Optimization Method Of Queueing System Considering Continuous Peak Period

The queueing phenomenon can be seen everywhere in real life.As an important branch of operations research,queueing theory has been an important research content of scholars at home and abroad.In the queueing system,due to the limitation of resources and environment,congestion often occurs during the continuous peak period,which will not only reduce customer satisfaction,but also cause loss to service providers.Aiming at the congestion in the queueing system,this paper analyzes the research status of queueing theory in detail,and then conducts research from two aspects,namely,the optimization analysis of the queueing system in the case of single-queue and double-queue.In order to optimize the service system with continuous peak period,this paper establishes a queuing model with trapezoid peak arrival,and studies the effect of customer time sensitivity on system optimization,and analyzes the revenue function of the queueing system under different time sensitivity conditions,and determines the service rate setting method for the maximum case of different revenue functions.The research results show that the unit service revenue and unit service cost of the queueing system determine whether service providers can set a sufficiently large service rate to satisfy all time sensitive customers.The high service rate leads to a waste of leisure time resources,and the low service rate leads to the departure of customers during peak periods.Therefore,service providers with lower unit costs set a larger service rate to attract more customers,and service providers with higher unit costs slightly increase the service rate to save some fixed costs.In the face of customers with different time sensitivity,it is a better choice for service providers to appropriately increase service rates and allow some customers to leave.After considering the trapezoidal arrival queuing model with different time sensitivity,this paper further studies the situation of customers with differentiated needs in the queueing system.Treating customers with personalized needs as ordinary customers and providing services will not only reduce customer satisfaction,but also cause companies to lose some potential customers and thus reduce revenue.This paper sets different service rates according to the individual needs of such customers,and compares the optimization problems of the single-queue dual-server and dual-queue dual-server models in the standard queueing system and the revenue optimization problem in the trapezoidal arrival queueing system.And then considers the case where impatient customers choose to leave when their expected waiting time exceeds the tolerance range.The research results show that when service providers face customers with personalized needs,if the service rate needs to be set sufficiently to meet the customer's needs,then the single queue model is a better choice for service providers.On the other hand,if a smaller service rate can meet the personalized needs of customers,the dual queue model is a better choice for service providers.