We develop a methodology for analyzing the performance and stability of a server that maintains a multilevel data structure to service a set of access operations for (key, value) records. A subset of the operations executed by the server (e.g., insert and delete) require the multilevel data structure be reorganized so that the sewer can execute all subsequent requests efficiently. We study how often the server should carry out data reorganization (i.e., maintenance) to maximize its performance. If the server is frequently idle then there is no need to impose the reorganization overhead on the operation requests. The reorganization overhead may be completely eliminated by utilizing server-idling periods. If the server is frequently busy, then the reorganization overhead can be minimized by performing a complete reorganization only after the server has served a sufficient number of insert/delete operations so that the amortized cost per operation is small. Therefore, the issue of how often one should perform data reorganization to minimize the average service time depends not only on the multilevel data structure maintained by the server but also on the type and intensity of the system workload. The proposed methodology is exemplified with a two-level sorted file with deferred maintenance. The performance and stability results are compared with those of a single-level binary tree data structure with on-the-fly maintenance. It is shown that deferred maintenance of the two-level sorted file outperforms on-the-fly maintenance of the single-level binary tree in both open and closed systems. Furthermore, deferred maintenance can sustain higher workload intensities without risking system stability.

We present a state reduction method that effectively reduces a two-dimensional Markov model to a one-dimensional Markov model for the performance analysis of a class of concurrent data structure maintenance policies. The reduced model allows the derivation of a closed form expression for the average service time per operation and facilitates the identification of priority allocation functions under which: the system is stable; and the service time per operation is minimized. The applicability of the model is exemplified with a binary tree data structure and the conditions under which concurrent maintenance strategies are better than a conventional incremental maintenance strategy are determined.>

The problem of sharing jobs among a set of parallel queues is discussed. The system is heterogeneous in the sense that different servers may have different speeds. Socially optimal policies that minimize the mean response time of all jobs ar of interest. Using semi-Markov decision processes, it is shown that an optimal policy that uses the instantaneous queue length independent of system utilization does not exist. Rather, the optimal decision of assigning a job to a server depends on the workload intensity. At light loads, the optimal policy tends to assign most jobs to fast servers. At heavy loads, slower servers are used to offload fast ones. Simulation results indicate that a simple heuristic, i.e., a generalization of the optimal policy for homogeneous systems derived from the analytic results, yields substantial performance improvement compared with no load sharing and outperforms the join-shortest-queue policy.>