A B757 CREW BRIEFED AND PROGRAMMED FOR THE LAX RIIVR 1 RWY 25L BUT WERE GIVEN RWY 24R. THEY WERE BEHIND THE ACFT BUT GIVEN ALT RELIEF BY ATC DURING THE ARR.

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WE PLANNED AND BRIEFED FOR THE RIIVR 1 ARR INTO LAX RWY 25L; AND PROGRAMMED THE FMC WITH THE RIIVR 1; HEC TRANSITION; RUNWAY 25L; FUELER TRANSITION. ATC CLEARED US TO CROSS GRAMM AT FL190 WITH A SPEED RESTR OF 270 KTS. WE COMPLIED. AT GRAMM; WE EXPECTED A CLRNC TO DSND VIA THE STAR. WE WERE NOT GIVEN LOWER (PROBABLY DUE TO FREQUENCY CONGESTION); WHICH PUT US HIGH ON THE ARR. STILL AT FL190; WE WERE HANDED OFF TO SOCAL 124.05. WE WERE CLEARED TO DSND VIA THE RIIVR 1 FOR RWY 24R ON 124.05; AND SLOWED TO 250 KTS. I READ BACK THE STAR; REQUESTED RWY CONFIRMATION FROM ATC (SINCE WE WERE EXPECTING RWY 25L) AND SET THE MCP FOR 14000 FT (HABSO). WE WERE APPROX 6 MILES FROM HABSO AND HIGH ON PROFILE. THE FO INITIATED AN IMMEDIATE DSCNT WHILE I TRIED TO GET A WORD IN EDGEWISE WITH ATC FOR ALTITUDE RELIEF ON THE PROFILE. WHILE TRYING TO CONTACT ATC (CONGESTION-UNABLE TO MAKE CALL WITHOUT STEPPING ON SOMEONE); I SELECTED RWY 24R IN THE FMC WHICH DUMPED THE ARR OUT OF THE FMC. I RESELECTED THE RIIVR 1 ARR; WHILE RECEIVING ALTITUDE RELIEF FROM ATC AND ANOTHER FREQUENCY CHANGE. THE NEXT SOCAL CTLR CLEARED US TO CONTINUE ON THE RIIVR 1 FOR RWY 24R; DELETING THE ALTITUDE RESTRS; AND SLOWING US TO 170K. WE BRIEFED RWY 24R; SET UP THE RADIOS; AND RESUMED THE PROFILE BY PALAC; FOR A STABILIZED; UNEVENTFUL APCH AND LNDG. WE WERE BUSY AND RUSHED DUE TO BEING HELD BY ATC AT FL190; AND RECEIVING A LATE RWY ASSIGNMENT. THOUGH WE RECEIVED ALTITUDE RELIEF AND DID NOT HAVE ANY DEVS; WE WOULD NOT HAVE BEEN ABLE TO COMPLY WITH THE AT OR BELOW CROSSING ALTS ON THE STAR WHILE DECELERATING. PREPROGRAMMING RWY 24R ON RTE 2 WOULD HAVE REDUCED OUR WORKLOAD; BUT WE STILL WOULD HAVE BEEN HIGH; RUSHED; AND HEADS DOWN IN THE FMC. ATC CONGESTION AND THE INABILITY TO MAKE A RADIO CALL AGGRAVATED THE SITUATION. WE ARE BOTH VERY FAMILIAR WITH LAX LATE DSCNT CLRNC; LATE RWY ASSIGNMENT; FREQUENCY CONGESTION; AND A CREW ERROR (SELECTING RWY 24R WITHOUT RESELECTING THE ENTIRE ARR) CREATED A VERY BUSY APCH AND UNNECESSARILY HIGH COCKPIT WORKLOAD. THIS COULD HAVE TURNED INTO AN UNSAFE SITUATION; ESPECIALLY IF A CREW IS UNFAMILIAR WITH LAX. SOCAL NEEDS TO CHANGE THEIR PROCS TO INCLUDE EARLIER RWY ASSIGNMENTS. THEY NEED BETTER UNDERSTANDING OF COCKPIT WORKLOAD AND REQUIREMENTS TO PROGRAM THE FMC. INSTEAD OF DECREASING CREW WORKLOAD; THE LAX RNAV ARRS INTRODUCE ADDITIONAL HAZARDS INTO THE COCKPIT; PARTICULARLY WHEN 'MODIFIED' BY ATC.