Production parallel systems are space-shared and employ batch queues in which the jobs submitted to the systems are made to wait before execution. Thus, jobs submitted to parallel batch systems incur queue waiting times in addition to the execution times. Prediction of these queue waiting times is important to provide overall estimates to the users and can also help meta-schedulers make scheduling decisions. In the first part of our research, we have developed an integrated framework PQStar for identification and prediction of jobs with short queue waiting times. Analyses of the job traces of supercomputers reveal that about 56 to 99% of the jobs incur queue waiting times of less than an hour. Hence, identifying these quick starters or jobs with short queue waiting times is Essential for overall improvement on queue waiting time predictions. An important aspect of our prediction strategy for quick starters is that it considers the processor occupancy state and the queue state at the time of the job submission in addition to the job characteristics including the requested number of processors and the estimated runtime. Our experiments with different Production supercomputer job traces show that our prediction strategies can lead to correct identification of about 20% more quick starters on an average and provide tighter bounds for these jobs, and result in about 24% higher overall prediction accuracy on an average than the next best existing method. We have also developed a framework for predicting ranges of queue waiting times for other classes of jobs by employing multi-class classification on similar jobs in history. Our hierarchical prediction strategy first predicts the point wait time of a job using dynamic k- Nearest Neighbor (kNN) method. It then performs a multi-class classification using Support Vector Machines (SVMs) among all the classes of the jobs. The probabilities given by the SVM for the predicted class (obtained from the kNN), along with its neighboring classes, are used to provide a set of ranges of wait times with probabilities. Our experiments with different production supercomputer job traces show that our prediction strategies can lead to about 8% improved accuracy on an average in prediction of the non-quick starters, compared to the next best existing method. Finally, we have used these predictions and probabilities in a meta-scheduling strategy that distributes jobs to different queues/sites in a multi-queue/grid environment for minimizing wait times of the jobs. For a given target job, we first identify the queues/sites where the job can be a quick starter to get a set of candidate queues/sites for the scheduling of the job. We then compute the expected value of the predicted wait time in each of the candidate queues/sites, and schedule the job to the one with minimum expected value, for the execution of the job. We have performed experiments with different production supercomputer job traces and synthetic traces for various system sizes, partitioning schemes and different workloads. These experiments have shown that our scheduling strategy gives much improved performance when compared to the existing scheduling policies by reducing the overall average queue waiting times of the jobs by about 47% on an average.