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0 -12 Td (Motivated by applications in computer and communication systems, the PIs consider a processor sharing queue where the number of jobs being) Tj
0 -12 Td (served is limited by K and the excess jobs wait in a buffer. Such a queue is called a limited processor sharing queue or an LPS queue.\r) Tj
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0 -12 Td (moments of the interarrival times and the jobsizes. These approximations are justified through a heavy traffic limit theorem, which guarantees) Tj
0 -12 Td (that these approximations are asymptotically correct when the system becomes critically loaded and sharing level K becomes large. The heavy) Tj
0 -12 Td (traffic limit theorem states that a certain stochastic process that keeps track of the system dynamics, when properly scaled, converges to a) Tj
0 -12 Td (diffusion process, whose parameters are mapped from the first two moments of the jobsize and interarrival times distributions. Since the jobsize) Tj
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0 -12 Td (measure-valued process to keep track of the system dynamics. Very few prior work deal with diffusion\r) Tj
0 -12 Td (approximations for measure-valued processes. In this research, the PIs carry out a complete program to prove the heavy traffic limit theorem for) Tj
0 -12 Td (measure-valued processes. The PIs first\r) Tj
0 -12 Td (study a measure-valued fluid model of an LPS queue and establish a fluid limit theorem. This work is documented in Zhang et al. \(2007a\).) Tj
0 -12 Td (These fluid limits play an critical role in establishing a diffusion limit theorem, which is proved in Zhang et al. \(2007b\). To use the diffusion) Tj
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0 -12 Td (the accuracy of two-moment approximations.\r) Tj
0 -12 Td (\r) Tj
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0 -12 Td (submitted to a journal from this research.\r) Tj
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0 -12 Td (1\) For a limited processor sharing \(LPS\) queue or a multi-server\r) Tj
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0 -12 Td (Jiheng is expected to receive his Ph.D. in 2008 academic year. The research projects from this grant have prepared him well for an) Tj
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