  In this paper, a multi-user multi-server queuing system is studied in which
each user is constrained to get service from a subset of servers. In the
studied system, rate allocation in the sense of max-min fairness results in
multi-level fair rates. To achieve such fair rates, we propose $CM^4FQ$
algorithm. In this algorithm users are chosen for service on a packet by packet
basis. The priority of each user $i$ to be chosen at time $t$ is determined
based on a parameter known as service tag (representing the amount of work
counted for user $i$ till time $t$). Hence, a free server will choose to serve
an eligible user with the minimum service tag. Based on such simple selection
criterion, $CM^4FQ$ aims at guaranteed fair throughput for each demanding user
without explicit knowledge of each server service rate. We argue that $CM^4FQ$
can be applied in a variety of practical queuing systems specially in mobile
cloud computing architecture.
