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The next generation of wireless system is expected to provide multimedia, multi class services any time anywhere with seamless mobility and Quality of Service (QoS). In such environment, vertical handoff management plays an important and challenging role. Some of the main functions of vertical handoff management are: to implement appropriate vertical handoff decision to minimize number of unnecessary handoff, to maintain minimum vertical handoff latency for seamless mobility and to provide guaranteed acceptable QoS required for user satisfaction. Thus, in this paper to avoid unnecessary handoff in integrated heterogeneous network we have proposed that the vertical handoff decision depends on coverage area of the network and the speed of the Mobile Node. Application specific cut-off speed for particular coverage range of network during which handoff is beneficial has been determined. Real time applications like HDTV, MPEG-4, and H.261 are considered in integrated heterogeneous network of UMTS (Universal Mobile Telecommunication System) and WLAN. Vertical handoff latency is analyzed for varied network traffic load, types of application and varied speed of Mobile Node. Effect of Mobile Node speed on packet loss is also analyzed. Finally, to satisfy user with acceptable end to end QoS, especially in the presence of heterogeneous integrated networks where every network has individual QoS, an end to end QoS mapping scheme between UMTS and WLAN integrated network has been proposed. The simulation is performed using Network Simulator NS-2 with NIST (National Institute of Standards and Technology) add on module.