An analysis of a queueing model of a contact center can often be reduced to an analysis of a Markov chain. However, in the contact centers with value-based or skill-based routing, the analysis of the queueing model often involves a multidimensional Markov chain to which existing analytical tools do not apply. Dimensionality reduction (DR) developed in Chapter 3 allows us to analyze (efficiently with high accuracy) some of the multidimensional Markov chains that model the contact centers with a value-based or skill-based routing.
For example, in Chapter 4, we have studied a multiserver system with multiple priority classes. This multiserver system with multiple priority classes can model a contact center with a value-based routing, where customers with higher priority are allowed to jump ahead of customers with lower priority. For example, big spenders or big investors may have higher priority at contact centers [8,29]. In Chapter 4, we have considered ``how many servers are best?'' given a fixed total capacity. However, in capacity planning at contact centers, they would be interested in questions such as ``what is the minimum number of agents so that the mean waiting time is less than a minutes?'' DR can be used to answer such questions as well.
In Chapter 7, we have studied the Beneficiary-Donor model (see Figure 7.1), which can model a contact center with a skill-based or value-based routing. For example, the donor server may be a bilingual agent, and the beneficiary server may be a monolingual agent [58,105,176,185,186]. Instead, the donor server may be a cross-trained or experienced agent who can handle all types of questions, and the beneficiary server may be a specialized agent who are trained to handle a specific type of questions [8,58,176]. Alternatively, customers served by the beneficiary server may have higher priority, and the donor server contributes to maintaining an adequate service level of the high priority customers; conversely, customers served by the donor server may have higher priority, and the excess capacity of the donor server may be used to help the (otherwise overloaded) beneficiary server [58]. In Chapter 7, we fixed the number of donor and beneficiary servers, and studied the mean response time and robustness of a wide range of threshold-based policies. However, DR applies to the Beneficiary-Donor model with an arbitrary number of donor and beneficiary servers (the running time increases with the number of servers), and allows us to determine the number of beneficiary and donor agents to be assigned at a contact center with a skill-based or value-based routing.