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The competitive market drives Telecom Operators to reduce the CAPEX (CAPital EXpenditure) and OPEX (Operational EXpenditure). The emerging Cloud Computing provides cheaper, easier to deploy and pay as you use model by using commodity computers. It provides the possibility to take over the workload on expensive dedicated hardware. But some of Telecom Network workload is latency sensitive of which current geographical distributed Cloud is incapable. This paper analyzed the latency in LTE network and Cloud then presents a new Cloud Computing infrastructure for latency sensitive applications in current Telecom Network. The simulation results show the new Cloud Computing infrastructure can limit the latency to around .2 ms with the CPU workload under 50%. It is sufficient to support sub-millisecond level latency sensitive applications in Cloud.