Air carrier Dispatcher reported frequent task saturation while over seeing flights was further complicated by the presence of volcanic ash in the flights vicinity.

Narrative

Flight encountered light volcanic ash during descent into MMMX on the ENAGA3A arrival between FL200 to 17000ft AGL. Aircraft was taken OTS (Out of Service). Cause: Workload. The desk has all of the ZZZ-MEX turns. In addition; two ZZZ-MGA turns; ZZZ-XPL; and ZZZ1-GUA. All those segments are at max payload and weight restricted based on max structural landing weight which requires additional coordination with the Captain and Load Planning. Popocatepetl was erupting and creating additional work modifying arrival and departure routes for ash avoidance. There were also two flight segments with extensive maintenance delays. This led to task saturation which created some loss of situational awareness. Suggestions: I was task saturated with no time to send a help message. This was due to desk being overloaded with too many segments that require extra time due to weight restrictions and difficult airports. On a routine day without weather or maintenance issues it still a hefty workload. Previous Help messages sent from the division have had uneven responses. Workload issues in the division is a continuous issue.