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-□ □Дослгджено вплив основних технологiчних napaMempie на ймовipнiсmь вгдмови та час безвгдмовно1 роботи вчас-ного приймання та вгдправлення транзитних вантажних погздгв. Встановлеш зaкономipносmi формування вгдмов при 3Mmi добового навантаження, meхнологiчного осна-щення транзитних паркгв та величини нepiвномipносmi вхгдного та вихгдного потокгв. Дослгдження проводились iмimaцiйним моделюванням (Java SE 7.0 (Oracle), середо-вище розробки Eclips, AnyLogic) на приклад типових норм техшчних станцш
Ключовi слова: meхнологiчнa надштсть, iмовipнiсmь
вгдмови, безвгдмовнгсть, iмimaцiйнe моделювання
Исследовано влияние основных технологических параметров на вероятность отказа и время безотказной работы своевременного приёма и отправления транзитных грузовых поездов. Установлены закономерности формирования отказов при изменении суточной нагрузки, технологического оснащения транзитных парков и размера неравномерности входного и исходящего потоков. Исследования проводились имитационным моделированием (Java SE 7.0 (Oracle), среда разработки Eclips, AnyLogic) на примере типовых норм технических станций
-□ □UDC 656.22 : 656.23
|DOI: 10.15587/1729-4061.2017.91074]
A STUDY OF THE TECHNOLOGICAL RELIABILITY OF RAILWAY STATIONS BY AN EXAMPLE OF TRANSIT TRAINS PROCESSING
V. M a t s i u k
PhD, Associate Professor Department of process control traffic State Economy and Technology University of Transport M. Lukashevicha str., 19, Kyiv, Ukraine, 03049 E-mail: vmatsiuk@ukr.net
Meeting the deadlines of cargo delivery (subject to safety) with a rational use of available production resources can be regarded as the main operational challenge of railways. Therefore, technical regulation, production planning and the overall arrangement of a rail transit system (hereinafter, RTS) should ensure an appropriate level of reliability.
In addition to purely technical and managerial (in terms of efficiency of decision-making by the personnel) components, the technological process itself, as a set of sequential queuing systems, must be reliable enough.
Therefore, a study of technological reliability - such as a study of the influence patterns of an existing set of parameters on the probability of failure and the average duration of trouble-free operational processes of train stations and other rail transport systems - are important scientific and applied problems.
Ensuring the reliability of technical systems remains quite an essential problem for the transport industry [1-8]. For rail transport, reliability is usually considered as part of evaluating operational parameters. Rationing itself is achieved in practice mostly by analytical methods, and it ensures efficient operation of RTSs within confidence intervals of appropriate calculated optima [7, 9, 10]. However, this approach can not guarantee the proper level of trouble-free operation of transport systems as it does not take into account
the possibility of exceeding the standards due to fluctuations in the transportation volume [11].
An objective difficulty in researching reliability of transport systems is their complexity and scale. A significant set of output parameters, their stochastic nature and the dynamics of the process as a whole challenge the feasibility of analytical models [3, 4, 5, 9, 10]. In most cases, the probability of failure and the uptime of technical systems may be determined only experimentally, by conducting complex and expensive tests of samples themselves (for technical facilities) [1] or models [2, 12].
Many researchers are trying to investigate multiphase processes by studying individual components of the processes [4], which prevents from determining the overall reliability, as the number of the system states can exceed tens of thousands and make calculations more difficult (or even impossible). Therefore, on balance, one of the few tools for researching the complex multiphase technological processes of railway transport may be simulation methods [12].
The influence of the human factor as a component of reliability on the stability and efficiency of rail transport is adequately covered in [13]. However, generally, the human factor mostly affects the operational organization of the technological process rather than its rationing and development of effective models.
Given the above, it can be argued that research of the technological reliability of operational processes at railway stations has been conducted insufficiently. Moreover, the rate of a probability of failure in receiving trains is typically determined in practice only when assessing the accuracy of complying with the timetable [7]. The lack of assessment methods for determining the reliability of the technological processes
at railway stations makes it impossible to find the objective level of failure of a timely receipt and timely dispatch of trains, which significantly complicates the development of standards of an effective interaction of the transport system elements.
The research is undertaken with the aim to evaluate the reliability of the RTS operational processes by an example of typical technological standards for the railways of Ukraine.
To achieve this purpose, it is necessary to solve the following tasks:
- to justify the criteria for assessing the technological reliability of the operational processes taking place at railway stations;
- to determine the factors that influence the acceptance and rejection in timely processing of trains in transit lines;
- to study the impact of the factors on technological failure.
Given the complexity and difficulty of the task, one of the few methods of this type of research is experimental measuring of simulation results.
