When digital broadcasting services are provided through cable television (CATV) networks, viewers watching interactive programs such as quizzes or auctions may respond to the program within a short period. If these responses are transmitted in the upstream channel of the CATV networks using TCP/IP, they will result in burst traffic. The numerous TCP connections will trigger congestion in the upstream transmission facilities and will cause a significant delay in conventional Internet services such as web-browsing. The present paper proposes a new method of controlling the CATV upstream channel to avoid such congestion. We introduce class-based queues at each cable TV station, in which each service class is related to a type of interactive service. The status of the queue is relayed to the cable modems of subscribers using a CATV-specific MAC protocol. This queue-status information is used to suspend further initiation of TCP connections at cable modems. As a result, the TCP connections will be arbitrated in the CATV network, while the delay of the response transmission is traded for smoothing of the burst traffic. We numerically evaluate the effect of the proposed method using the time distribution of responses to an actual quiz program. The results show that the proposed method successfully suppresses interference of the burst traffic with conventional best-effort services.