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One way of improving the performance of a cellular network is to build a second tier (layer) called the macrocell on top of the single-tier called the microcell. Multi-tier cellular networks provide mobility solutions to both the high speed and low speed users. Since dropping an ongoing call when a mobile user moves from one cell to another is an undesirable event, several techniques have been previously proposed to solve this problem. In a cellular network, this problem can be solved by delaying the handoff call using a queue, until it's able to maintain a channel. In this paper, a new Markov model is developed for a two-tier cellular network having a FIFO queue in the macrocell, which takes into account the mobility and the queue time of users. Later, the analytical model of the cellular system is solved and its performance is calculated. The results are then compared with previously proposed models.