基于可变速率M/M/c排队的接触匹配模型分析

Analysis of Contact Matching Model Based on M/M/c Queue with Variable Rate

【目的】针对实际生活中利用手机软件呼叫出租车的排队场景,建立并分析了可变到达率和可变服务率的接触匹配的M/M/c排队模型。【方法】利用概率分析方法导出拟生灭过程的状态转移规律及无穷小生成元矩阵,利用矩阵几何解方法给出系统的稳态平衡条件、稳态概率分布及系统的主要性能指标。【结果】通过数值分析讨论系统参数对于性能指标的影响,并建立系统收益函数研究系统最优收益。【结论】得到了系统参数对系统性能指标及系统收益的影响关系,表明在接触匹配中应当同时调整服务率及接触匹配成功率才能显著提高系统收益。

[Purposes]Combined with the actual queuing scene of DiDi taxi in life, it studies the M/M/c queueing model of contact matching with variable arrival rate and variable service rate. [Methods]It obtains the state transition law of quasi birth and death process and the infinitesimal generator matrix with probability analysis method, and gives the steady-state condition, steady-state probability distribution and main performance indices of the system by using the matrix geometric solution method. [Findings]The numerical analysis is presented to demonstrate the influence of system parameters on performance indices.The system profit function is established to discuss system optimal profit. [Conclusions]The influence relationship of system parameters on system performance indices and system profit are obtained, which shows the service rate and contact matching success rate in contact matching model should be adjusted at the same time in order to significantly improve the system benefit.