In this paper we address the overall message delay analysis of IEEE 802.16 wireless metropolitan area network with contention-based multiple access of bandwidth requests. The overall delay consists of the reservation and scheduling components. Broadcast polling is used for bandwidth reservation with binary exponential backoff (BEB) collision resolution protocol and a simple scheduling is applied at the base station. An analytical model is developed with Poisson arrival flow for the Non Real-Time Polling Service (nrtPS) class. The model enables asymmetric traffic flows, different message sizes at the subscriber stations and also allows for Best Effort (BE) service class. An approximation of the mean overall delay is established for the nrtPS service class. The analytical model is verified by means of simulation.