DUE TO FREQ CONGESTION; FLC OF A B757-200 WERE UNABLE TO NOTIFY ATC OF THEIR NEED TO DEVIATE AROUND TSTMS RESULTING IN ATC INTERVENTION JUST AS THEY WERE HEADING BACK TO REJOIN THE AIRWAY.

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NEARING A SMALL CELL ON OUR RTE; FO AND I DECIDED DEV WOULD BE UNNECESSARY AS TSTM WAS DIMINISHING AND WE WOULD SAFELY OVERLY IT. AS WE NEARED IT; HOWEVER (10-15 MI); WE OBSERVED LIGHTNING FROM THE CELL; BOTH LATERALLY AND VERTLY. THIS CAUSED US TO DECIDE TO DEVIATE APPROX 10 DEGS R AS BULK OF CELL WAS TO OUR L AND ONLY A SMALL JOG TO THE R (1-2 MI) WOULD BE SUFFICIENT TO CLR IT. WE BEGAN OUR TURN (FO FLYING ON AUTOPLT) TO THE R AND I ATTEMPTED TO ADVISE ZAB. FREQ WAS VERY CONGESTED HOWEVER AND I WAS UNABLE TO BREAK IN. I TRIED 2 XMISSIONS IN THE OVER 2 MINS OF NON STOP FREQ TFC. BOTH CAUSED BLOCKED XMISSIONS OF OTHER ACFT. BY THIS TIME; WE HAD ESTABLISHED OURSELVES ON A HEADING TO REINTERCEPT OUR INITIAL COURSE. IT WAS AT THIS TIME; CTR SAID; 'TURN L ON COURSE. R DEV UNABLE.' THOSE WERE PRETTY CLOSE TO HIS EXACT WORDS. I ACKNOWLEDGED WITH 'ROGER' AND THERE WAS NO FURTHER MENTION BY EITHER OF US (SELF OR CTR) REGARDING OUR DEV. UPON REFLECTION OF THIS SIT; I CANNOT SEE WHAT I COULD HAVE DONE DIFFERENTLY. I COMPLETELY UNDERSTOOD THE CTLR'S NEED TO BE AWARE OF WHAT I WAS DOING AND TRIED WHOLE- HEARTEDLY TO COMMUNICATE MY ACTIONS TO HIM. IT WAS SIMPLY TOO CONGESTED TO DO THAT.