Performance Parameters Measurement and Stochastic Processes

In this chapter, the emphasis is on the analysis of performance parameters, assigned to different system components, functions or processes, together with the methodology of their statistical assessment based on limited measured samples, fulfilling the condition of normal distribution. The practical examples of GNSS (Global Navigation Satellite Systems) applications assessment and certification are presented.


Introduction
In this chapter, the emphasis is on the analysis of performance parameters, assigned to different system components, functions or processes, together with the methodology of their statistical assessment based on limited measured samples, fulfilling the condition of normal distribution.The practical examples of GNSS (Global Navigation Satellite Systems) applications assessment and certification are presented.

Definition of performance parameters
The methodology for the definition and measurement of following individual system parameters is being developed within the frame of complex system's assessment.The basic performance parameters can be defined as follows:


Accuracy is the degree of conformance between system true parameters and its measured values that can be defined as the probability Pp p    (1) that the difference between the required system parameter i p and the measured parameter m,i p will not exceed the value 1  on probability level 1  where this definition is applicable for all N system parameters 12 N p, p , . ., p . Reliability is the ability to perform a required function (process) under given conditions for a given time interval that can be defined as the probability that the difference between required system functions (processes) represented by parameters t v  and the vector of measured parameters m,t v  will not exceed the value 2  on probability level 2  in each time interval t from the interval 0,T . Availability is the ability to perform required functions (processes) at the initialization (triggering) of the intended operation that can be defined as the probability that the difference between the required rate 1 of successful performing of the function i (process i) i q and the measured m,i q will not exceed the value 3  at the probability level 3  . Continuity is the ability to perform required functions (processes) without nonscheduled interruption during the intended operation that can be defined as the probability Pr r    (4) that the difference between the required rate of successful performing of the function i (process i) without interruption i r and the measured m,i r will not exceed the value 4  at the probability level 4  . Integrity is the ability to provide timely and valid alerts to the user, when a system must not be used for the intended operation, that can be defined as the probability PS S    (5) that the difference between the required rate of successful performing of the alert limit (AL) i not later than predefined time to alert (TTA) i S and the measured m,i S will not exceed the value 5  on the probability level 5  . Safety can also be covered among the performance parameters, but the risk analysis and the risk classification must be done beforehand with a knowledge of the system environment and potential risk, and then the safety can be defined as the probability   im , i 66 PW W    (6) that the difference between the required rate of i risk situations i W and the measured ones m,i W will not exceed the value 6  on the probability level 6  .
A substantial part of the system parameters analysis is represented by a decomposition of system parameters into individual sub-systems of the telematic chain.One part of the analysis is the establishment of requirements on individual functions and information linkage so that the whole telematic chain can comply with the above defined system parameters.
The completed decomposition of system parameters will enable the development of a methodology for a follow-up analysis of telematic chains according to various criteria (optimisation of the information transfer between a mobile unit and a processing centre, maximum use of the existing information and telecommunication infrastructure, etc.).
The following communication performance parameters quantify the quality of telecommunication service [16]: Q is the number of successful experiments (successful performing of the function i, successful performing of the process i) and Q is the number of all experiments (both successful and unsuccessful).Performance indicators described for communications applications must be transformed into telematic performance indicators structure, and vice versa.Such transformation allows for a system synthesis.
Transformation matrix construction is dependent on detailed communication solution and its integration into telematic system.Probability of each phenomena appearance in the context of other processes is not deeply evaluated in the introductory period.Each telematic element is consequently evaluated in several steps, based on a detailed analysis of the particular telematic and communications configuration and its appearance probability in the context of the whole system performance.This approach represents a subsequent iterative process, managed with the goal of reaching the stage where all minor indicators (relations) are eliminated, and the major indicators are identified under the condition that relevant telematic performance indicators are kept within a given tolerance range.

Quality of measured performance parameters
In this chapter, unified approach applicable for all above mentioned performance parameters [18] will be introduced.

Absolute measuring error (
 Accuracy (δ) of a measuring system is the range around the real value in which the actual measured value must lie.The measurement system is said to have accuracy δ if: or straightforwardly: Accuracy is often expressed as a relative value in ±  %.


Reliability (1-) of a measuring system is the minimal probability of a chance that a measuring error a  lies within the accuracy interval   where P(.) means the probability value.


