Performance Analysis Of E-Hailing Taxi Queueing Model With Contact Matching Mechanism

Queuing theory is a mathematical discipline that studies stochastic service systems and the phenomenon of congestion.Based on the queuing model of real-life research,there exists a large number of double-end queuing model applications,that is,when the number of customers is larger than the number of service counters,customers form one end of the queue,and when the number of service counters is larger than customers,service counters form one end of the queue.Among them,the study of double-end queuing model based on taxi queuing phenomenon has attracted the attention of many scholars at home and abroad.In recent years,sharing economy has become one of the hot spots that people keep paying attention to,and the emergence of e-hailing taxi has made the traditional taxi industry undergo a radical change.With the continuous development of online taxi,how to make the customers,online taxi drivers and online taxi system maximize the revenue has become a topic of constant research and discussion.Based on the above practical background,the paper establishes a queuing model and does numerical analysis to draw relevant conclusions on the phenomena of purchase priority,online taxi system dispatch rate changes and shared carpooling in the actual operation of online taxis.First,the queuing model with non-preemptive priority contact matching is studied.It is assumed that after a customer enters the online taxi system,there will be a contact matching process with the online taxi driver,the driver can choose to accept or reject the matching according to the road conditions and the actual situation of the order,and the customer can choose to leave the system or buy the priority service to avoid waiting during the peak period according to their own situation.The M/M/c+m queuing model with non-preemptive priority contact matching is developed,and the main system performance indexes are given,and finally the effects of system parameters on the system performance indexes are discussed by numerical examples.Second,the queuing model with variable arrival and service rates for contact matching is analyzed.It is assumed that the customer arrival rate and the service rate of the server will change according to the number of waiting customers in the system while the customer enters the e-hailing system for contact matching with the e-hailing taxi driver.The probabilistic analysis method is used to derive the state transfer law of the proposed generation and extinction process and the infinitesimal generating element matrix.The steady-state equilibrium condition,steady-state probability distribution and main performance indexes of the system are given by using the matrix geometric solution method,and the influence of system parameters on the performance indexes is discussed by numerical analysis and the system revenue function is established to study the optimal revenue of the system.Finally,the M/M/c+m queuing model with variable matching rate for shared carpool matching is developed.The online carpool starts service after matching the first customer,and can continue matching with the carpool customer during the service period.if the match is successful,the two customers enjoy the carpool service together,and if the match fails,the first customer enjoys the fast carpool service.In addition,considering that when there are more online taxi customers,the system can improve the carpool matching success rate to adjust the carpool order dispatch rate in order to reduce the waiting time of customers.Finally,the effects of different system parameters on the system performance indexes are discussed through numerical analysis.The revenue functions are established from customers,online carpool drivers and online carpool system respectively,and the impact of the changes of different system parameters on the revenue of customers,online carpool drivers and online carpool system is discussed.