I was curious as to when the best time to call NOPD in 2016 was so I made this table of dispatch times (all figures in hours: minutes: seconds with self-initiated calls with a dispatch of under 10 seconds removed).

Day of Week Early Morning Morning Afternoon Evening
Sunday 0:45:03 1:00:35 1:19:47 1:02:38
Monday 0:34:46 1:17:11 1:24:51 0:57:06
Tuesday 0:26:05 1:02:06 1:20:13 0:57:30
Wednesday 0:22:10 1:07:00 1:22:22 0:51:43
Thursday 0:26:00 1:09:38 1:15:56 0:53:40
Friday 0:29:17 1:09:28 1:25:43 1:03:11
Saturday 0:43:12 1:10:12 1:17:27 1:03:25

Early Morning - Midnight to 6 AM

Morning - 6 AM to Noon

Afternoon - Noon to 6 PM

Evening - 6 PM to Midnight

Turns out that Wednesday morning before 6 AM is best at just over 22 minutes on average. Monday and Friday afternoons have the worst times approaching nearly an hour and a half.