Error probability ( ) of a measuring system is the probability that a measured value lies further from the actual value than the accuracy: The reliability of measuring system is often controlled by the end-user of the measurement system while error probability is generally assessed by the International Organization for Legal Metrology (OIML). Dependability ( ) of an acceptance test is the probability that -on the basis of the sample -a correct judgment is given on the accuracy and reliability of the tested system: The desired dependability determines the size of the sample; the higher the sample, the higher the dependability of the judgment.

Estimation of performance parameters 4.1 Tests of normality
With regard to [12] normal distribution will be expected, because using different kinds of statistics, such as order statistics (distribution independent) for small sample sizes, typical for performance parameters, the result may be fairly imprecise.Testing normality is important in the performance parameters procedure, because in analyses containing a lot of data this data is required to be at least approximately normally distributed.Furthermore, the confidence limits assessment requires the assumption of normality.Several kinds of normality tests are available, such as [1]: X , X ,..., X with a common distribution function F(x).Under the null hypothesis, F(x) is the normal distribution.Denote the observations ordered from the smallest to the largest as (1) (2) (n) X , X ,.., X .The empirical distribution function, n F( x ), is defined as Note that n F( x ) is a step function that takes a step of height 1/n at each observation.This function estimates the distribution function F(x).At any value x, n F( x )is the proportion of observations less than or equal to x, while F(x) is the probability of an observation less than or equal to x. EDF statistics measure the discrepancy between n F( x )and F(x).
In the following part the Pearson test (Chi-Square Goodness-of-Fit Test) will be introduced as a practical example of EDF tests.The chi-square goodness-of-fit statistic 2 q  for a fitted parametric distribution is computed as follows: where L is the number of histogram intervals, i m is the observed percentage in i-th histogram interval, n is the number of observations, i p is the probability of i-th histogram interval computed by means of theoretical distribution.The degree of freedom for the chisquare test 2   is equal to L-r-1, where r is parameters number of theoretical distribution (in case of normal distribution r=2).

Estimation of measuring system's accuracy, reliability and dependability
Let us assume we have a normally distributed set of n measurements of performance parameters a,1 a,2 a,n , ,...,   (absolute error between prescribed and measured parameters as defined in (7)).
If the mean value or a standard deviation is not known we can estimate both the mean value a  and standard deviation a s from the measured data as follows: Let n be non-negative integer, ,   are given real numbers   0,1   and let a,1 a,2 a,n a,y , ,..., ,   be n+1 independent identically distributed random variables.
Tolerance limits are defined as values so that the probability is equal to  that the limits include at least a proportion   1  of the population.It means that such limits L and U satisfy: A confidence interval covers population parameters with a stated confidence.The tolerance interval covers a fixed proportion of the population with a stated confidence.Confidence limits are limits within which we expect a given population parameter, such as the mean, to lie.Statistical tolerance limits are limits which we expect a stated proportion of the population to lie within.
For the purpose of this chapter we will present only results derived under the following assumptions:  ).


The symmetry about the mean or its estimation is required.


The tolerance limits are restricted to the simple form aa ks   and aa ks   , where k is a so called tolerance factor, a  and a s are sample mean and sample standard deviations, respectively, given by ( 16).
Under the above given assumptions, the condition ( 17) can be rewritten as follows: where  is the distribution function of the normal distribution with mean zero and standard deviation equal to one: The solution of the problem to construct tolerance limits depend on the level of knowledge of the normal distribution, i.e., on the level of knowledge of mean deviation a  and standard deviation a s .
In the following part the accuracy, reliability and dependability of the measuring system will be mathematically derived for a known mean value and standard deviation, for a known mean value and unknown standard deviation, and for both an unknown mean value and standard deviation.

Known mean value and standard deviation
We can start with the equation [3]: where a,y  is the measured value, 00 ,   are known mean value and standard deviation and we can find in statistical table 0.975 z1 .9 6  ) .
Based on (20) we can decide that measuring system's accuracy Because the mean value and standard deviation are known, the measuring system's dependability is equal to 1   .

www.intechopen.com
Performance Parameters Measurement and Stochastic Processes 9

Known standard deviation and unknown mean value
Now we expect that the mean value is estimated according to (16).Then we can write the equation [3]: where 2 0  is the known variance and k is computed from the following equation: (1 ) (1 ) 22 zz kk 1 nn where the function   u  was defined in (19) and sample a  computed according to (16).
Based on the equation ( 22) we can say that for the predefined values of measuring system's reliability   1  and dependability  and the number of measurements n the accuracy of measuring system will be

