Game Theory Based Server Self-interest Behavior Research And Service System Management Mechanism Design

In traditional research of manufacturing systems and service systems,the server(people)is modeled as a machine or part of a machine with a fixed service rate.However,the biggest difference between people and machines lies in self-consciousness.Under the effect of consciousness,people can seek advantages and avoid disadvantages,and rationally make behavior that maximize their own interests.The self-interested behavior will affect the efficiency of service system.On the other hand,if the operating rules of the system did not meet the interests of the server,such rules cannot be implemented by the server actively.Due to the existence of self-interested behavior,the traditional management method of relying solely on assignment and supervision not only increases the operating cost but also is ineffective.This paper aims to analyze the self-interest behavior of service providers in queuing service systems through game theory and queuing theory,and evaluate their impact on service efficiency,and then establish a corresponding management mechanism to improve service efficiency.The self-interested behavior studied in this paper has two forms: competition and cooperation.For these two basic behaviors,we study from the following four aspects.The first part studied a queueing model wherein two heterogeneous(different skill level)servers compete for the arriving customer.In the asymmetric competition game between servers with different capacity costs(heterogeneous servers),the competitive behaviors of the servers may adversely affect the system.A high-cost server may be unable to obtain profit from the competition,and thus,will be forced to withdraw,and making the low-cost server become the monopolist.Through the analysis of Nash equilibrium points,we show that the main cause of monopoly is the high-level reward,rather than the difference between the capacity costs of the servers.Moreover,the profit gained by a server may increase with a decrease in the equilibrium service rate.Driven by the profit,the servers may deliberately delay to obtain more profits.We found that the occurrence of this deliberate delay not only depends on the high pay but also on the difference between the capacity costs.To avoid the monopoly and deliberately delay,we provide a matching method of servers and set the reward in a feasible range.The second part studies the competition problem in variable value service system.The basic assumption of the variable value service is that the service value increases with the service time.However,to get more rewards,the service provider will shorten the service time.With the shortening of the service time,the value of the service obtained by the customer will be decrease,and the loss of the service value will be borne by the firm.However,administrator cannot directly control the service rate of the server and can only adjust service rate through the compensation system.We compared two kinds of compensation systems,piece-based and team-based piece-by-piece and presented the selection method of compensation scheme and the calculation method of optimal reward.In addition,by comparing the changing trend of maximum profit and optimal reward.We also found that in the process of increasing service capabilities by increasing reward,it should be noted whether the target exceeds the limits of the system.If the limit of the service provider is exceeded,the total profit cannot be increased by using the method of increasing the reward.The third part deals with the server cooperation in a form of M/M/1 queue.The servers can reduce customer wait time when they cooperate into M/M/1 queues.Based on this idea,administrator will be pooling the servers,but if the pooling results do not meet the interests of the service provider,the arrangement cannot be implemented by server actively.Therefore,the pooling approach that follows the interest coalition of the servers can be stabilized.To analyze the pattern of server coalition,we established a cooperative game model with transfer utility,and we proved that the initiative of the service provider to participate in coalition.We find that with the expansion of scale of coalition,monopoly coalition will emerge.Then we provide a method for determining the structure of coalition.Finally,this paper compares different coalition structures generated by the two customer behaviors and the service efficiency generated by the coalition structure.The fourth part deals with the similar server cooperation problem with the third part.Different with M/M/1 queuing mode cooperation,cooperation in the form of M/M/s queues is not a server with accumulation of service rates,but a queueing system with multiple parallel identical servers.We analyze the customers allocation policy in multiple M/M/s queues.We demonstrate that server will actively cooperate and eventually form two competing coalitions.Then we provide a condition of stable coalition and provide a way to determine the stable coalitions structure.Finally,we compared coalition structures and corresponding service efficiencies under different customer behaviors.