In hierarchical network where a macro cell includes multiple small scale cells such as micro, femto cells and Wi-Fi hot-spots, preventing unnecessary handover is one of the most important matters due to so many inter-tier handovers. From the observation that there are many temporary visitors who stay in a small scale cell with short residence time, some recent handover schemes propose to delay the handover from macro to small scale cell to prevent unnecessary handovers made by those temporary visitors. Using such a conservative admission policy, we can prevent temporary visitor being handed over to small cell so that the number of inter-tier handovers can be significantly decreased. As a new concern of performance, we analyze the negative side effect of delayed handover scheme by using the theory of probability. Based on the analysis, we present some insights to determine the proper delay parameter to minimize the negative side effect probability.