for Exponentially Distributed Frame Lengths
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For some frames, X/R <= τ' and E = τ'. For other frames, X/R > τ' and E = τ'(X/R). X/R is an exponentially distributed RV with mean E[X]/R, so:
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Note that the following must hold true for the system to be in a stable state:
Average Transfer Delay for Fixed Length Frames
The expression for T above can be simplified for single frame operation with fixed length frames:
Average Transfer Delay for Exponentially Distributed Frame Lengths
The expression for T above can be simplified for single frame operation with exponentially distributed frame lengths:
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