Known mean value and unknown standard deviation
For a known mean value and unknown standard deviation we can write the equation:   Based on the equation (24) we can say that for predefined values of measuring system's reliability   1  and dependability  and the number of measurements n the accuracy of measuring system will be:

Unknown mean value and standard deviation
This variant is the most important in many practical cases, but the solution is theoretically very difficult.However, a lot of approximation forms exist based on which the practical simulation could be feasible.where the sample mean value a  and sample standard deviation a s are estimated from n samples according to (16).
Howe [4] defines a very simple approximation form for k: Bowker [5] defines: Ghosh [6] defines the next approximation form: If we take the approximation forms for x z for x>0.
or a much simpler approximation form from [3]: 2 The approximation error is not greater than 0.003 3 For x 0.01,0.99 and 20   the absolute error of approximation is not greater than 0.001 www.intechopen.comthen the analytical equation for the estimation of measuring system's accuracy  based on an estimated mean value and standard deviation of n-sample data with the predefined measuring system's reliability   1   and measuring system's dependability  can be computed.

Illustrative example 1 -Simulation result
A very important question can be addressed with regard to accuracy: How the measuring system's accuracy  depends on the number of measurements for the prescribed measuring system's reliability and measuring system's dependability?We consider the following prescribed values for ,   : In MATLAB, a set of 1000 samples of normal distribution with zero mean and standard deviations equal to one was generated.From the first 30 samples the mean value and standard deviation were estimated (16).Then the interval   aa aa ks, ks    was selected in accordance to (26) and the probability of falling into interval was computed from the whole set of 1000 samples -which is a procedure of how to compute measuring system's reliability.
The above mentioned procedure was repeated 5 000 times, and the probability of exceeding the predefined measuring system's reliability limit was computed -thus the test of measuring system's dependability was performed.
The obtained results for measuring system's dependability through simulation will be summarized as follows: a. 0.553  b.


The test was repeated many times and the predefined parameters for measuring system's reliability and dependability were achieved in all experiments.

Assessment of safety performance parameters
We can suppose N sensors data available where the probability of right error detection is marked as RD P and the probability of non-correct error detection as FD P .Because of the enormous safety and economical impact in case of non-correct error alert, the method of filtering "M from N" will be presented.
Let us have N sensors and for simplicity let us suppose the same probabilities of correct RD P and non-correct error detection FD P on each sensor.If this assumption is not fulfilled the method can be easily extended to a more general case.
As mentioned above, the hypothesis 0 H represents perfect system behavior (non system error, no sensor error) and hypothesis 1 H as a state with detected error (error of system, or error of sensors).
In the next equation, the probability of error detection on k sensors of N sensors (N-k sensors do not detect errors) is given in case the system does not display any error (conditioned by hypothesis 0 H ): In the same way, the probability of error detection by k of N sensors is given in case the system is in an error state (conditioned by hypothesis 1 H ): The main idea of "M from N" filtering is in selection of value M (threshold) defining the minimum number of sensors that detected error.If M sensors detect error then this error is taken as the real system error and the system starts sending error alert signals.The threshold M should be selected with respect to the following probabilities: where FD P, P means probability of a false alert (an error is detected but the system works without any errors) and the probability of the right detection (the system error is correctly detected).
The number of detectors N and the threshold M can be chosen based on sensors parameters RD P , FD P and required probabilities FD P, P .
Methods of data fusion and comparison are the main tools for estimation of system performance parameters (accuracy, reliability, integrity, continuity, etc.) and can be used for a derivation of an exact definition of false alert and right detection probabilities.

