Date: 202105
Local time of day: 1201-1800
Location: ZZZ.ARTCC, US
Flight conditions: VMC
Light: Daylight
Aircraft: EMB ERJ 145 ER/LR
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Cruise; Descent
Airspace: Class A ZZZ1
ATC / advisory: Center ZZZ; TRACON ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Communication Breakdown; Situational Awareness; Time Pressure; Workload
Anomaly: ATC Issue All Types; Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Fuel Issue
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: Planned fuel was 6;040 and got fueled to 6;200. We took off with roughly 6;000 pounds of fuel and minimum fuel was 5;564. So we left with well above minimum required fuel according to release. We were enroute and about halfway to 2/3 of the way through as I monitored our fuel burn. I noticed based on current conditions at that time (winds aloft were greater than planned and ATC requested Mach .77 or greater while .76 is planned); that we would be about 700 pounds under planned landing fuel. So as a crew we quickly setup for long range cruise and contacted ATC that we needed to slowdown even though they insisted we maintain a high speed. So we slowed to Mach .63 for long range cruise and then ATC descended us to 27;000 feet from 31;000 feet starting down early because we were slower than surrounding traffic.Then we get instructions shortly after to change arrivals keeping us away from other traffic. Once we finally got situated with the changes; dispatch beat me to notifying them and sent us an ACARS asking about the route changes and fuel. So we told them current plan and situation and based on the information back from dispatch; we had sufficient fuel as long as we maintained LRC (Long Range Cruise speed) to ZZZ allowing us to land with just 100 pounds of fuel more than planned and dispatch had us landing at roughly 1;850 pounds. At some point ATC also queried us asking about why we would be taking off with less fuel than we need to do the flight; even though we didn't. We actually took off with more fuel than planned. ATC was actually being unprofessional about the whole thing and giving us a hard time; because we asked to slow down to conserve fuel as stated over the radios in order to avoid getting into a bad fuel situation later or having to declare minimum fuel; and then he put us on different arrival and etc. It just created more workload and pressure by his attitude and questions as if it was our fault than it needed to be and ATC did not help with that even though they're there to help us.He made us sound bad on the radio as if we didn't know what we were doing about our fuel. Then sometime later while setting up for new arrival; ZZZ does a runway change as well after we got our LDR (Landing Distance Required) and brief; so that added more workload trying to update everything and re-brief in addition to ACARS taking longer than usual to respond. During all of that; Center then instructs us to level at 19;000 feet after getting the first descend via due to VFR traffic at 17;500 feet!  After traffic passes Center then gives us descend via again with immediate handoff to Approach in the same transmission. So First Officer does the handoff while I'm assessing and starting down seeing how quick we need to descend.  I saw we needed to do 6;000 feet or more a minute in order to meet the crossing restriction. I knew that wasn't going to happen so right as I was going to tell First Officer to let ATC know we can't make the restriction because of the level off earlier due to traffic as he was checking on; Approach immediately on initial contact asked if we would make the crossing restriction and we said no.He immediately then got upset and asked if we told the previous controller who would be Center and we said no because we didn't have time as we literally just switched and got the clearance at the same time and literally a few seconds later discovered we couldn't make it work. So we explained that to Approach but he wasn't accepting that and blamed us for not making the restriction or notifying Center before talking with Approach. But we literally had no time between the clearance and handoff at the same time and during the frequency switch that's when we noticed the issue and first transmission with Approach we weren't given the time to tell him that before he asked and queried us. So Approach then gives us two small delay vectors and rejoin arrival. But Approach said we should've told them early on we couldn't make itbut again we explained the situation and that we were not given that chance to do so. So we then continued on after that with no further issues.Insufficient fuel planning on release as it never reflects the actual fuel burn since release doesn't account for delay vectors or vectors on approach. The issues with ATC and last second changes to arrival and runways were a result of not having enough fuel at normal cruise followed by slow ACARS affected our ability to fly the planned arrival causing a higher workload for us and ATC which then caused the hiccup with crossing restrictions and with crossing traffic as well.  For fuel; we slowed for LRC and got a couple shortcuts once on the banker arrival. We were able to gain most of our fuel back because of LRC and landed with 2;200 pounds. For the crossing restriction; we just explained the situation to ATC and along with Center; Approach gave us a hard time and we notified them we couldn't do it; then we carried on with no further issues after that.For fuel planning and fuel contingency; we should be doing a minimum of like 500 pounds and 750-1;000 pounds extra on IFR days. Also for holding fuel; that should be 600 pounds minimum as we realistically burn more than 400 pounds on a go-around on a VFR day. As far as ATC goes after discussing with my First Officer as the situation that unfolded after another as a result; we maybe should have declared Minimum fuel early on knowing we wouldn't have enough unless we slowed down. But because of LRC and little to no delay vectors we determined to have enough hence why we never declared. However; if we declared min fuel early on that would've maybe given ATC more understanding even as frustrating as it may be; and allow us priority to slow and not have to descend via and etc. And that maybe would've avoided the issue with crossing at ZZZZZ1 and etc. One thing led to another; so next time maybe declare min fuel and decline a descend via to stay up high longer and to reduce workload. It was a good learning experience except for lack of professionalism and help from ATC.




Synopsis: Air Carrier Captain reported being unable to comply with ATC speed assignments due to fuel concerns and was unable to comply with a crossing restriction due to ATC stopping their descent for VFR traffic. The Captain reported Center and Approach Controllers criticized and questioned them on the frequency over both issues.