Stochastic modeling is a widely used technique for the purpose of system performance evaluation and decision making. Compared with deterministic models, stochastic models capture the randomness existing in the actual systems such that they are much closer to the reality, and therefore have attracted a lot of attention from both industrial and academic circles.

In Chapter 2, we consider the stochastic modeling and optimization of a call center composed of in-house servers and outsourcers. An increasing number of companies choose to route part of their customers to outsourcers for saving cost. Compared with the in-house servers, outsourcers usually have lower employment cost and are more efficient in doing some simple or duplicate work. However, some of the customers served by...[ Read more ]

Stochastic modeling is a widely used technique for the purpose of system performance evaluation and decision making. Compared with deterministic models, stochastic models capture the randomness existing in the actual systems such that they are much closer to the reality, and therefore have attracted a lot of attention from both industrial and academic circles.

In Chapter 2, we consider the stochastic modeling and optimization of a call center composed of in-house servers and outsourcers. An increasing number of companies choose to route part of their customers to outsourcers for saving cost. Compared with the in-house servers, outsourcers usually have lower employment cost and are more efficient in doing some simple or duplicate work. However, some of the customers served by outsourcers may need further service which cannot be accomplished by outsourcers, such as some special technical support or some VIP service. These customers are then routed to the in-house servers who are well trained by the company. In this sense, the in-house servers can serve both the incoming customers and the customers rerouted from the outsourcers. We build a queueing network with a rerouted path to model this system. We propose a stang policy which balances the number of in-house servers and outsourcers such that the employment cost is minimized while some specific quality of service (QoS) constraints can be satisfied. In terms of the staffing size, we propose a corresponding routing policy which determines the customer flow in the queueing network to optimize the waiting cost of the customers. We show that the policies are asymptotically optimal when the system is large.

Models are often built to evaluate system performance measures and to make quantitative decisions. For instance, we build a queueing model to determine the staffing level and the routing rule in Chapter 2. These models usually involve unknown input parameters that need to be estimated statistically using data. In these situations, a statistical method is typically used to estimate these input parameters and the estimates are then plugged into the models to evaluate system performance measures or to make decisions. This is what we call a two-step approach, first estimating the parameters and then evaluating the performance measures. In the two-step approach, parameter estimation and performance evaluation are considered separately, and good parameter estimators may not necessarily lead to good performance estimators, which are exactly what we care about. In Chapter 3, based on the two-step approach, we propose a simulation-based learning approach to linking parameter estimation and performance evaluation together. We show that the new estimator, which we call a simulation-based learning estimator, is consistent and has a smaller bias than the two-step estimator.