An Invitation Control Policy for Proactive Service Systems: Balancing Efficiency, Value and Service Level

Proactive service systems permit a controllable arrival rate managed by the service provider, which is different from classic service systems. Conceptually, some (or all) of the customers are invited to the system, so as to allow for a better control over operational indicators and profitability. Such a proactive service system is used, for example, to model an online chat service system, or for planning preventive care strategies for health care service providers.
Through an empirical study of a proactive chat service system, the validity of customer ranking information is elaborated for optimizing invitation control. It is also shown that service level measures can be formulated in terms of penalty for abandonment and cost of waiting. We also discuss the difference between external and internal waiting observed in such systems.
As a result, we develop an infinite-time-horizon multiclass multiserver queueing system with impatient invited customers. We find an asymptotically optimal policy using a fluid approximation, by solving a linear programming problem that maximizes revenues. The asymptotic optimal invitation policy we developed invites customers by their rμ ranking in decreasing order until there are no idle servers. Then, an equivalent threshold policy is proposed that is easy to implement in practice. Numerical simulations were performed to demonstrate the performance of the policy and identify its limitations. We show that the fluid policy has a good performance but is also crude.
In order to refine the fluid policy, we analyzed a fluid approximation of the system under a more flexible threshold policy, that is easily applicable. The equilibrium is found to be asymptotically stable and strongly depend on system parameters, including customers’ patience that was previously ignored. Moreover, it depends on the threshold value applied. In order to propose an invitation policy that balances revenues and service level, the probability of implementing admission control is approximated, as well as other performance metrics.
Joint work with Yueming Xie and Liron Yedid-Zion