The difference in the heliocentric distances at which the Voyager 1 and Voyager 2 spacecraft crossed the termination shock (TS) is likely due to a combination of the heliospheric asymmetry caused by the interstellar magnetic field (ISMF) and time-dependent boundary conditions at the Sun. We analyze both effects numerically. It is shown that an increase in the ISMF makes the termination shock more asymmetric, but results in an increasingly large discrepancy between the calculated and observed distributions of the solar wind (SW) velocity in the inner heliosheath. We analyze possible effects of the solar cycle on the SW properties in the inner heliosheath. The possibility is explored of the SW velocity to have a rather small gradient as V2 penetrates deeper into the heliosheath. To analyze the effect of the solar cycle we also perform the calculations of the SW - interstellar medium interaction with the inner boundary conditions extracted from the Ulysses data obtained during its first and third pole-to-pole flybys.