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The average transfer delay can be expressed in the form:
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Single Token Operation
In multiple single token operation, an idle token or the next busy token is generated immediately after the data frame leaves the source host. The effective service time is X/R, show below:
Average Transfer Delay in General
In general, the average transfer delay for multiple token operation is:
Average Transfer Delay for Fixed Frame Lengths
Average Transfer Delay for Exponentially Distributed Frame Lengths
Single Token Operation
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 >= 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 < 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.
The 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 >= 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 < 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.
The normalized ring latency, a', is similar to the normalized propagation delay, a = τ/(E[X]/R), in random access LANs. The normalized ring latency can be expressed as:
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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
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:
We can express the average effective service time E[E] as:
And, the average transfer delay can be expressed as:
Note that the following must hold true for stability:
R, so:
We can express the average effective service time E[E] as:
And, the average transfer delay can be expressed as:
Note that the following must hold true for stability:
Multiple Token Operation
In multiple token operation, an idle token or the next busy token is generated immediately after the data frame leaves the source host. The effective service time is X/R, show below:
Average Transfer Delay in General
In general, the average transfer delay for multiple token operation is:
Average Transfer Delay for Fixed Frame Lengths
Average Transfer Delay for Exponentially Distributed Frame Lengths
Single Frame Operation
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