Routing and Staffing in Customer Service Chat Systems with Generally Distributed Service and Patience Times.

This article studies customer service chat (CSC) systems where agents can serve multiple customers simultaneously, focusing on routing and staffing decisions when service and patience times follow general (nonexponential) distributions. It formulates a routing linear program (LP) to determine optimal customer-to-agent matching rates and introduces a dynamic routing policy, called the latest-level-down-first policy, which does not require knowledge of arrival rates or staffing levels and accounts for both level and agent selection decisions. The paper also develops closed-form approximations for key performance metrics such as abandonment probability and expected time in the system, and proposes a staffing LP to determine minimal agent numbers to meet service targets. Extensive simulations demonstrate the accuracy of these approximations, highlight the significant impact of service and patience time distributions on system performance and staffing, and show that the proposed routing policy improves performance notably compared to simpler policies, especially in systems with inefficient multitasking levels.