呼叫中心到达过程的建模与预测

Modelling and forecasting of call center arrival process

呼叫中心到达量的拟合和预测对呼叫中心人力需求计算和排班有着重要作用.根据用户在呼叫中心的不同阶段,可以将到达量分为交互式语音应答(interactive voice response,IVR)到达量和人工服务到达量.国外学者主要对人工服务到达量进行拟合和预测,非齐次泊松过程作为一种模拟到达过程的方法得到广泛使用.而这里首次提出对IVR到达量进行研究,对比实际数据与非齐次泊松过程的均值和方差,发现该呼叫中心IVR到达量呈现"过离散(overdispersion)"现象,不能使用泊松分布拟合.因此选择时间序列模型对IVR到达量进行拟合和预测,用残差的白噪声检验拟合效果,平均绝对误差(mean absolute error,MAE)值判断模型预测优劣.最后使用线性回归模型分析IVR到达量与人工服务到达量之间的关系.结果表明:自回归滑动平均ARIMA(autoregressive integrated moving average)(1,0,1)模型能更好地对该呼叫中心正常天数(normal days,ND)的IVR到达量进行短期预测,而Winters指数平滑法能更好地对春节期间(Spring Festival,SF)的IVR到达量进行短期预测;通过回归模型可以预测呼叫中心人工服务到达量.

Fitting arrival process and forecasting future arrivals are crucial to staffing and scheduling in call centers.According to different stages of a call center,arrivals are classified into IVR arrival and agent arrival. Nonhomogeneous Poisson process has been widely used overseas for modeling stochastic agent arrival process. However,this study initially proposed IVR arrival fitting and forecasting. The IVR arrival process of this call center appears to be ＂overdispersed＂when comparing the mean arrival rate and its variance with the corresponding Poisson process.Therefore,time series was used to model and predict the IVR arrival process. White noise test of residuals was applied and the MAE（ mean absolute error） was adopted to evaluate the goodness of fit. The results show thatARIMA（ 1,0,1） is preferable for predicting the IVR arrival in a short period of normal days and Winters is preferable for the Spring Festival period. Finally,the regression method was employed to describe the relationship between IVR arrival and agent arrival,and predict the agent arrival.