at first glance there is not advantage of a WAP over a router. here are the reasons why.Consider using a WLAN router for the following reasons:
IP address sharing: WLAN routers offer strong benefits in the home and small office setting. For example, you can subscribe to a cable modem service that provides a single IP address through DHCP to the router, and the router then provides IP addresses via DHCP to clients on your local network. NAT then maps a particular client on the local network to the ISP-assigned IP address whenever that client needs to access the Internet. As a result, you need a router if you plan to have more than one networked devices on a local network sharing a single ISP-assigned address. Instead of having one box for the router and another box for the access point, a WLAN router provides both in the same box.
Connect multiple networks: WLAN routers are also ideal for wireless networks in public areas, especially if there are multiple networks that are accessible. For instance, a University may have a separate network in each of its buildings. Students sitting outside might want to gain access one or more of these networks and also surf the Internet. A WLAN router enables them to access everything through the wireless connection.
Improve network management: WLAN routers in an enterprise environment give network administrators an extra way to monitor and update their networks. In addition to being able to log on either locally or remotely via the wired network, they will be able to log on wirelessly and make any observations or changes.
Improve network performance: Because routers only send packets to specific, directed addresses, they do not forward the often numerous broadcast packets that are sent out by other devices. This results in an increase in throughput because of lower utilization on the network and less work needed by the router. This enables WLANs to operate much more effectively. The router, however, will offer more delay than an access point, but the impacts are generally unnoticeable.
Increase security: A strong advantage of WLAN routers is that they provide an added layer of security, both on the wired side and wireless side. The wired side is usually protected by a firewall and has extensive access control filters. These filters can be set based on MAC (medium access control) address, IP address, URL, domain name, and even a set schedule that allows access only at certain times. If an unauthorized user tries to access the network, an e-mail alert is immediately sent to the network administrator. For supporting sensitive information, many WLAN routers support multiple and concurrent IPSec sessions, so users can more securely access networks through a range of virtual private network (VPN) clients. Most WLAN routers also implement wired equivalent privacy (WEP) encryption