  Impact of mobility will be increasingly important in future generation
wireless services and the related challenges will need to be addressed. Sojourn
time, the time duration that a mobile user stays within a cell, is a
mobility-aware parameter that can significantly impact the performance of
mobile users and it can also be exploited to improve resource allocation and
mobility management methods in the network. In this paper, we derive the
distribution and mean of the sojourn time in multi-tier cellular networks,
where spatial distribution of base stations (BSs) in each tier follows an
independent homogeneous Poisson point process (PPP). To obtain the sojourn time
distribution in multi-tier cellular networks with maximum biased averaged
received power association, we derive the linear contact distribution function
and chord length distribution of each tier. We also study the relation between
mean sojourn time and other mobility-related performance metrics. We show that
the mean sojourn time is inversely proportional to the handoff rate, and the
complementary cumulative distribution function (CCDF) of sojourn time is
bounded from above by the complement of the handoff probability. Moreover, we
study the impact of user velocity and network parameters on the sojourn time.
