A goal of a routing policy is to provide high accessibility or short waiting times with a fixed number of agents. Thus, in designing and choosing a routing policy, it is important to understand the performance (e.g. mean waiting time) under various routing policies under various parameter settings. An efficient analysis of queueing models is useful in evaluating the performance of various routing policies by changing various parameters such loads and service time variability, as the running time of simulation is too long.
For example, in Chapters 5-7, we have repeatedly seen the effectiveness of resource sharing such as cycle stealing. Specifically, cycle stealing can significantly improve upon the Dedicated policy (without cycle stealing) with respect to mean response time. In contact centers, particular customers are often served by particular agents, e.g. due to the skill level of the agents, as discussed above. However, the effectiveness of cycle stealing suggests that training some of the agents and allowing them to serve multiple types of customers, can significantly improve mean response time.
In Chapter 7, we have studied a more sophisticated type of resource sharing towards minimizing mean response time. Specifically, we have studied a broad class of threshold-based policies for the Beneficiary-Donor model, and found that a single-threshold policy (the T1 policy) can improves upon cycle stealing, but the improvement of a multi-threshold policy over the T1 policy is only marginal.
In Chapter 7, we have also studied robustness of the threshold-based policies for the Beneficiary-Donor model. Specifically, we find that the T1 policy excels in static robustness (robustness against misestimation of load) but lacks dynamic robustness (robustness against fluctuations in load), while a multi-threshold policy (the ADT policy) excels in both static and dynamic robustness. Such lessons are useful in choosing an appropriate routing policy for a contact center. Specifically, if future loads can be forecasted with high accuracy, the T1 policy is sufficient, as it can provide low mean response time and excels in static robustness; otherwise, the ADT policy is a better choice.
Also, in Chapter 4, we have studied the impact of the variability in service demand and the impact of prioritization in multiserver systems. Specifically, we find that the impact of service demand variability on mean response time can be much higher when the number of servers is small (i.e. at small contact centers). Also, we find that the impact of prioritization on the mean response time of lower priority jobs can be much higher at small contact centers. These lessons suggest that smaller contact centers may not want to prioritize high priority customers if their service demand has very high variability, since it can significantly worsen the mean response time of low priority customers. Also, if the variability of the service demand is high, a smaller contact center may instead want to prioritize those customers whose service times are more likely to be short.
In Chapter 5, we have proposed a size-based task assignment policy with cycle stealing under central queue (SBCS-CQ), which combats the impact of service demand variability. Under SBCS-CQ, customers whose service times are expected to be short (``short'' customers) are routed to the ``short'' agent, and other customers (``long'' customers) are routed to the ``long'' agent. This prevents the short customers waiting behind a long customer. Further, under SBCS-CQ, when there are no long customers to be served, the long agent serves short customers. This increases the utilization of the long agent. In contact centers, service demand may be estimated based on the record of interaction at the (interactive) voice response unit (VRU) and the customer information available at the customer data server, as well as the history of measured service demands.