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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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The average transfer delay can be expressed in the form:
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 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.
Average Transfer Delay for 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].
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:
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:
For fixed frame lengths:
For exponentially distributed frame lengths:
Single Token Operation
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Average Transfer Delay for Fixed Frame Lengths
Average Transfer Delay for Exponentially Distributed Frame Lengths
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.
Average Transfer Delay in General
In general, 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:
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:
Examples
Example 1
Assume:
- ring length of 1 km
- link rate of 4 Mbps
- average frame length of 1000 bits
- 40 hosts in ring
- Poisson arrivals at rate 10 frames/second per station
- host latency of 1 bit
- propagation velocity of 5 us/km
- single token operation
So:
- R = 4 Mbps
- E[X] = 1000 bits
- M = 40
- λ = 10 frames/second
- B = 1 bit
Thus we can find the ring latency:
the normalized ring latency:
and the normalized throughput:
We don't know the frame distribution, but we do know how to solve for fixed length and exponentially distributed. If frames are fixed length, then since a' < 1:
If frame lengths are exponentially distributed, then:
Example 2
Assume the same as Example 1, except the station latency, B = 10 bits. Then the ring latency, normalized ring latency, and normalized throughput can be computed as:
If frames are fixed length, then since a' < 1:
If frame lengths are exponentially distributed, then:
Performance of Token Rings
Special Case: Light Traffic Load
Under light traffic load, meaning S is approximately 0, the average time waiting for service of previous arrivals into the network is negligible. Thus the average transfer delay can be approximated by:
Special Case: Small Normalized Ring Latency
With a small normalized ring latency, meaning a' is approximately 0, the average transfer delay for fixed length frame is approximately:
and for exponentially distributed frame lengths, the average transfer delay is approximately:
These results are independent of the token management technique.
Comparing Token Management Techniques with Exponentially Distributed Frame Lengths
For exponentially distributed frame lengths and a fixed normalized ring latency of a', we can compare the performance of single token, multiple token, and single frame token ring operations.
The graph above indicates that multiple token operation yields the best performance, followed by single token, and single frame operation with the worst performance. The best performance was achieved by minimizing the normalized ring latency, a', where performance is approximately the same for all three operating modes. It can also be observed that for a fixed normalized throughput, S, the number of hosts, M, impacts performance primarily through its effect on a'. Instability occurs for some values of S less than 1 if operating in single token or single frame mode.
Comparing Token Management Techniques with Fixed Frame Lengths
For fixed frame lengths and a fixed normalized ring latency a', it can be observed that the best performance is achieved with multiple token operation. On the other hand, the poorest performance is achieved with single frame operation. The performance for single token and multiple token are the same for a' <= 1, and the performance of single frame and single token are approximately the same for very large a' (which was previously shown for exponentially distributed frame lengths). There is however a lower delay for fixed length frames than exponentially distributed frame lengths.
Single Token Operation with Different Network Loads and Exponentially Distributed Frame Lengths
When single token operation is used with exponentially distributed frame lengths, it can be observed that the transfer delay is approximately independent of a' for small values of a'. Higher throughput, S, places more sever constraints on ring latency, and high ring latency severely restricts the allowable throughput.
