The Tor network is probably one of the most popular online anonymity systems in the world. It has been built based on the volunteer relays from all around the world. It has a strong scientific basis which is structured very well to work in low latency mode that makes it suitable for tasks such as web browsing. Despite the advantages, the low latency also makes Tor insecure against timing and traffic analysis attacks, which are the most dominant attacks on Tor network in recent past years. In this paper, first all kinds of attacks on Tor network will be classified and then timing and traffic analysis attacks will be described in more details. Then we present a new circuit scheduling for Tor network in order to preserve two properties, fairness and randomness. Both properties are trying to make pattern and timing analysis attacks more difficult and even in some cases impractical. Our scheduler distorts timing patterns and size of packets in a random way (randomness) without imposing artificial delays or paddings (fairness). Finally, by using our new scheduler, one of the most powerful attacks in this area is debilitated, and by it is shown that analyzing traffic patterns and size of packets will be more difficult to manage.