If you want to reduce various delays associated with packet size, use LFI (link fragmentation and interleaving).
MTU limits maximum size of packet to a certain size, but what if the size of information is say 100 bytes? You then have L4 header (TCP/UDP), L3 header (IP), L2 Header (ETH,HDLC,PPP etc). It all adds up to say 160 bytes - packet like that cannot traverse the link. So the router has to divide the packet at the third layer (IP). This fragmentation is done at process level, and often not possible.
QoS LFI tools on the other hand fragment the packets at the second layer, leaving L3 header and everything beyond intact.
MTU means maximum transmission Unit which is actually summation of media MTU and Protocol header. It comes out to be 1518Bytes in case of ethernet.
similarly with E1/T1 ckts, the default media MTU is 1504Bytes. The change in MTU size at one end would result in fragmentation of packets and subsequently occupies buffer space. This would definitely result in drops.
Try ip df command on interface with lower MTU size with stateful routemap policy on interface. This would enable rest of the traffic to flow in normal fashion and specific traffic as per PBR would use user-defined MTU.
Maximum Transmission Unit is the specification for the largest data block that can be sent on a physical medium within the protocol definition. The limitation is usually imposed by the physical devices that interface at L1/L2, which is why it can vary on the same physical medium, such as with "standard" Ethernet on "older" devices and "Jumbo frame" Ethernet on "newer" devices.
"Do the MTU settings need to be the same on both ends of the link ?"
Usually a good idea. However, as long as the sender never makes a data block larger than what the receiver can process, it should work. For instance, "old" Ethernet hub or switch wired to "new" Ethernet switch. As long as the latter doesn't sent jumbos to the former, all should be okay.
"Does changing the MTU force HDLC to fragment large packets into smaller parts or does it simply discard oversize packets ? "
Not sure whether HDLC addresses this, but IP supports a DF (don't fragment) bit within the packet. If set, IP will drop the packet if too large for next segment's MTU (will attempt to notify the sender). If not set, IP will break the packet into as many fragments as necessary, each next segment's MTU, except for the last. (Believe IP fragmented packets are not logically reassembled until received by the destination.)
The other posters have touched on other issues, such as why you normally want to avoid IP fragmentation and how better to do it for VoIP, e.g. LFI
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