• Irina A. Turenova, National research Tomsk state university (Tomsk, Russia)
• Svetlana P. Moiseeva, National research Tomsk state university (Tomsk, Russia)
• Maria A. Shklennik, National research Tomsk state university (Tomsk, Russia)

With the constantly growing number of online platforms and intensifying competition among marketplaces, optimizing their operations and improving management efficiency are becoming crucial tasks. Mathematical modelling of sales processes on marketplaces allows predicting changes in conditions and minimizing risks. Models must consider various factors such as demand seasonality, competition, changes in logistics, and marketplace policies. This helps suppliers optimize prices, inventory, and logistics processes, reducing financial losses and enhancing business stability. Marketplaces like Amazon, Wildberries, or Ozon process an enormous number of transactions and customer interactions daily, requiring the development of mathematical models for management systems and forecasting. This article explores mathematical models based on queuing systems (QS) describing their principles and potential applications in e-commerce. For predicting customer flows and optimizing the sales funnel on marketplaces, single- and two-phase queuing models with repeated requests are proposed, allowing forecasting parameters of planned marketing campaigns and assessing their impact on revenue and customer base. For modelling the sales funnel, multi-phase models are suggested, estimating the time a potential buyer spends at each funnel level, enabling evaluation of the effectiveness of different funnel stages and identifying bottlenecks that can reduce conversion; developing recommendations for sales funnel optimization, such as changing interface design, improving search systems, or offering more favourable payment terms; and predicting sales volume and optimizing product inventory based on analysing application flows at different funnel stages. The article lays the foundation for further research on adapting these models to real processes, including empirical validation, parameter determination, and algorithm development for optimizing seller sales strategies.

E-commerce platform, sales funnel, econometric-mathematical modelling, stochastic methods, queuing systems, request flows, repeat inquiries, multi-phase QS

2026-09-03