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The ring latency is the time requires for a token to circulate around the ring if all stations are operating in receive mode. The ring latency, τ' = Mw, which we can relate to the propagation delay and the host latencies as:
Delay Analysis
Finding Average Transfer Delay
The average transfer delay, T, is the sum of the average access delay, plus the average transmission time, plus the average latency, or T = W + E[X]/R + average latency.
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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.
X/R >= 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.
X/R < 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.
Average Transfer Delay
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:
The average transfer delay is expressed differently for different frame distributions. Let's consider fixed length frames and exponentially distributed frame lengths.
Fixed Length Frames
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:
and:
So:
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].
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:
Single Frame Operation
In single frame operation, the idle or next busy token is generated immediately after the end of the data frame returns to the source host.
The average transfer delay for single frame operation is:
Note that the following must hold true for the system to be in a stable state:
Fixed Length Frames
The expression for T above can be simplified for single frame operation with fixed length frames:
Exponentially Distributed Frame Lengths
The expression for T above can be simplified for single frame operation with exponentially distributed frame lengths:
Examples