Abstract: This paper studies a most observable retrial queue via the quasi birth and death process theory. From the viewpoint of economics, we discuss decision-making problems of the customers, the society and the administrator, and obtain their optimal threshold strategies. Then, we give some numerical examples to illustrate the effect of the service payments on the three optimal threshold strategies. The results showed that customer decision threshold is the biggest one, the social decision threshold the second biggest and the monopolist decision threshold the minimum one. Finally, we gave the corresponding management enlightenment from the points of view of the social and the manager: with different service payments, respective entrance fees are charged to force the behaviors of customers to satisfy the social decision threshold and the monopolist decision threshold.

Key words: operation research, most observable retrial queueing, quasi birth and death process theory, customer behavior, social optimization

摘要： 通过采用拟生灭过程理论,研究了几乎可视重试排队模型。从经济学角度讨论了顾客、社会及垄断者的决策问题,并且得到了三者最优的门限策略。通过数值算例描绘了服务报酬对三个最优门限的影响。研究结果表明,顾客决策产生的门限最大,社会决策产生的门限次之,垄断者的门限最小。最后,从社会和管理者的角度出发,给出了相应的管理启示:在不同服务报酬下,通过收取相应的入场费迫使顾客的行为分别满足社会和管理者的最优门限。

关键词: 运筹学, 几乎可视重试排队, 拟生灭过程理论, 顾客行为, 社会最优