Route Change Requests from Gateways:

Internet routing tables are initialized by hosts from a configuration file at system startup, and system administrators seldom make routing changes during normal operations. Gateways exchange routing information periodically to accommodate network changes and keep their routes up-to-date. The general rule is , Gateways are assumed to know correct routes; host begin want minimal routing information and learn new routes from gateways. The GATEWAY INTERNET ADDRESS field contains the address of a gateway that the host is to use to reach the destination mentioned in the datagram header. The INTERNET HEADER field contains IP header plus the next 64 bits of the datagram that triggered the message. The CODE field of an ICMP redirect message further specifies how to interpret the destination address, based on values assigned as follows :

Code Value                           Meaning
0                                   REDIRECT DATAGRAMS FOR THE NET
1                                   REDIRECT DATAGRAMS FOR THE HOST
2                                   REDIRECT DATAGRAMS FOR THE TYPE OF SERVICE AND NET
3                                   REDIRECT DATAGRAMS FOR THE TYPE OF SERVICE AND HOST
Gateways only send ICMP redirect requests to hosts and not to other gateways.

Detecting Circular or Excessively Long Routes : 
Internet gateways compute a next hop using local tables, errors in routing tables can produce a routing cycle for some destination. A routing cycle can consist of two gateways that each route a datagram for a particular destination to other, or it can consist of several gateways. To prevent datagram’s from circling forever in a TCP/IP internet, each IP datagram contains a time-to-live counter, sometimes called a hop count. Gateway decrements the time-to-live counter whenever it processes the datagram and discards the datagram when the count reaches zero. Whenever a gateway discards a datagram because its hop count has reached zero or because a timeout occurred while waiting for fragments of a datagram, it sends an ICMP time exceeded message back to the datagram's source, A gateway sends this message whenever a datagram is discarded because the time-to-live field in the datagram header has reached zero or because its reassembly timer expired while waiting for fragments.
The code field explains the nature of the timeout:
Code Value                           Meaning
0                                    TIME-TO-LIVE COUNT EXCEEDED
1                                    FRAGMENT REASSEMBLY TIME EXCEEDED
Fragment reassembly refers to the task of collecting all the fragments from a datagram.
Reporting Other Problems: 
When a gateway or host finds problems with a datagram not covered by previous ICMP error messages it sends a parameter problem message to the original source. To make the message unambiguous, the sender uses the POINTER field in the message header to identify the octet in the datagram that caused the problem. Code 1 is used to report that a required option is missing; the POINTER field is not used for code 1.
Clock Synchronization and Transmit the estimation: 
ICMP messages are used to obtain the time from another machine. A requesting machine sends an ICMP timestamp request message to another machine, asking that the second machine return its current value of the time of day. The receiving machine returns a timestamp reply back to the machine making the request. TCP/IP protocol suite includes several protocols that can be used to synchronize clocks. This is one of the simplest techniques used by TCP/IP. The TYPE field identifies the message as a request (13 ) or a reply ( 14 ); the IDENTIFIER and SEQUENCE NUMBER fields are used by the source to associate replies with requests. The ORIGINATE TIMESTAMP filed is filled in by the original sender just before the packet is transmitted, the RECEIVE TIMESTAMP field is filled immediately upon receipt of a request, and the TRANSMIT TIMESTAMP field is filled immediately before the reply is transmitted. Hosts use the three timestamp fields to compute estimates of the delay time between them and to synchronize their clock. A host can compute the total time required for a request to travel to a destination, be transformed into a reply, and return. In practice, accurate estimation of round-trip delay can be difficult and substantially restrict the utility of ICMP timestamp messages. To obtain an accurate estimate to round trip delay one must take many measurements and average them.
 Obtaining a Subnet Mask:

Subnet addressing is used by the hosts to extract some bits in the hosted portion of their IP address to identify a physical network. To participate in subnet addressing, hosts need to know which bits of the 32-bit internet address correspond to the physical network and which correspond to host identifiers. The information needed to interpret the address is represented in a 32-bit quantity called the subnet mask. To learn the subnet mask used for the local network, a machine can send an address mask request message to a gateway and receive an address mask reply. The TYPE field in an address mask message specifies whether the message is a request ( 17 ) or a reply ( 18 ). A reply contains the network’s subnet address mask in the ADDRESS MASK field. The IDENTIFIER and SEQUENCE NUMBER fields allow a machine to associate replies with requests.