The performance of wireless data systems has been extensively studied in the context of a single base station. In the present paper we investigate the flow-level performance in networks with multiple base stations. We specifically examine the complex, dynamic interaction of the number of active flows in the various cells introduced by the strong impact of interference between neighboring base stations. For the downlink data transmissions that we consider, lower service rates caused by increased interference from neighboring base stations result in longer delays and thus a higher number of active flows. This in turn results in a longer duration of interference on surrounding base stations, causing a strong correlation between the activity states of the base stations. Such a system can be modelled as a network of multi-class processor-sharing queues, where the service rates for the various classes at each queue vary over time as governed by the activity state of the other queues. The complex interaction between the various queues renders an exact analysis intractable in general. A simplified network with only one class per queue reduces to a coupled-processors model, for which there are few results, even in the case of two queues. We thus derive bounds and approximations for key performance metrics like the number of active flows, transfer delays, and flow throughputs in the various cells. Importantly, these bounds and approximations are insensitive, yielding simple expressions, that render the detailed statistical characteristics of the system largely irrelevant.