In this paper, we analyze a discrete-time priority queue with session-based arrivals. We consider a user population, where each user can start and end sessions. Sessions belong to one of two classes and generate a variable number of fixed-length packets which arrive to the queue at the rate of one packet per slot. The lengths of the sessions are generally distributed. Packets of the first class have transmission priority over the packets of the other class. The model is motivated by a web server handling delay-sensitive and delay-insensitive content. By using probability generating functions, some performance measures of the queue such as the moments of the packet delays of both classes are calculated. The impact of the priority scheduling discipline and of the session nature of the arrival process is shown by some numerical examples.