State-dependent M/G/1/K queuing model for hard disk drives

Abstract

Storage system is the infrastructure of big data. Performance analysis of hard disk drive (HDD) plays a fundamental role to improve the efficiency of storage system. State-dependent M/G/1/K queue is used to model HDD, but it does not have a closed-form solution in the literature. In this paper, we use an M/G/1/K with state-dependent service time to formulate the dynamics of disk random access, where the service time depends on the queue length (batch size of requests determined by the queue length). A numerical computation approach is then proposed to compute the steady state distribution of this queuing model. By utilizing the block structure of transition probability matrix, we further develop an approach to speed up the computation, which can reduce the model complexity from O(K6) to O(K3). Finally, we apply this approach to a case study of hard disks of Western Digital Corp. It demonstrates the efficiency of our approach and gains useful insights for the optimization of storage system.