Illustrative example -Geo-object detection
In this example the measurement data comparison will be used as a tool for better geo-object detection in, e.g., electronic tolling application.
We can suppose N available position measurements of a geo-object where the probability of the right geo-object detection is marked as RD P and the probability of non-correct (false) geo-object detection as FD P .Let the hypothesis 0 H represent the assumption of a perfect geo-object detection (no detection error reported).The hypothesis 1 H represents a non-correct geo-object detection (error caused, for example, by wrong position accuracy, etc.).
The probability of k non-correct geo-object detections of N measurements for the final assumption that the geo-object is perfectly detected (conditioned on the hypothesis 0 H ) can be given: The probability of k correct geo-object detections of N measurements for the final assumption of non-correct geo-object detection (conditioned on hypothesis 1 H ) is given: The main idea of "M matches from N measurements" principle is in the selection of the threshold M with respect to the following probabilities: where FD P, P means the probability of a false alert of geo-object detection (the geo-object is detected even though the vehicle did not go through it) and the probability of a right geoobject detection (the right geo-object is detected based on the measured data, and the vehicle went through it).
The number of measurements N and the threshold M can be chosen based on the position probabilities FD P , RD P and the required probabilities FD P, P .Further discussion will be presented within an illustrative example below.
There are two parallel roads (one under tolling, the other one free of charge) and the distance D between them of 20 meters, as it is shown in Fig 3 .The length L is supposed to be 1 kilometer.
In this example, we will try to tune the parameter to increase the probability of the correct toll road detection in order to reach the expected value of more than 99%.
We expect a maximum vehicle speed of 200 km/h or 55 m/s.If the length is 1000 m and the GPS receiver monitors the position every second, we can obtain as many as 18 position measurements per one road.The road can be distinguished by GPS received with probability app.70% (we can assign the measurement to the right road, if the error is lower than D/2 which is in our case 10 meter -this accuracy is typically achieved by a GPS receiver at a probability level of 70%).Using the equations (38), the probabilities FD P, P for different parameters M will be as given in Tab.1.If the parameter M is 6 or 8, we can achieve the requested probability of the geo-object detection higher than 99%.On the other hand, for M=6 the probability of lost vehicles is higher (the vehicles used the toll road, but the system did not detect them).For M=8 we can achieve a better balance between both probabilities FD P, P .If the user needs to minimize the loss of a vehicle and to keep the acceptable detection probability, the variant M=10 could be a good compromise.

Performance cluster of telematic applications using GNSS
Transport telematics architecture [22] displays the arrangement of subsystems and functional blocks, including information relationships according to the defined point of view.The task also covers the selection of representative telematics applications ("cluster") that shows identical systems requirements.
Among the individual representative applications using GNSS (Global Navigation Satellite Systems) the following may be included:


Securing the movement of a means of transport in a transport infrastructure (from the point of view of performance parameters within the GNSS, it is a question of securing accuracy, reliability, availability, integrity, etc., at exactly defined points of the transport infrastructure -the application lays high stress both on the locator proper and the information transmission and processing systems; the solution should comply with the "fail-safe" principle; for typical transport telematics applications we may refer to railway interlocking technology, monitoring the transport of dangerous goods, or monitoring the movement of means of transport at the airport.


Navigation of the means of transport in a transport network (from the point of view of performance parameters, it is a matter of coverage with a signal, time lag in on-line navigation, requirements as for the exactly working maps of an entire geographical area, requirements on the speed of information processing, both within a mobile unit and the processing centre, as well as minimisation of the delay when establishing the position -TTFF -Time to Fix Face); as typical transport telematics applications, the following may be referred to: the navigation of safety and rescue units for a localised accident place or dynamic and/or on-line automobile navigation.


Monitoring and operating the maintenance of transport networks (from the point of view of performance requirements, it is particularly a matter of an exact transport infrastructure information retrieval, interoperability of individual GIS (Geographical Information Systems) systems of various organisations dealing with maintenance, and achievement of high statistical accuracy in establishing position); as it concerns typical transport telematic applications, the following ones should be mentioned: mapping the river channel by means of a measuring ship, or measuring the carriageway parameters by means of special measuring vehicles.


Monitoring the movement of persons and goods in a transport infrastructure (from the point of view of performance requirements, it is a matter of transmission and central processing of large amount of information from resources of various accuracy, fast identification of individual sub-sets of the objects of transport, sophisticated information processing in the centre, for instance, the "Floating Car Data"); as typical transport telematic applications, the following can be referred to: the use of taxi cabs, public transport passenger vehicles or other utility vehicles equipped with the GNSS systems for traffic flow modelling, or the use of localised mobile telephones for modelling the mobility of persons.


Transport infrastructure charging according to its utilisation (from the point of view of performance parameters, it is a matter of reliability, integrity and time lag because the GNSS system is used to calculate the amount of the charge and, furthermore, the application places demands on the "fail-safe" principle in terms of the distance covered -if there is an uncertainty about correct charging of the driver, the distance covered is not taken account of); as a typical transport telematic application, it is electronic charging of the transport infrastructure according to the vehicle parameters and distance covered.
As a follow-up to the completed analysis and decomposition of performance parameters to individual subsystems, a table can be obtained containing performance requirements of the above mentioned representatives as for the locator proper, telecommunications environment or the information processing centre.

