A method of remote execution of services required by at least one mobile device, in particular on board a vehicle , via a cellular communication network according to a communication protocol of at least fourth generation, a service being executed by a virtual machine (VM) of a computing server (MEH c ), referred to as the current host server, the mobile device sending a service request having a position belonging to a geographical area of current cellular communication coverage (4 1 ), said current host server being associated with the geographical area of current coverage, the method being characterized in that same comprises the following steps, implemented by a processor of said current host server (MEH c ), for a given service request, received during a current time interval: - a) for the current time interval (t), calculation of a probability vector with K components, each component being associated with a given moment of time (T k ) of a predetermined set of K moments of time (T 1 ,...T i ,.., T K ), each component of the probability vector corresponding to a probability of migration at the associated moment of time, the migration consisting of at least one replication of the virtual machine (VM) executing said service on a chosen host server (MEH j ) belonging to a geographical area of coverage contiguous to said current geographical area of coverage, the calculation of the components of the probability vector implementing a set of K weights, each weight being associated with a migration moment of time and representative of a gain predicted for a migration at said associated migration moment of time, - b) selection from said set of K moments of time of a moment of time, referred to as the selected migration moment of time, according to the calculated probability vector, the selected migration moment of time having a maximum corresponding probability of migration in the calculated probability vector, - c) determination , for the migration at the selected migration moment of time, of a number of replications of the virtual machine to be performed at the selected migration moment of time so as to minimize a cost in terms of replication energy while ensuring a level of continuity of service, and calculation of a predicted gain for said migration at the selected migration moment of time. - a) for the current time interval (t), calculation of a probability vector with K components, each component being associated with a given moment of time (T k ) of a predetermined set of K moments of time (T 1 ,...T i ,.., T K ), each component of the probability vector corresponding to a probability of migration at the associated moment of time, the migration consisting of at least one replication of the virtual machine (VM) executing said service on a chosen host server (MEH j ) belonging to a geographical area of coverage contiguous to said current geographical area of coverage, the calculation of the components of the probability vector implementing a set of K weights, each weight being associated with a migration moment of time and representative of a gain predicted for a migration at said associated migration moment of time, - b) selection from said set of K moments of time of a moment of time, referred to as the selected migration moment of time, according to the calculated probability vector, the selected migration moment of time having a maximum corresponding probability of migration in the calculated probability vector, - c) determination , for the migration at the selected migration moment of time, of a number of replications of the virtual machine to be performed at the selected migration moment of time so as to minimize a cost in terms of replication energy while ensuring a level of continuity of service, and calculation of a predicted gain for said migration at the selected migration moment of time. <EOS>