1. An update management system, comprising: service monitor circuitry configured to monitor a communication service executed by a virtual server; and virtual communication function management circuitry configured to generate old and new correspondence data indicating correspondence between a new version virtual server and an old version virtual server; and instruct virtualization resource management circuitry to generate the new version virtual server based on the old and new correspondence data; to update and switch from the old version virtual server to the generated new version virtual server, that corresponds to the old version virtual server; and notify the service monitor circuitry that there is startup of the new version virtual server based on the old and new correspondence data, wherein the virtualization resource management circuitry is configured to manage each of virtualization resources including a physical server in which the virtual server executing the communication service is generated; generate the new version virtual server; and update and switch from the old version virtual server to the generated new version virtual server, the virtualization resource management circuitry is configured to update the old version virtual server to the new version virtual server by: initially connecting the new version virtual server to the network without disconnecting the old version virtual server from the network, and disconnecting, the old version virtual server from the network when there is no process continued from before switching or when a predetermined new-version monitoring period expires, and the update management system further includes distributor circuitry configured to distribute a destination of a packet from outside in the update management system, wherein after the new version virtual server is initially connected to the network without disconnecting the old version virtual server from the network, the distributor circuitry is configured to distribute the destination of the packet from outside in the update management system to the new version virtual server in an order from a newly starting process.