Vertical search engines focus on specific slices of content, such as the Web of a single country or the document collection of a large corporation. Despite this, like general open web search engines, they are expensive to maintain, expensive to operate, and hard to design. Because of this, predicting the response time of a vertical search engine is usually done empirically through experimentation, requiring a costly setup. An alternative is to develop a model of the search engine for predicting performance. However, this alternative is of interest only if its predictions are accurate. In this paper we propose a methodology for analyzing the performance of vertical search engines. Applying the proposed methodology, we present a capacity planning model based on a queueing network for search engines with a scale typically suitable for the needs of large corporations. The model is simple and yet reasonably accurate and, in contrast to previous work, considers the imbalance in query service times among homogeneous index servers. We discuss how we tune up the model and how we apply it to predict the impact on the query response time when parameters such as CPU and disk capacities are changed. This allows a manager of a vertical search engine to determine a priori whether a new configuration of the system might keep the query response under specified performance constraints.