不同信息下N-策略休假排队系统中患者均衡行为分析

Analysis of Patients’ Equilibrium Behavior in N-Strategy Vacation Queueing Systems under Different Information

摘要: 患者到医院诊疗时，某些体检项目需要用到大型机器进行检查，若机器一直处于开机状态则会持续发热、加快损耗和长时间辐射，甚至可能发生故障。为解决此问题，本文主要考虑了带有N-策略和双阶段休假策略的M/M/1排队模型。本文采用“收益–成本”结构来量化患者的等待时间成本和服务后收益，由于患者往往是追求最大化自己的收益来决定去留，从而患者与患者之间出现了博弈现象。假设患者在到达时可以通过获取系统信息来做出进队或止步的决策，当受到不同信息水平影响时，患者会出现不同的思考与选择。通过构造马尔可夫状态转移方程，研究在完全可见和几乎不可见两种情形下系统的稳态分布和患者进队的均衡策略。最后本文将用一些数值例子说明，在不同信息水平下，主要参数变化对患者均衡进队概率的影响。

Abstract: When patients come to the hospital for diagnosis and treatment, certain physical examination items require the use of large machines for examination. If the machine is constantly turned on, it will continue to heat, accelerate loss, and cause long-term radiation, and may even malfunction. To ad-dress this issue, this article mainly considers a M/M/1 queueing model with N-strategy and two-stage vacation strategy. Here, the “benefit-cost” structure is used to quantify the waiting time cost and post service benefits of patients. As patients often seek to maximize their own benefits to decide whether to stay or not, there is a game phenomenon between them. Assuming that patients can make decisions to enter or stop by obtaining system information upon arrival, when influenced by different levels of information, patients have different thoughts and choices. By constructing a Markov state transition equation, we will study the steady-state distribution of the system and the equilibrium strategy for patient admission in both fully visible and almost invisible situations. Fi-nally, some numerical examples are used to illustrate the impact of changes in main parameters on the balanced admission probability of patients at different levels of information.