  We present results of numerical analysis of several simple models for the
microstructure of a double auction market without intermediaries which were
introduced in cond-mat/9808240. We perform computer simulations of the minimal
model in order to verify liquidity scaling laws. A logarithmic correction to
the scaling law for midmarket variance is observed, but not for bid-offer
spread or its fluctuation, because they are fundamentally different quantities.
  Time to midmarket sale ($\tau_S$) is found to scale as 1/J while its
fluctuation goes as $0.73/J$. A ``reduced'' time ($\tau_{reduced}$) is also
studied, and found to scale in a non-trivial way. Asymmetric fluxes are
introduced to the minimal model and analytical result derived earlier for the
speed of the moving midmarket agrees with numerical results. Simulation of the
two-liquid model which describes a market with both market order and limit
order traders, reveals widening of the bid-offer spread when the flux of market
order traders exceeds that of limit order traders. The variation of the spread
with the fraction of market-order traders is investigated. The formula for
asymmetric fluxes is applied to the two-liquid model and its predictions are
found to agree with experiment. The critical point is approximately determined,
and the ratio of the midmarkets for $f = 0.0$ and $f = 0.5$ (where $f$ is the
fraction of market-order traders) is calculated.
