Packet scheduling constitutes the core problem in efficient fair allocation of bandwidth to competing flows. To date, numerous algorithms for packet scheduling have been suggested and tested. However, only a few of them are currently deployed. One of the key reasons for rarity of applied packet scheduling methods lies in the complexity of their implementation. This paper describes a family of randomized algorithms for packet scheduling. These algorithms are simple to implement and require small amounts of computation time. Specifically, we present an O(1) probabilistic weighted fair queuing algorithm that emits packets from flows with an improved delay jitter. Experimental results of the proposed randomized algorithms suggest that the randomized approach is a viable alternative to the currently deployed deterministic fair queuing algorithms.