带接触匹配的M/M/C排队模型

M/M/C Queuing Model with the State of Matching and Abondoning

结合实际生活中餐饮业,文娱业等广泛采用线上排队的情况,考虑顾客结束排队等待时不是无条件直接接受服务,而是需要历经接触匹配期的M/M/C排队模型.引入接触匹配期这个新状态,规定若接触期间顾客及时到达系统,则可成功匹配并接受服务,若未及时到达,服务方则选择将顾客暂时抛弃并顺延.首先建立考虑接触匹配的M/M/C模型,接着得到拟生灭过程状态图和方程组及生成元矩阵,最后基于Neuts的矩阵几何解方法给出稳态下系统的稳态平衡条件、稳态概率分布及其他若干系统指标.

Considering the fact that online queuing is widely used in the catering indus-try and entertainment industry in real life,when customers stop waiting in line,they will not directly receive services unconditionally,but instead need to go through the period of matching and abandoning.This article introduces a new state called“Matching&Abandoning Period",stipulating that if the customer arrives in the system in time during the contacting period,he can successfully match and accept the service.If he does not arrive in time,the service party will probably choose to temporarily abandon him and postpone to the next customer.This paper firstly establishes an M/M/C model,which includes the state of matching and abandoning,and then obtains the diagram and equation set of the Quasi-Birth-Death process and the generator matrix.Finally,based on the matrix geometric solution built by Neuts,this paper gives the equilibrium conditions of the system,steady-state probability distribution and other related system indicators.