The judicial process is a set of interrelated procedures and roles for deciding disputes by an authoritative person or persons whose decisions are regularly obeyed.
Taking into account what New Yorker cartoon poster print by J.B. Handelsman says: "In the interest of streamlining the judicial process, we'll skip the evidence and go directly to sentencing", streamlining the judicial process means improving the efficiency of a process, by simplifying or eliminating unnecessary steps or taking other approaches.
As with the early drug courts of the 1980s, the purpose of special sentencing/probation courts is often to streamline the process and move the offender through as quickly as possible.