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In my work, requests from multiple sources are queued and completed in order of priority so that I can focus on one task at a time. My boss sets overall priorities, though I have a broad degree of freedom to move tasks around based on common sense and, if they are small and easy, on my initiative and little gaps between big tasks. I use these gaps to help with minor requests.
However, there is one particular group of people (sales, bizdev) where both the department head and their individual members try to skip the queue by coming to me personally and asking me to do something for them then and there on the spot.
Sometimes, this behavior interrupts me in the middle of intensive work and it really gets on my nerves. I need to analyze a lot of data or communicate with multiple people, which can be handled on the computer, but these sales/bizdev people keep coming to my desk and asking:"Hey when can this be done?", joking "Hey are you ignoring me?", "Come on man, I've been waiting for so long!", "Can't we do this sooner? We really need this now!", "Can't you just hop over and do it straight away?", etc.
I feel emotionally trapped in those moments; I feel tension and either answer "Ok, ok..." to try and get rid of them or make a grumpy face and say "I'll get back to you later". I literally don't know how to smile in such circumstances - and I guess that doesn't come across well.
Is there a better and more professional way to make it clear to them that I am busy and cannot talk to them? And that ideally they should send the requests rather than keep chasing me in person?