By　effectively　assigning　and　migrating　tasks　based　on　service　requirements,　the　success　rate　of　task　execution　in　cloud-edge-end　collaborative　computing　can　be　significantly　enhanced,　thereby　ensuring　the　provision　of　high-quality　services　for　users.　The　majority　of　conventional　cloud-edge-end　task　offloading　approaches　primarily　focus　on　static　scenarios,　posing　challenges　in　ensuring　the　success　rate　of　task　execution　in　mobile　scenarios.　It　is　imperative　to　address　the　problem　of　constructing　a　joint　optimization　scheme　for　task　allocation　and　migration　that　is　suitable　for　mobile　scenarios.　This　paper　re-define　the　latency,　energy,　and　migration　model　for　task　processing　in　mobile　scenarios.　Furthermore,　we　propose　a　Deep　Reinforcement　learning　(DRL)-based　Task　allocation　and　Migration　optimization　algorithm　(DRTM)　to　enhance　the　efficiency　of　task　completion　and　minimize　the　total　cost.　DRTM　introduces　the　traditional　Actor-Critic　with　a　mirror　deep　deterministic　policy　gradient　(DDPG)　and　establishes　a　duel　Q-network　to　update　parameters　on　respective　gradients　for　optimal　policy　acquisition.　DRTM　incorporates　two　target　networks　to　effectively　improve　stability　and　convergence　speed　during　training　while　reducing　computational　complexity.　The　experimental　results　demonstrate　that　DRTM　can　offer　a　high-performance　task　assignment　and　migration　scheme　in　mobile　scenarios,　thereby　significantly　reducing　the　total　cost　of　the　task　execution　life　cycle.　©　2023　IEEE.