Logarithmic asymptotics for a single-server processing distinguishable sources
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We consider a single-server first-in-first-out queue fed by a finite number of distinct sources of jobs. For a large class of short-range dependent and light-tailed distributed job processes, using functional large deviation techniques we prove a large deviation principle and logarithmic asymptotics for the joint waiting time and queue lengths distribution. We identify the paths that are most likely to lead to the rare events of large waiting times and long queue lengths. A number of examples are presented to illustrate salient features of the results.
KeywordsFunctional large deviations Single server FIFO Waiting time Queue length
Mathematics Subject Classification (2000)Primary 60K25 Secondary 60F10 90B05
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