  It is by now well-known that wireless networks with file arrivals and
departures are stable if one uses alpha-fair congestion control and
back-pressure based scheduling and routing. In this paper, we examine whether
?alpha-fair congestion control is necessary for flow-level stability. We show
that stability can be ensured even with very simple congestion control
mechanisms, such as a fixed window size scheme which limits the maximum number
of packets that are allowed into the ingress queue of a flow. A key ingredient
of our result is the use of the difference between the logarithms of queue
lengths as the link weights. This result is reminiscent of results in the
context of CSMA algorithms, but for entirely different reasons.
