Research On Dynamic Pricing And Equilibrium In Queuing Systems With Rate Control

With the rapid development of social network,the cost of obtaining service information for managers and consumers has dropped significantly.As the information management technology is becoming more and more advanced,managers can continuously adjust the prices of their service according to market demand.This is the so-called dynamic pricing strategy.Dynamic pricing can effectively affect customers' behavior.Considering the variety of customers in the market and the existence of multi-stage services in the service process,this paper conducts researches on the dynamic pricing of multiple classes of customers and dynamic pricing in tandem queues.At the same time,this paper also studies an equilibrium queuing system with double thresholds.Customers make their own decision based on the information announced by the company and they will adjust their strategies with the change of service rates.The detailed work is as following:Firstly,this thesis considers dynamic pricing in a two-class queuing system with adjustable arrival and service rates.By establishing a social welfare function,the optimal arrival rate and service rate are obtained to maximize the long run average social welfare.Then,based on the optimal arrival rate and service rate,the corresponding dynamic price is further obtained.The behavior of two classes of customers is guided by the dynamic price.In the problem of rate control,this paper applies sensitivity-based optimization theory and iterative algorithm to obtain the optimal arrival rate and service rate of two classes of customers.Then,the recursive algorithm is used to obtain the sojourn time.What's more,we give the corresponding optimal dynamic price based on the sojourn time.Finally,a numerical example is carried out to show the differences of dynamic prices between two classes of customers under different waiting costs.It is found that: when the waiting cost is relatively low,the optimal prices of two classes of customers are both increasing in the number of the same class of customers,and decreasing in the number of different class of customers.When the waiting cost is relatively high,the price for the customers who have higher waiting cost will increase in the total number of customers,that is,the increase in the number of customers of either class will cause an increase in the optimal price of the class of customers with higher waiting costs.Secondly,this thesis considers the optimal dynamic pricing in a tandem queuing system with limited resources.To improve the long-run average social welfare,managers not only need to set appropriate dynamic prices to increase revenue,but also need to allocate appropriate resources to two servers with limited resources with the goal of reducing costs.This paper uses sensitivity-based optimization to obtain the optimal state-dependent arrival rates and service rates firstly.Through the marginal revenue function,the relationship between price and arrival rate is established.Then,based on the optimal rates,the sojourn time is derived by using an iterative algorithm and the corresponding dynamic prices are also given.Finally,the above theory is applied to the dynamic pricing in an automobile inspection company.It is shown that when the waiting cost of the car owner is low,the optimal price increases with the increase of cars.While,when the waiting cost is high and the number of cars at the second server is very large,the optimal price will decrease firstly and then increase with the increase of cars at the first server.Finally,this thesis considers an equilibrium queuing system with double thresholds.Customers' equilibrium and socially optimal balking strategies are studied.The service shuts down when the system becomes empty and resumes when the number of customers reaches to m.During the service period,the server provides services at two service rates,high and low.When the number of customers in the system is lower than N,the system provides services at a low service rate.Once the number of customers in the system reaches to N,the server begins to serve customers at a high service rate.This paper considers two unobservable queuing systems: the fully unobservable queue and the almost unobservable queue.Solving the balance equations,we obtain the stationary probability distribution and the mean queue length.The social welfare function is also built relying on the reward-cost structure of the system.Finally,we carry out some numerical experiments to illustrate the effect of the information levels as well as double thresholds and some other parameters on the stable equilibrium and socially optimal arrival rates.