Turnaround time on mail sent to LISTSERV or to lists on my server is poor.

On unix machines, it is probable that you will need to tune your MTA for better performance.  Please consult the documentation for your MTA for that purpose.

Sites that are forwarding their outgoing mail through another machine (typically Windows sites using the SMTP_FORWARD and SMTP_FORWARD_n site configuration variables) should note that their turnaround time is also a function of how quickly the SMTP forwarding host(s) process the outgoing mail. In other words, LISTSERV may process the mail in seconds, but getting through the SMTP forwarding host's queue could take a lot longer, depending on the mail transfer agent being used by the forwarding host as well as the existing load on that forwarding host. If you are forwarding to a host running a broken or old Sendmail, for instance, you cannot expect lightning-fast delivery.

Please also note that LISTSERV can’t be held responsible for general network problems such as gateway hosts being down, buggy name servers, and the like. If the users who are complaining are generally located in a single domain or in a specific country, the issue is probably connectivity rather than anything LISTSERV itself is doing. For instance, if the main gateway host for a specific domain is turned off every Friday night and isn’t rebooted until Monday morning (and unfortunately this does indeed happen), obviously users behind that gateway aren’t going to get their mail over the weekend.