N-策略工作休假M/M/1排队系统中的顾客行为研究

考虑N-策略M/M/1排队,休假期间服务员并未停止工作而是以较低的速率为顾客服务.系统的决策主体是顾客,基于"收益-成本"结构,利用马尔可夫过程理论,采取均值分析的方法,以顾客追求利益最大化为出发点,分析了全可见和几乎可见两种情况下的顾客行为.通过求解平衡方程,得到几乎可见情况下系统的稳态概率,进而求得几乎可见状态下顾客的期望逗留时间.构建均衡社会收益函数,并通过数值模拟,分析系统的各个参数对社会均衡收益的影响.

Analysis of customer behaviors in M/M/1 queueing systems with N-policy and working vacation

Consider an M/M/1 queue with N-policy where the server works at a lower service rate rather than completely stops working during a vacation period. In this system, customers will decide whether to join or balk upon arrival. Based on the "reward-cost" structure and the theory of Markov process, starting from the customers maximizing their reward, customers' behavior is analyzed by the method of mean value analysis under two cases:full observable and almost observable. By solving the balance equations, the stationary probability and the customer's expected sojourn time under the almost observable case are obtained. Finally, the equilibrium social benefit function is constructed, and the effect of parameters on the equilibrium behavior is illustrated via numerical examples.