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This paper studies virtual machine (VM) scheduling in a queueing cloud computing system with stochastical arrivals of heterogeneous jobs by considering jobs' delay requirements. The delay-optimal VM scheduling in such a cloud computing system is formulated as a multi-resource multi-class problem minimize the average job completion time, which is often NP-hard. To solve such a problem, we first propose a queueing model that buffers the same type of VM jobs in one virtual queue. The queueing model then divides the VM scheduling into two parallel low-complexity algorithms, i.e., intra-queue buffering and inter-queue scheduling. A min-min best fit (MM-BF) policy is used to schedule the jobs in different queues to minimize the remaining system resources, while a shortest-job-first (SJF) policy is used to buffer the job requests in each queue based on their job lengths in an ascending order. To avoid job starvation for the long-duration jobs in SJF-MMBF, we further propose a queue-length-based MaxWeight (QMW) policy based on Lyapunov drift to minimize the queue lengths of VM jobs, which is called SJF-QMW. Simulation results show that, SJF-MMBF and SJF-QMW achieve low delay performance in terms of average job completion time and high throughput performance in terms of job hosting ratio.

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