Illustrative example -Assessment of telecommunications solution of GNSS monitoring system on airport surface
Described system methodology can be demonstrated on the telematic application based on GNSS (Global Navigation Satellite System) developed for the airport area moving objects management with good potential to be integrated into the already operated airport monitoring and management system.
The service central server collects and processes data received from all service vehicles.The obtained information is combined with the data gained from the existing systems.Processed and obtained result is distributed not the only to the airport management, but as well as to each vehicle equipped with active On-Board Unit (OBU) equipped with display of relevant size and quality.Each OBU receives also the managerial data generated by either airport control system or by dispatchers.Principal schema of the subsystem organization is displayed on Figure 4.Even though WiMax was selected as the core mobile access system for the airport critical areas, the whole airport area coverage with this technology is not economical.Some of alternative access solutions (EDGE/GPRS/UMTS or even WiFi) for Mobile WiMax difficult/irrelevant areas can be applied, if system parameters of these technologies meet these areas system parameters requirements.For such case multi-path solution like CALM, IEEE 802.21 based or by authors announced adaptive multi-path alternative (see e.g. in [20] - [21].) are identified as the appropriate alternatives.
The L2 ring based solution of terrestrial chain part with the local QoS management (Hirschman) was applied to fulfill time limits of the whole chain.
The applied method nosily disqualified such communications "gurus" like the MPLS backbone terrestrial networking or GPRS/EDGE wireless access and combination of the wireless solution based on IEEE Std.802.16d with terrestrial L2 switching solution with QoS management tools implemented were applied as core technology, they were tested and reasonable results were obtained.Critical issue, however, represent implementation of the effective decision processes to manage the multi-path solution to be kept in the required time limits -see [13] -[20].

Certification and testing of telematic applications
General methodology for telematic certification and testing of performance parameters [21] is figured on Fig. 5.The simulated signal was influenced at first for whole measurement series, this approach was later changed to influencing the signal for various tests in the series, always another way, such as switching on and off the satellites at a defined angle above the vehicle, respectively above the ground (road plane).Signal influence has been prepared based on detailed description of possible signal influence.For the tests the spherical characteristics of the receiving antenna were chosen, with an open top of the antenna (i.e. position of the antenna on the roof of the vehicle).
Running of the tests has been recorded in the "log file" stored directly in the hardware unit.
Based on this data further processing took place already on PC.The hardware unit recorded the following data of a virtual gate passage:  virtual gate passage time;  ID and a description of the gate (defined positions and azimuth).
Each measurement result was then classified as "passed" or "failed" according to the following categorization:  passed, if all the following conditions are true:  gate is identified on the running road;  gate is not identified in other nearby road;  any upstream gate is not identified;  more passages through the same gate during one test are not evaluated;  failed in other cases.
Results of carried out testing are listed in Tab.4 [22].Based on the measurements, it was demonstrated, that the results of the passage identification varies for different parameters of the GNSS signal, environment and other influences on the signal reception.The relatively low percentage of successful running gate identification may be due to high sensitivity software in the OBU.It can be assumed that for usage of OBU for telematic applications the higher success rate for negative detection of upstream or neighbouring gates will be demanded.Proposed test protocol is divided into a part of recording the individual measurements and a part of evaluation of the application as a whole, including evaluation of system parameters.It is already possible on the basis of pilot testing to summarize the partial results and define partial requirements for selected system parameters of tested applications:

