the world can be found in (Zamparini, 2007; de Jong, 
2009; Feo-Valero, 2011; Report for the Ministry of 
Infrastructure  and  the  Environment,  Significance, 
The Hague, 2013). The study (RAND Europe, SEO 
and  Veldkamp/NIPO,  2004)  is  one  of  the  first  to 
present the value of freight transportation reliability 
in  the  form  of  standard  deviation  of  transportation 
time. The key result in (Significance, VU University, 
John  Bates  Services,  TNO,  NEA,  TNS  NIPO  and 
PanelClix, 2013) is that most of the empirical results 
of  freight  reliability  assessment  are  related  to  the 
proportion  of  shipments  that  arrive  too  late 
(sometimes with a minimum delay threshold).  
The works (Hague Consulting Group, Rotterdam 
Transport Centre and NIPO, 1992) discuss the use of 
the  factor  cost  method  for  the  cost  estimation  of 
transportation time. It is argued that the study of the 
cost  estimate  of  time  for  freight  transportation  is 
necessary  to  determine  the  "marginal  time 
transportation  costs":  transportation  costs  that  will 
change as a result of changes in transportation time. 
It is a derivative of the total logistics cost function of 
transportation  time.  Total  logistics  costs  are 
comprised of transportation personnel costs, fuel and 
energy costs, vehicle costs, overhead costs, which are 
all  costs  incurred  by  carriers  and  transportation 
companies,  as  well  as  costs  of  damage  to  goods, 
interest  costs  on  the  value  of  goods  during 
transportation and the cost of having a safety reserve 
(the  last  three  factors  directly  affecting  the 
transportation component in the price of goods). 
A  number  of  authors  consider  the  use  of 
mathematical  models  to  assess  the  reliability  of  the 
transport process and the creation, on their basis, of 
appropriate  modules  in  information  management 
systems. The use of methods to assess and ensure the 
reliability of transportation based on business process 
modeling is particularly important for increasing the 
competitiveness  of  transport  companies  in  unstable 
economic conditions (Kurganov, 2018).  
Studies  have  appeared  recently  in  the  field  of 
reliability  of  intermodal transportation, in  particular 
transportation with the use of railway-automotive and 
railway-water transport. According to the goals stated 
by many countries, by 2030 30% of freight transport 
over  300  km  should  be  transferred  from  road 
transport  to  other,  more  environmentally  friendly 
modes  of  transport.  Most  importantly,  this 
assumption  applies  to  rail  transport  and  water 
transport. Rail transport has the best chance of taking 
over some of the freight traffic in the coming years.   
Rail  transport,  like  water  transport,  has  much 
more  inertia  (larger  vehicles  and  ships  used  for 
transportation,  longer  transportation  times,  etc.). 
Goods transported by  these modes of transport tend 
to have a lower cost per tonne than goods transported 
by road and air, therefore, the transport component in 
the price of goods will be relatively small. 
The  development  of  rail  transportation  depends 
on  its  ability  to  adapt  to  a  number  of  market 
requirements  related  to  transportation  time,  cost, 
flexibility,  information  flow  and  reliability  of  the 
production process.  Currently, the main obstacle to 
development is its low competitiveness, especially in 
relation  to  road  transportation.    This  is  mainly 
influenced  by  low  flexibility,  limited  cost-
effectiveness  over  long  distances,  and  lack  of 
reliability, manifested mainly in problems with timely 
transportation  (Zhao, 2020). The bottleneck may be 
an underdeveloped railway connection (Roso, 2013), 
the low flexibility of rail transport (Behrends, 2015), 
the  low  quality  of railway  infrastructure,  the  use  of 
different information systems, the reluctance to share 
information  (Kramarz,  2021),  the  higher  priority  of 
passenger  trains  over  freight  trains,  the  lack  of 
integration between transportation tasks and terminal 
tasks  (Hu,  2019).    Such  limitations  reduce  the 
reliability  of  the  entire  transport  system. 
Transportation  services  performed  with  such 
restrictions will not be able to meet the requirements 
of modern supply chains, which require a high degree 
of flow reliability (Elbert, 2017). 
3  MATERIALS AND METHODS 
Carriers,  operators  and  owners  of  railway  rolling 
stock  estimate  delivery  time  through  the  costs  of 
providing  transportation  services.  If  transportation 
time were reduced, vehicles and personnel would be 
freed  up  to  perform  other  productive  activities, 
resulting  in  savings  in  vehicles  and  labor.    Greater 
reliability  means  that  the  carrier  and  operator  can 
have  confidence  when  planning  transportation.  The 
results of foreign researchers obtained to date show 
that the value of time related to transport services is 
indeed more or less equal to the cost of the vehicle 
and labor per hour (de Jong, 2009). 
For shippers, the valuation of transportation time 
is directly related to the goods themselves. It includes 
the working capital invested in the goods during the 
time required for transportation (especially important 
for high-value goods), the potential reduction in value 
of  perishable  goods  during  transportation,  and  the 
possibility of disruption of the production process due 
to lack of resources or inability to deliver due to lack 
of inventory. The two latter factors play a significant 
role  in  assessing  the  reliability  of  freight