The functional existence of a technological line of trains& processing can be presented as a discrete event process. Each application served by the system discretely is serviced by a particular technological element. Going through the processing steps is a conditional boundary that does not have its own duration. Simulation, according to the technology of processing trains, will reflect a gradual transition of applications through program units of one of the free channels. Each program unit delays an application for some time that corresponds to the pre-set or calculated duration of a relevant technological operation. The conditional transition boundary between technological operations will coincide with the moment of the application transition from one unit to another (Fig. 1). This principle allows the applied software to record the time of the application entry to the program unit, which manifests the beginning of an appropriate technological operation, and the time of the application exit from the unit, which corresponds to the completion of the technological operation. In fact, the results& gathering consists in recording the points of applications& moves between certain units (between the phases of train processing), which will further facilitate data processing as well as determining the likelihood of failure versus non-failing operations of the RTS. The duration of an application stay in a particular unit is defined as the difference between the points of the application&s entering a next unit and the moment of its entering the calculation unit:
where tin, unit z is the time of the application entry to the unit z; tin, unit z+i is the time of the application entry to the unit z+1. The latter time coincides with the time of the application coming out of the unit z.
The whole process of servicing transit trains on the tracks of receiving and dispatching depots can be represented as an interaction of three Queuing Systems (QSs) (Fig. 2).
The first QS: the arrival station is a receiving and dispatching depot; it is a single-channel queuing system (provided there is a consecutive acceptance of trains to the depot tracks). The second QS is complex, n-channel, with m phases of service, where each track of the transit depot is a service channel, so the number of the service channels is equal to the number of the receiving and departure tracks of the depot; each receiving and departure track provides a train with a set of technological operations, which are performed in parallel as well as sequentially to one another. All operations can be roughly grouped into two successive processes:
The third QS: the receiving and dispatching depot is a station of departure; it is a single-channel queuing system (provided there is a consecutive dispatch of trains on the connecting tracks).
port in No 1
port out No 1
port out
port out
Unit No I Unit No 2 Unit No m
-El- of application -a—a- of application -B- • • • -H- of application -0delay delay \\ delay l
A ¿delay 1 A?delay2 \\ A/dclaym
tdni. fin, unit ] unit 2
Application processing simulation, t
Fig. 1. The principle of a discrete event simulation of the technological process of a RTS at a sequential execution of operations
A QS set in the structure of the technological line of processing transit trains of technical stations with appliance sets to service phase 1 ({Mi}) and phase 2 ({M2}) of QS-2
Given the above, the goal is to study the probability of failure and the factors that affect it when applications are received in QS-2 (the probability of failure of a timely receipt) and when applications are received in QS-3 (the probability of failure of a timely dispatch of trains).
. = t„
at z = 1, 2,
To assess the reliability of the process of operating rail (1) transport systems, the most essential criteria [1] are:
These indicators should also be considered in terms of the existing and required reliability:
- the existing process reliability can be understood as structural or design reliability: it is the maximum threshold of reliability, which can be provided with adequate technical parameters, local conditions, and the manner of transport operation;
- the required (planned) technological reliability: the maximum level of reliability, which is required (planned) to be provided in accordance with the scale of the planned work, its structure, and nature.
In this study, the desired probability of failure will be represented by the value of ^n=0.05, which corresponds to the desired probability of a timely receipt and a timely dispatch of trains being 0.95.
The chosen simulation model development tool is the object-oriented programming language Java SE 7.0 (Oracle). The development media are Eclips and AnyLogic 6.4.1 with the major libraries.
According to the object-oriented paradigm of Java, the standard classes of the library Enterprise AnyLogic are supplemented with specially created classes:
The model architecture is developed in accordance with the "physical" operations of receiving and processing trains. The main physical characteristics of the process are a model time and binary spatial coordinates. A more detailed description of the simulation model is presented in [11, 12].
The model is developed, taking into account and ensuring the following:
p(Jin), att < Jlr p(t), att > Jn
where p(t) is the density of distributing the probability of an interval for trains arrival for processing; Jin is the minimal acceptable interval of trains arrival from the running line to the station according to the existing means of automation, remote control, and communications;
The model is implemented by an example of typical flow processes of technical railway depots of Ukraine. The initial parameters are the following:
While developing the model, it is assumed that:
The model was validated by testing all of its units separately. During the model code testing, its individual elements were corrected. The model code itself was compiled successfully, confirming absence of software errors.
The adequacy assessment of the simulation results and the simulation model effectiveness is complicated by the fact that the simulation concerns a typical workflow. Therefore, it is impossible to conduct a comparative evaluation of the actual and estimated results. Besides, the structure of the technological timetable of the model rules itself does not contain elements of downtime to wait for process operations. However, if only the duration of the operations is summed up, the obtained duration will be the time that is regulated by standard specifications.
