PROBABILITY AND OPTIMAL CONTROL APPROACH IN ANALYSIS OF TAXI DRIVER'S MOTION STRATEGY

Аннотация

The Taxi Driver Issue is a practical model of process research and optimal management science based on Markov decision processes. This issue aims to find the optimal strategy that will give the driver the maximum benefit based on the different options of action in each city situation. Using an iterative algorithm, the optimal stationary strategy is determined based onprobabilities and rewards. This article analyzes the movementsbetween towns A, B and C and identifies the strategy of waiting for the most useful decision – queue waiting. The issue is used in theservice management, transportation and logistics management sectors. Keywords:Process research, optimal management, Markov decision process, iterative algorithm, probability, benefit function, strategic planning, taxisystem, status and action, stationary strategy, service system, probabilitymatrix,maximum profit, cost-effectiveness. Annotatsiya: Taksi haydovchisi masalasi jarayonlar tadqiqoti va optimal boshqaruv fanining Markov qaror jarayonlariga asoslangan amaliy modelidir. Ushbu masala haydovchining har bir shahar holatida turli harakat variantlari asosida maksimal foyda keltiradigan optimal strategiyasini topishga qaratilgan. Iteratsion algoritm yordamida ehtimolliklar va mukofotlar asosida optimal statsionar strategiya aniqlanadi. Mazkur maqolada A, B va C shaharchalari o‘rtasidagi harakatlar tahlil qilinib, eng foydali qaror – navbat kutish strategiyasi aniqlangan. Masalaxizmat ko‘rsatish, transport va logistikani boshqarish sohalarida qo‘llaniladi. Kalit so‘zlar: Jarayonlar tadqiqoti, optimal boshqaruv, Markov qaror jarayoni, iteratsion algoritm, ehtimollik, foyda funksiyasi, strategik rejalashtirish, taksi tizimi, holat va harakatlar, statsionar strategiya, xizmat ko‘rsatish tizimi, ehtimollik matritsasi, maksimal foyda, iqtisodiy samaradorlik. Аннотация: Задача таксиста — это практическая модель исследования процессов и науки оптимального управления, основанная на марковских процессах принятия решений. Эта задача направлена ​ ​ на поиск оптимальной стратегии водителя, которая максимизирует прибыль на основе различных вариантов действий в каждом городе. С помощью итерационного алгоритма определяется оптимальная стационарная стратегия на основе вероятностей и вознаграждений. В этой статье анализируются перемещения между городами A, B и C и определяется наиболее выгодное решение — стратегия ожидания в очереди. Задача используется в сферах обслуживания, транспорта и управления логистикой. Ключевые слова: Исследование процессов, оптимальное управление, марковский процесс принятия решений, итерационный алгоритм, вероятность, функция прибыли, https://ijmri.de/index.php/jmsi volume 4,issue3,2025 740 стратегическое планирование, система такси, состояние и действия, стационарная стратегия, система обслуживания, матрица вероятностей, максимальная прибыль, экономическая эффективность. Introduction: Process research and optimal control are the sciences that serve to make decisions in complex systems and ensure the most efficient use of available resources. Markov decision processes play an important role in this science, as they allow to ensure the maximum expected benefit through a sequence of actions. In this study, the goal is to find the optimal strategy by modeling a real-life situation in which ataxi driver may be in different urban situations (A, B, C). In each situation, there are several solutions (actions), each of which is represented by different probabilities and rewards. The goal is to find the strategy that will bring the driver the greatest benefit. Literature review A review of scientific research on process research and optimal control shows that decision- making systems based on probabilistic models are effectively used in the service and transport sectors. Dynamic programming and Markov processes developed by R. Bellman create the main theoretical basis in this regard. G. Dantzig's work is focused on determining optimal strategies using linear and nonlinear programming. L. Kantorovich, on the other hand, connected the theory of optimal resource allocation with economic models. At the moment, models using Markov processes provide effective solutions in service systems, especially in transport and taxi systems. Research methodology The study is aimed at determining the most profitable strategy for a taxi driver based on the probabilities that can be in three cities - A, B and C. The methodological approach includes the followingstages: 1. Mathematical modeling - a model is built based on the probabilities and rewards correspondingtoeach action; 2. Iterative calculation algorithm (value iteration) - the maximum expected profit is calculated foreachcase; 3. Optimal strategy selection - the profit for each solution is evaluated and the best action is determined; 4. Stationary strategy determination - when the selected solutions do not change in all cases, this strategy is considered optimal. The study found that for all cases, the most prof