Processor-sharing queues: some progress in analysis
Queueing Systems: Theory and Applications
SIGMETRICS '97 Proceedings of the 1997 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
The M/G/1 Processor-Sharing Queue with Bulk Arrivals
Proceedings of the IFIP TC6 Task Group/WG6.4 International Workshop on Performance of Communication Systems: Modelling and Performance Evaluation of ATM Technology
Analysis of LAS scheduling for job size distributions with high variance
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Two-level processor-sharing scheduling disciplines: mean delay analysis
Proceedings of the joint international conference on Measurement and modeling of computer systems
Analysis of the M/G/1 processor-sharing queue with bulk arrivals
Operations Research Letters
The processor-sharing queue with bulk arrivals and phase-type services
Performance Evaluation
ACM SIGMETRICS Performance Evaluation Review
Waiting times for M/M systems under state-dependent processor sharing
Queueing Systems: Theory and Applications
Batch processor sharing with hyper-exponential service time
Operations Research Letters
Sojourn times in a processor sharing queue with multiple vacations
Queueing Systems: Theory and Applications
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We analyze a Processor-Sharing queue with Batch arrivals. Our analysis is based on the integral equation derived by Kleinrock, Muntz and Rodemich. Using the contraction mapping principle, we demonstrate the existence and uniqueness of a solution to the integral equation. Then we provide asymptotical analysis as well as tight bounds for the expected response time conditioned on the service time. In particular, the asymptotics for large service times depends only on the first moment of the service time distribution and on the first two moments of the batch size distribution. That is, similarly to the Processor-Sharing queue with single arrivals, in the Processor-Sharing queue with batch arrivals the expected conditional response time is finite even when the service time distribution has infinite second moment. Finally, we show how the present results can be applied to the Multi-Level Processor-Sharing scheduling.