The service technician will likely have a router with them. However, as mentioned, you should check to see if you were to have received the router in advance or not. If you were, then you need to track down that shipment as you will be responsible for the equipment (and if the technician installs new router, they will charge you for that device as well -- either purchase or rental).
Now, it is possible that if you were arranging new service including television and/or phone that they did not ship any equipment to you as they knew a service technician or "truck roll" would be needed. In which case, they will show up with everything they need to do your installation.