What characteristic of networking/TCP causes linear relation between TCP activity and latency?

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http://serverfault.com – The core of this problem is that our application uses websockets for real-time interfaces. We are testing our app in a new environment but strangely we're noticing an increasing delay in TCP websocket packets associated with an increase in websocket activity. For example, if one websocket event occurs without any other activity in a 1-minute period, the response from the server is instantaneous. However, if we slowly increase client activity the latency in server response increases with a linear relationship (each packet will take more time to reach the client with more activity). For those (HowTos)