Type
a. Accuracy -the required value of 15 meters in the horizontal plane at 95 % level of probability.Thus defined accuracy corresponds to usual accuracy requirements on OBU GPS unit using a standard statistical distribution of signal parameters.The tested OBU and its software configuration were selected based on the required accuracy.Accuracy of the OBU can be further increased.b.Reliability -the specific desired value will be defined on basis of experience in the follow-up testing.Assuming a value of around 90 %, eventually higher, at 95 % probability level.After pilot tests result with 60.4 % success of virtual gate passage detection can be seen that the higher reliability will be required for the approval.To approve the usage of tested OBU it will be necessary to adjust the software in OBU or to use another OBU.Reliability is affected by the security parameter, see below.c.Availability -the specific desired value will again be defined on the basis of experience in further testing.Assuming the OBU unit activation at start-up of travel and the availability value up to 60 seconds.Pilot testing showed in most cases the availability of tens of seconds.d.Continuity -for telematics application this is not a critical system parameter.Depends on ability of the telematic system to assess and calculate the travelled route in case of system failure while driving the vehicle; this parameter does not depend only on the OBU and GNSS signal reception.In case of the usage of virtual sections or more virtual gates on the road sections the requirements on this parameter are significantly decreasing.e. Integrity -this parameter has not been considered for the tested systems, mainly because it represents rather the quality of OBU diagnostics, resp.informing the user within a reasonable time for failure of proper OBU function.This parameter is not so much related to position determining or frequency of the virtual gates and sections passage records.f.Safety -"dangerous conditions" are defined for both tested applications in the field of electronic toll system (EFC).This is a situation where the system assesses charges, which in fact did not occur.This is part of the conditions to test status "failed" -socalled "false alarms" -i.e. the identification of neighbouring gates or division, identification or evaluation of multiple transits the same gate or the same road section.With regard to safety (as one of the important system parameters of tested applications) appropriate testing scenarios were selected by pilot tests -all the scenes are containing unpleasant situation in a similar gate on nearby parallel road (i.e. identically oriented and situated at a distance of tens of meters from the passing road).It should be emphasized that effort to eliminate false alarms is associated with a reduction on the reliability parameter of applications, i. e. reducing the probability of passed gates/sections correct detection.It is therefore necessary to seek to balance, which on the one hand significantly reduces the risk of false positives, on the other hand, provides useful reliability parameter.This balanced condition can be found by testing various OBU units, resp.by testing one OBU at various software settings.

5 
www.intechopen.comPerformance Parameters Measurement and Stochastic Processes Availability -(i) Service Activation Time, (ii) Mean Time to Restore (MTTR), (iii) Mean Time between Failure (MTBF) and (iv) Virtual Connection Availability  Delay -is an accumulative parameter effected by (i) Interfaces Rates, (ii) Frame Size, and (iii) Load / Congestion of all active nodes (switches) in the line  Packet/Frames Loss  Security a  ) is the difference between a measured value and the real value or the accepted reference real value or accepted reference  Relative measuring error ( r  ) is the absolute measuring error divided by a true value

4 . 4 For
) the measuring system's accuracy  is given a ks   .For finding the parameter k the equations (30), (31) and (32) were used.The Fig.1and Fig.2show the dependence of the parameter k on the number of measurements n for cases a) and b) respectively.Illustrative example 2 -Simulation result Can the results from example 1 be proved by a simulation, if the number of measured values is n=30? the values of k were found in Fig.1and Fig.2 respectively:a.k=1.0584, b. k=2.797.

Fig. 3 .
Fig. 3. Two parallel roads and Toll detection being on one the roads Based on the above mentioned assumptions, we can summarize the following parameters:

Fig. 4 .
Fig. 4. Telematic service structure (WL -wireless, A-SMGCS -Advanced Surface Movement Guidance & Control System)An airport area is precisely and transparently regulated area.The telematic sub-system performance indicators are introduced in Table2.

Fig. 5 .
Fig. 5. General certification system for performance evaluation of telematic applications Telematic application certification process consists of these steps:

Fig. 8 .
Fig. 8. Simulation output of the position on road II/605

Table 1 .
Probabilities FD P, P and their dependence on parameter M

Table 2 .
[14]ired Telematics Performance Indicators in airport applicationUsing a transformation method described in[14]-[16] the telematic performance indicator "accuracy" was identified as the performance indicator with the dominant impact on the whole system performance.Its dominance is caused by the specific character of studied application.The requested level of accuracy (see Table2) must be reached for every object moving with speed up to 120km/hour, If 1m GNSS sensor accuracy can be reached (the differential GNSS alternative must be applied) 195ms remain for the delay caused by all devices including the potential error healing in case of any sub-system problem (all on probability level 99% -see table2).Mobile WiMax (IEEE Std.802.16d) was identified as the only possible alternative of the wireless access solution for the critical areas of the airport.All the other available access systems like GSM based products DTMF, HSCSD GPRS and EDGE as well as UMTS were identified as inappropriate.WiFi system operated in the open frequency band does not provide any service quality guarantee.Table3displays the obtained dynamical parameters of the WiMax channel (ART -Average Round Trip delay) in two critical stages of the Signal to Noise Ratio (SNR)

Table 3 .
Principle parameters of the WiMax access

Table 4 .
Results of pilot testing, depending on the segment, direction and type of test Within implementation of a sufficiently large count of measurements the resulting values in Tab.4 show the probability of conformity of the tested OBU properties with the desired properties of the measured applications.