TTL stands for Time To Live. When a TCP packet is sent, its TTL is set, which is the number of routers (hops) it can pass through before the packet is discarded. As the packet passes through a router the TTL is decremented until, when the TTL reaches zero, the packet is destroyed and an ICMP "time exceeded" message is returned. The return message's TTL is set by the terminating router when it creates the packet, and decremented normally.
Trace Route works by setting the TTL for a packet to 1, sending it towards the requested destination host, and listening for the reply. When the initiating machine receives a "time exceeded" response, it examines the packet to determine where the packet came from - this identifies the machine one hop away. Then the tracing machine generates a new packet with TTL 2, and uses the response to determine the machine 2 hops away, and so on.
Unfortunately not all TCP stacks behave correctly. Some TCP stacks set the TTL for the ICMP "time exceeded" message to that of the message being killed. So if the TTL is 0, the packet will be killed by the next machine to which it is passed. This can have two effects on a trace. If the computer is an intermediate machine in the trace, the entry will remain blank. No information is returned to the machine conducting the trace because the "time exceeded" message never makes it back. If the machine you are doing a trace to has this bug in its TCP stack, return packets won't reach the originating machine unless the TTL is high enough to cover the round trip. So Trace Route will show a number of failed connections equal to n (the number of hops to the destination machine) minus 1.
Machines running MacTCP display this bug . Open Transport handles TTLs correctly. The original distributions of 4.3 BSD had this error, so some UNIX machines display the problem.
The times in Trace Route are total round trip times in seconds. The Min/Avg/Max should increase from machine n to machine n+1, but they may not, for a variety of reasons. To start with, the times are based on the number of tests listed in the results column (generally 3 for a completed trace). Response times vary depending on network usage. Additionally, returning a "time exceeded" message requires more computational time than routing a packet onwards. Finally, packet paths may not be the same coming and going.
See the Interarchie for further details.