To ensure reliability of the simulation, it is necessary to determine the maximum number of iterations (with the same initial parameters) and the duration (model time) of modelling. The solution is based on the principle that the determined number of iterations should provide an arithmetic mean value whose deviation from the statistical expectation does not exceed the specified error level.
It should be noted that because the developed simulation model simulates a technological process in which most elements are of stochastic (although clearly formalized) nature, the outcomes of the "model run" will also be stochastic. Then, for this type of experiments, the key issue is to establish the distribution (and its parameters) of the simulation results.
Therefore, several series of experiments were conducted under various durations of the simulation but at the same initial parameters. Each series contained 400 iterations. The measuring and the analysis were carried out with regard to the selected most important calculation factor, which was the percentage of applications that had been delayed when entering the service channels in QS-2, and in fact it meant the probability of failure in admitting a train to the tracks of the transit park.
The samples& evaluation for a hypothesis about the normal distribution law was confirmed with a high probability of 99 % by the criterion of x2. The calculations were conducted in MS Excel (analysis package) by a method of an interval series distribution (Fig. 3).
Fig. 3. The density of the normal distribution for the test results from Table 1
According to the property "symmetry" of the normal distribution, ninety-five per cent confidence intervals (a relative error of less than 5 % is accepted for most processes in the transport sector) (Fig. 4 and Table 1) will be the boundaries of, respectively:
M (x) - kö (x); M (x) + kö (x),
where k is the number of standard deviations, corresponding to 95 % of the confidence interval of the normal distribution of k=1.96.
The minimum number of iterations in which their average values will deviate from the expected value less than the pre-set relative error (10 %, 5 %, and 1 %), along with other results, are presented in Table 1.
Assessment of a series of experiments with the simulation model
The experiment parameter The serial number of the experiment
The model time, in months 1 6 12 24 60 90 150
Assessment of M(x) 4.99 5.03 5.03 5.10 5.03 5.06 5.07
Assessment of o(x) 2.92 1.26 0.85 0.58 0.41 0.33 0.24
Assessment of v(x) 0.59 0.25 0.17 0.11 0.08 0.07 0.05
The left margin of the 95 % of the confidence interval -0.73 2.56 3.36 3.96 4.24 4.42 4.60
The left margin of the 95 % of the confidence interval 10.71 7.50 6.69 6.25 5.83 5.70 5.54
The minimum number of iterations to ensure reliability 90 % 132 25 11 6 3 2 1
To ensure reliability of the results of the model simulation, it is possible to choose any connection between "the model time and the number of iterations" at an appropriate level of reliability. Given the principle that for most of transport processes the acceptable level of reliability is 95 %, as well as in view of the full-scale monitoring of the simulation,
each experiment relied on the chosen ratio of 12.5 years (150 months) and 4 iterations.
arrivals and departures at the probability of failure in timely acceptance of trains (^n) and the inter-operational downtime are shown in Fig. 9-12.
e =3 10
al v d rot 8
^ y = 9,8718x"0&128 R2 = 0,9344
: 1,0078ln(x) + 0,1691 R2 = 0,8834
The model time, in months
--The left margin of the 95 % of the confidence interval
--The right margin of the 95 % of the confidence interval
Fig. 4. The estimated confidence (95 %) intervals of a series of experiments (Table 1)
A group of four experiments has produced the following results.
The applications for servicing were received:
- in time: 256,051 (93.6 %);
- late: 17,473 (6.4 %);
- with a probability of failure to receive the trains to the station tracks being ^..st .=0.064.
The density of distributing the waiting time in admitting trains to the tracks of the transit park with a strong probability (of 95 %) is subject to exponential distribution (Fig. 5) at an intensity of M(x)=49.3 min, when the standard deviation is a(x)=48.12 min and the variance is v(x)=0.98.
Experimental frequencies -Theoretical frequencies (exponential distribution)
The middle of the intervals, min
Fig. 5. The density of distributing the waiting time for admitting trains to the tracks of the transit park
The density distribution of trouble-free uptime has a significant left-side asymmetry (Fig. 6): M(x)=3,355 min (2.33 days), the standard deviation is a(x)=5,752 (3.99 days), and the variation is v(x)=1.8.
The density of distributing the duration of the total time of a transit train servicing is close to the exponential value (Fig. 7), where M(x)=65.6, a(x)=39.8, and v(x)=0.61.
The relative amounts of productive uptime and unproductive downtime (pending operations) in servicing trains as well as the main subunits of QS-2 are shown in Fig. 8.
