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 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 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 (56, 80) 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 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 (56, 80) of a predicted gain for said migration at the selected migration moment of time.