When you create a Linux virtual machine (VM) on Windows Azure, the VM will have only a port 22 open by default (for ssh). Apparently this setting is by design for security reasons. If you would like to open up additional ports, you can do so as needed, via Windows Azure management console.
To open ports on Windows Azure VM, go to Windows Azure management console. Click on "Virtual Machines", choose your VM, and click on "ENDPOINTS" link at the top. Click on "Add Endpoint", and fill in details: protocol (TCP/UDP), public port, and private port.
Public/private ports can be different if you are using Windows Azure Load Balancer. Otherwise, you can use the same private/private port numbers. When Load Balancer is used, traffic to public port is redirected to private port based on your configuration.
Note that Windows Azure does not allow ICMP traffic in and out of VMs from an external network's perspective. So you cannot ping Azure VM from an external host, or ping any external host from Azure VM. To verify connectivity or measure latency, you will need layer-3 measurement tools such as TCPing, and open up any necessary port(s).
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