Moments of Response Time for Systems With Hierarchical Memories

Storage systems in current day computing machines are in a variety of forms: registers, caches, main memory, disks, tapes, network storage systems, and so on. Each storage system provides the basic functions of storing data and holding the data until it is retrieved at a later time. The main differences between the various storage systems are their speed, cost, size, and volatility. The hierarchical nature of memory is prevalent in almost all computing systems ranging from the stand-alone desktop to grid computing environments. The rapid advancement of modern computer architecture and enterprise computing environments further extends this hierarchy. In this paper we abstract this hierarchcal nature of memory in order to examine the variance, and in general, all moments of the distribution of time memory access. The existence of an unbounded variance for the response time can lead to extremly long wait queues and a particular class of distributions that has this property is the power tailed distribution. We present an analytical model to study the response time. We show that under reasonable assumptions for the values of the parameters involved. in the memory levels the response-time for such a hierarchical memory system is power tailed. Mention about the hγ` > 1 as the ”rule of thumb” for the designers as a selling point