The impact of changing the number of maintenance teams (the devices of servicing the first phase of QS-2), the number of train locomotives (the devices servicing the second phase of QS-2), the minimum intervals between the
£ -o 0,8 £ § -Û S
^ ^ j # t $ ^ #
The middle of the intervals, days
Fig. 6. The density distribution of uptime when receiving transit trains
Experimental frequencies
-Theoretical frequencies
(exponential distribution) -Integral probability of experimental frequencies
The middle of the intervals, min
Fig. 7. The density distribution of time for servicing trains on the tracks of the transit park
(performed
operations)
Downtime
(pending
operations)
Transit trains
Maintenance teams Train locomotives
Fig. 8. The relative rates of productive uptime and unproductive downtime of the basic elements of the simulation model
Î ■ I «
^ The number of maintenance teams "§ ^ ^
-■-The average time of waiting for acceptance ^
—i The average time of waiting for TI
-W-The average time of waiting for the train locomotive ^ -SK-The average time of waiting for departure
The probability of failure in a timely acceptance of trains
Fig. 9. The dependence ^n=f(STI), where STI is the number of concurrently working inspection teams
When the parameter p exceeds a value of 0.65-0.7, there happens a rapid increase in the probability of failure of a timely arrival (Fig. 12), which means a possible system failure - a condition in which the process reliability can be ensured only after improving or modernizing the standards and rules. The reason is, probably, the constant increase of the average time
of waiting for departure, which begins to increase abruptly at such values of p. The same situation is observed when there is a decrease below the calculated value (M<26) of the operational parameter such as the train locomotives fleet (Fig. 10).
S g 2 °
&3"° 0
¡5 23 24 25 26 27 28 29 30 31 32 33 34 35 The operational fleet of train locomotives The average time of waiting for acceptance The average time of waiting for TI The average time of waiting for the train locomotive The average time of waiting for departure
The probability of technological failure in a timely acceptance of trains
Fig. 10. The dependence ^n=f(M), where M is the estimated number of train locomotives
° H S ® .s °
"3 8 J31
The rate of changes in the minimum interval between associated arrivals, a
• The average time of waiting for the train locomotive ,b
• The average time of waiting for acceptance
• The average time of waiting for TI
• The probability of failure in a timely acceptance of trains
Fig. 11. The dependence i;n=f(atarrivJ, where a is the rate of the average value of the arrival interval tarriv.; a£[0; 1] with a step of 0.01
™ o o S
The rate of changes in the minimum interval "o a
between associated departures, p ^
Q • The average time of waiting for acceptance (limited to 20 min) ^
• The average time of waiting for TI
• The average time of waiting for the train locomotive
• The average time of waiting for departure (limited to 20 min)
• The probability of failure in a timely acceptance of trains
Fig. 12. The dependence i;n=f(Ptdepart.), where p is the rate of the average value of the departure interval tdepart.; pe[0; 1] with a step of 0.01
The results of the research clearly demonstrate an advantage of simulation modelling (despite the relative complexity of developing models) over the analytical estimates of multiphase processes of railways, and it confirms that the real time when trains stay on the receiving and departure tracks is far longer than the time that is stipulated by the common rules.
Due to the fact that the number of service channels in QS-2 and the devices of servicing them do not match the number and nature of the random flow of trains for processing, there are technological conflicts that result in inter-operational downtime. According to the simulation results, such conflicts account for about 50 % of the time of processing trains; therefore, technological conflicts can be understood as common in complex technological processes of a RTS. Moreover, it is necessary to acknowledge that there exists a marginal, technologically rationalized rate of downtime, which should be taken into account in order to normalize process operations on railways.
The existing procedure for rationalizing the time of trains staying on the receiving and departure tracks should take into account the stochastic nature of the technological processes and the work volumes. If the operational process is supplied with standards of required reliability - the required level of technological failure versus uptime, it will facilitate objective assessment of reliability of an existing transportation process.
It should be noted that these results reflect a general principle of assessing the operational process reliability. However, the considered approach and the benchmarks could be considered as universal for studying technological reliability of any railway station.
The tests on the technological reliability of the operational process in the RTS were conducted with regard to the typical standards of technical stations and with the following findings:
decreases. When the minimum interval between passing trains& departures increases, the probability of failure
gradually increases, and after a point of 70-80 % of the average daily interval of arriving trains, the increase becomes stepwise. This proves the impossibility of timely departures of trains at equal intensities of arrivals and departures (the
same number of timetable threads). To ensure an adequate level of failure in a timely dispatch of trains (less than 0.05), the number of dispatch timetable threads should be at least 30 % bigger than the number of threads for arriving trains.
References
