In this paper we have proposed a priority based Erlang service distribution with k-phases for cloud computing architecture. The multiple users from the public cloud entering into two serially connected M/M/s and M/Ek/1 (Erlang service queue) queues are served based on the non-pre-emptive priority discipline. We have assumed each user of different priority class i, (i ≥ 2) desired to wait until the current user is being served if priority of the service is similar, as per FCFS policy. If the servers are free, users can enter into the M/M/s queue, then enter into the M/Ek/1 queue with probability φ and leave the system after service completion or leave the system with probability (1 – φ) without entering into the ESQ. We have obtained waiting time for both the queues in the cloud system and shown numerically the total waiting time is lower than the existing system. Copyright © 2019 Inderscience Enterprises Ltd.