QoS works toward making policies or promises to improve packet delivery from a sender to a receiver.!, it includes prioritization, queuing, traffic shapping, traffic engineering, compression etc.
For a simple example, one solution under Different service (DiffServ) model can looks like: voice traffic and traffic from dean's office are given highest priority and garanteed high delivery (usually near 100%), telnet traffic, SNMP traffic and traffic from staffs' offices are garanteed second-highest delivery, www traffic third and others fourth.
!
class-map match-all voice_dean
match access-group 111
class-map match-all telsnmpsta
match access-group 122
class-map match-all www
match access-group 133
!
policy-map china
class voice_dean
bandwidth 1406
class telsnmpsta
bandwidth 328
class www
bandwidth 100
class class-default
bandwidth 50
!
So the problem is very clear: if your traffic falls into the lower priority, you are allocated much less bandwidth and make your facing a large rate of packet drops/queuing latency.
Usually QoS policy is implemented by admin/ISP, you will have almost no way to change it.
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