Interpret deviance residual plot in poisson regression

Below is a deviance residual plot obtained from a poisson regression.

Since deviance residuals is a form of standardized residuals, we do expect it to have a constant variance. However, when there are lines of points how can we interpret the plot.

The apparent curved lines stem from the fact that actual observations are discrete numbers, while the modeled expectations are continuous. At each $\eta$, the vertical distance between the curves should be an integer multiple of $1/\sqrt{\mu}$ ($\mu$ being the fitted value).
What interests you is whether the spread is the same for each $\eta$. In the above case, I'd say "no": For $\eta < -2$ the data and the fit match almost perfectly, while for $\eta > 0$ they noticeably differ.
• This is not good advice - it looks like that line corresponds to the observed $0$ values. It is also generally a bad looking plot for fitted values less than $2$ (which is roughly $\hat {\eta}<0.69$ -most of the data) – probabilityislogic Aug 1 '18 at 10:30