
 
Table 1: Time segments which influence the transmission 
delay value. 
Time Segments  Remark 
Latency of 
application 
interface 
T
ai
  The data transfer between application 
module and communication module 
may influence the transmission delay 
value remarkably. 
Latency of 
implemen-
tation 
T
i
  The implementation of the 
communication module influences the 
transmission delay value remarkably. 
User data 
length 
L
ud
  The user data length is related to the 
data which is generated or consumed 
by the automation application. 
Data rate  Bd
ud
 This rate is the radio transmission rate 
of the user data. Sometimes a symbol 
rate is given. In this case a symbol may 
consist of more than one bit. The 
header of a packet containing the user 
data may be transmitted with another 
data rate. 
Technology 
constant 
T
tc
  The technology constant contains all 
technology relevant protocol overheads 
which are the same for each 
transmission such as fixed idle times or 
the time to transmit headers or tails. 
Technology 
variable 
T
tv
  The technology variable contains all 
technology relevant protocol overheads 
which may vary for different 
transmissions such as the time to get a 
clear channel or the back-off time. 
Depending on the technology, 
acknowledgments are required to 
complete a transmission. 
umber of 
retries 
N
r
  If a transmission is disturbed, the 
packet is usually retransmitted. This 
may be possible at different layers. 
Transmission 
deadline 
DL  In some cases the transmission is 
terminated when a deadline is 
exceeded. 
Time 
allocation of 
additional 
connections 
Tac If there is more than one connection 
established, the time allocated to the 
other connections within the same 
system has to be taken into account. 
Global time 
slot 
T
GTS
 In systems with TDMA the maximum 
transmission delay can be calculated 
considering the global time slot. 
The random nature of the transmission delay is 
being caused by the latency of the application 
interface and implementation, by the technology 
variable, the number of retries and the time 
allocation for additional connections. In contrast to 
wired communication, the wireless transmission is 
affected much more by environmental influences. 
Therefore, the random behaviour of the technology 
variable together with the number of retries and the 
time allocation for additional connections may 
influence the transmission delay remarkably 
Taking into account the time segments listed in 
Table 1, the dependency of the transmission delay 
can be described in different ways. The first way is 
the given formula      (1) and is illustrated in Figure 
3. 
()
td ai i ai i ud ud tc tv r ac
T =f T (p),T (p),T (c),T (c),L ,Bd ,T ,T ,N ,T      (1)
Tai(p) Tai(c)Ttc1 Lud/BdudTi(p) Ti(c)Ttv2 …Tac
* Nr
Ttd
Ttv1 Ttc2
 
Figure 3: Time segments of transmission delay depending 
on re-transmissions, data rate and data length. 
The second way to describe the transmission is 
given in formula          (2) and Figure 4. The 
maximum transmission delay is fundamentally 
influenced by the maximum allowed deadline which 
covers the random behaviour of the media related 
time segments. 
tdmax ai i ai i
T  = f(T (p), T (p), T (c), T (c), DL)            (2)
Tai(p) Tai(c)Ti(p) Ti(c)DL
Ttdmax
 
Figure 4: Time segments of transmission delay depending 
on a transmission deadline. 
The third way to describe the transmission delay 
is given in formula          (3) and shown in Figure 5. 
The maximum transmission delay is fundamental 
depending on the number of retries and the global 
time slot. 
tdmax ai i ai i r GTS
T  = f(T (p), T (p), T (c), T (c), N , T )            (3)
Tai(p) Tai(c)Ti(p) Ti(c) N
r
* T
GTS
Ttdmax
 
Figure 5: Time segments of transmission delay depending 
on a global time slot. 
As an example typical results of transmission 
delay measurements are depicted in Figure 6. The 
lower part of the figure shows the number of 
packets, relative to the sample size, with certain 
transmission delay values. The above described 
random nature of the transmission delay can be 
observed. The reasons for the different values are 
HOW TO ASSESS RELIABILITY OF INDUSTRIAL WIRELESS SOLUTIONS
125