The solar cycle has a profound influence on the solar wind (SW) interaction with the local interstellar medium (LISM) on more than one timescales. Also, there are substantial differences in individual solar cycle lengths and SW behavior within them. The presence of a slow SW belt, with a variable latitudinal extent changing within each solar cycle from rather small angles to 90°, separated from the fast wind that originates at coronal holes substantially affects plasma in the inner heliosheath (IHS)--the SW region between the termination shock (TS) and the heliopause (HP). The solar cycle may be the reason why the complicated flow structure is observed in the IHS by Voyager 1. Here, we show that a substantial decrease in the SW ram pressure observed by Ulysses between the TS crossings by Voyager 1 and 2 contributes significantly to the difference in the heliocentric distances at which these crossings occurred. The Ulysses spacecraft is the source of valuable information about the three-dimensional and time-dependent properties of the SW. Its unique fast latitudinal scans of the SW regions make it possible to create a solar cycle model based on the spacecraft in situ measurements. On the basis of our analysis of the Ulysses data over the entire life of the mission, we generated time-dependent boundary conditions at 10 AU from the Sun and applied our MHD-neutral model to perform a numerical simulation of the SW-LISM interaction. We analyzed the global variations in the interaction pattern, the excursions of the TS and the HP, and the details of the plasma and magnetic field distributions in the IHS. The resulting numbers are compared with Voyager data as functions of time in the spacecraft frame. We also discuss solar cycle effects which may be reasons for the recent decrease in the TS particles (ions accelerated to anomalous cosmic-ray energies) flux observed by Voyager 1.