User's Manual

TS4000 Radio Modem User’s Manual AirNet Packet Protocol 39
Tslot = Slot Time
PDR = Packet Detection Ratio
TI = Transmission Index
N = Backlogged Nodes
PR = (TI - 1)/TI
Average Delay = Tslot x (1 + PDR - PR
N
)
PDR x ln(1/PR)
Where: ln symbolizes the natural log function.
Using the values from the previous example, calculate the average delay for
various backlogs.
Tslot = Slot Time = 30 ms = 0.03 sec
PDR = Packet Detection Ratio = 0.33 (from previous example)
TI = Transmission Index = 44 (from previous example)
PR = (TI - 1)/TI = (44 - 1)/ 44 = 0.977
Average Delay = Tslot x (1 + PDR - PR
N
) = 0.03(1 + 0.33 - 0.977
N
)
PDR x ln(1/PR) 0.33 ln(1/0.977)
= 0.03(1.33 - 0.977
N
) = 3.91(1.33 - 0.977
N
)
0.00768
Backlogged Nodes (N) 10 25 50 75 100
Average Delay (sec) 2.1 3.0 4.0 4.5 4.8
The probable delay calculation allows the user to calculate the expected delay
given some probability that the transmission actually occurs. The probable delay
value can be used for calculating a packet timeout value for a system where the
ACK packets do not use an immediate ACK and have a transmission index the
same as the data packets. It can also be used to calculate timeouts for layers of
the protocol stack above the modem on the host system. Note that the probable
delay value does not include any transmission times due to relays and
acknowledgement packets.
The basis of the probable delay is the average delay calculated above. As noted
before, the average delay will vary based on the actual number of backlogged
nodes in a system.
Probable Delay = Average Delay x ln(1/(1 - Probability of Sending))
Where:
The Probability of Sending is a fractionalized percentage (i.e. 50% =
0.50, 95% = 0.95).
Calculate the probable delay for various probabilities of sending in terms of the
average delay.
Probability of Sending (%) 25 50 75 90 95 99 99.9
Probable Delay (Avg. Delays) 0.29 0.69 1.38 2.30 3.00 4.61 6.91
Note that the 50% probability of sending value is not equal to the average delay.
This is because the delay spread is a statistical distribution where the mean and
median delays are not the same.
Example:
Probable Delay
Example: