In this paper, we have considered a Markovian bulk-service queue for cloud computing architecture. The multiple class i users from the public cloud entering into the queue are naturally based on the FCFS discipline. Partial batch service mode and full batch service mode have considered for accessing cloud database. The requesting and service of the public cloud has been modelled using queueing theory as a single server bulk service model. If the server is free, each user from the public cloud can enter into the M/M[Y]/1 with probability ϕ or leave the system with probability (1-ϕ) without accessing the cloud database. Our proposed work is based on public cloud and request management application has been proposed and analysed in terms of waiting time defined as Quality of Service criteria (QoS). The results obtained in our proposed model are calculating the performance measures of different class i of units in the cloud system and also compare the results of both the partial and full batch service model. © Research India Publications.